Created on Sat Sep 04 2010, 03:31:46 CEST GENUS: 2 NUMBER OF RECORDS: 117 NUMBER OF MAPS: 17 REFLEXIBLE MAPS: 13 CHIRAL MAPS: 4 #TYPE I: 9 #TYPE II: 8 CAYLEY MAPS: 17 NON-CAYLEY MAPS: 0 ISOMORPHISMS Representatives [ 1, 7, 25, 33, 39, 43, 46, 51, 89, 93, 97, 99, 105, 109, 111, 114, 116 ] Classes [ {@ 1, 2, 3, 4, 5, 6, 19, 20, 21, 22, 23, 24 @}, {@ 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 @}, {@ 25, 26, 27, 28, 29, 30, 31, 32 @}, {@ 33, 34, 35, 36, 37, 38 @}, {@ 39, 40, 41, 42 @}, {@ 43, 44, 45, 48, 50, 52, 57, 59, 63, 65, 67, 68, 73, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 @}, {@ 46, 47, 49, 61 @}, {@ 51, 53, 54, 55, 56, 58, 60, 62, 64, 66, 69, 70, 71, 72, 74, 75 @}, {@ 89, 90, 91, 92 @}, {@ 93, 94, 95, 96 @}, {@ 97, 98 @}, {@ 99, 100, 101, 102, 103, 104 @}, {@ 105, 106, 107, 108 @}, {@ 109, 110 @}, {@ 111, 112, 113 @}, {@ 114, 115 @}, {@ 116, 117 @} ] MAP : A2.1 NOTES : type II, reflexible, isomorphic to DBar({3,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, (x.2^-3 * x.3^-1)^2, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 251)(51, 260)(52, 259)(53, 241)(54, 244)(55, 242)(56, 266)(57, 261)(58, 263)(59, 257)(60, 262)(61, 271)(62, 269)(63, 270)(64, 265)(65, 284)(66, 281)(67, 258)(68, 282)(69, 275)(70, 283)(71, 267)(72, 268)(73, 250)(74, 252)(75, 254)(76, 249)(77, 276)(78, 274)(79, 273)(80, 278)(81, 248)(82, 264)(83, 255)(84, 256)(85, 246)(86, 247)(87, 245)(88, 277)(89, 287)(90, 286)(91, 253)(92, 285)(93, 272)(94, 288)(95, 280)(96, 279)(97, 200)(98, 216)(99, 207)(100, 208)(101, 198)(102, 199)(103, 197)(104, 229)(105, 202)(106, 204)(107, 206)(108, 201)(109, 228)(110, 226)(111, 225)(112, 230)(113, 239)(114, 238)(115, 205)(116, 237)(117, 224)(118, 240)(119, 232)(120, 231)(121, 213)(122, 215)(123, 209)(124, 214)(125, 223)(126, 221)(127, 222)(128, 217)(129, 195)(130, 203)(131, 212)(132, 211)(133, 193)(134, 196)(135, 194)(136, 218)(137, 236)(138, 233)(139, 210)(140, 234)(141, 227)(142, 235)(143, 219)(144, 220) MAP : A2.2 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, (x.2^-3 * x.3^-1)^2, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 288)(50, 272)(51, 279)(52, 280)(53, 286)(54, 287)(55, 285)(56, 253)(57, 274)(58, 276)(59, 278)(60, 273)(61, 252)(62, 250)(63, 249)(64, 254)(65, 247)(66, 246)(67, 277)(68, 245)(69, 264)(70, 248)(71, 256)(72, 255)(73, 269)(74, 271)(75, 265)(76, 270)(77, 263)(78, 261)(79, 262)(80, 257)(81, 283)(82, 275)(83, 268)(84, 267)(85, 281)(86, 284)(87, 282)(88, 258)(89, 244)(90, 241)(91, 266)(92, 242)(93, 251)(94, 243)(95, 259)(96, 260)(97, 200)(98, 216)(99, 207)(100, 208)(101, 198)(102, 199)(103, 197)(104, 229)(105, 202)(106, 204)(107, 206)(108, 201)(109, 228)(110, 226)(111, 225)(112, 230)(113, 239)(114, 238)(115, 205)(116, 237)(117, 224)(118, 240)(119, 232)(120, 231)(121, 213)(122, 215)(123, 209)(124, 214)(125, 223)(126, 221)(127, 222)(128, 217)(129, 195)(130, 203)(131, 212)(132, 211)(133, 193)(134, 196)(135, 194)(136, 218)(137, 236)(138, 233)(139, 210)(140, 234)(141, 227)(142, 235)(143, 219)(144, 220) MAP : A2.3 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.3 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 244)(51, 246)(52, 241)(53, 268)(54, 266)(55, 265)(56, 270)(57, 279)(58, 278)(59, 245)(60, 277)(61, 288)(62, 280)(63, 272)(64, 271)(65, 264)(66, 256)(67, 247)(68, 248)(69, 262)(70, 263)(71, 261)(72, 269)(73, 259)(74, 243)(75, 252)(76, 251)(77, 257)(78, 260)(79, 258)(80, 282)(81, 276)(82, 273)(83, 250)(84, 274)(85, 267)(86, 275)(87, 283)(88, 284)(89, 253)(90, 255)(91, 249)(92, 254)(93, 287)(94, 285)(95, 286)(96, 281)(97, 198)(98, 197)(99, 200)(100, 199)(101, 194)(102, 193)(103, 196)(104, 195)(105, 214)(106, 213)(107, 216)(108, 215)(109, 210)(110, 209)(111, 212)(112, 211)(113, 206)(114, 205)(115, 208)(116, 207)(117, 202)(118, 201)(119, 204)(120, 203)(121, 230)(122, 229)(123, 232)(124, 231)(125, 226)(126, 225)(127, 228)(128, 227)(129, 222)(130, 221)(131, 224)(132, 223)(133, 218)(134, 217)(135, 220)(136, 219)(137, 238)(138, 237)(139, 240)(140, 239)(141, 234)(142, 233)(143, 236)(144, 235) MAP : A2.4 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.3 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 244)(51, 246)(52, 241)(53, 268)(54, 266)(55, 265)(56, 270)(57, 279)(58, 278)(59, 245)(60, 277)(61, 288)(62, 280)(63, 272)(64, 271)(65, 264)(66, 256)(67, 247)(68, 248)(69, 262)(70, 263)(71, 261)(72, 269)(73, 259)(74, 243)(75, 252)(76, 251)(77, 257)(78, 260)(79, 258)(80, 282)(81, 276)(82, 273)(83, 250)(84, 274)(85, 267)(86, 275)(87, 283)(88, 284)(89, 253)(90, 255)(91, 249)(92, 254)(93, 287)(94, 285)(95, 286)(96, 281)(97, 224)(98, 232)(99, 239)(100, 240)(101, 222)(102, 223)(103, 221)(104, 213)(105, 234)(106, 236)(107, 238)(108, 233)(109, 212)(110, 210)(111, 209)(112, 214)(113, 207)(114, 206)(115, 237)(116, 205)(117, 200)(118, 208)(119, 216)(120, 215)(121, 229)(122, 231)(123, 225)(124, 230)(125, 199)(126, 197)(127, 198)(128, 193)(129, 219)(130, 235)(131, 228)(132, 227)(133, 217)(134, 220)(135, 218)(136, 194)(137, 204)(138, 201)(139, 226)(140, 202)(141, 211)(142, 203)(143, 195)(144, 196) MAP : A2.5 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3 * x.2)^3, x.3^-1 * x.2 * x.3 * x.2 * x.3^-3 * x.2 * x.3^-2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 245)(51, 248)(52, 247)(53, 242)(54, 241)(55, 244)(56, 243)(57, 262)(58, 261)(59, 264)(60, 263)(61, 258)(62, 257)(63, 260)(64, 259)(65, 254)(66, 253)(67, 256)(68, 255)(69, 250)(70, 249)(71, 252)(72, 251)(73, 278)(74, 277)(75, 280)(76, 279)(77, 274)(78, 273)(79, 276)(80, 275)(81, 270)(82, 269)(83, 272)(84, 271)(85, 266)(86, 265)(87, 268)(88, 267)(89, 286)(90, 285)(91, 288)(92, 287)(93, 282)(94, 281)(95, 284)(96, 283)(97, 195)(98, 203)(99, 212)(100, 211)(101, 193)(102, 196)(103, 194)(104, 218)(105, 213)(106, 215)(107, 209)(108, 214)(109, 223)(110, 221)(111, 222)(112, 217)(113, 236)(114, 233)(115, 210)(116, 234)(117, 227)(118, 235)(119, 219)(120, 220)(121, 202)(122, 204)(123, 206)(124, 201)(125, 228)(126, 226)(127, 225)(128, 230)(129, 200)(130, 216)(131, 207)(132, 208)(133, 198)(134, 199)(135, 197)(136, 229)(137, 239)(138, 238)(139, 205)(140, 237)(141, 224)(142, 240)(143, 232)(144, 231) MAP : A2.6 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3 * x.2)^3, x.3^-1 * x.2 * x.3 * x.2 * x.3^-3 * x.2 * x.3^-2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 245)(51, 248)(52, 247)(53, 242)(54, 241)(55, 244)(56, 243)(57, 262)(58, 261)(59, 264)(60, 263)(61, 258)(62, 257)(63, 260)(64, 259)(65, 254)(66, 253)(67, 256)(68, 255)(69, 250)(70, 249)(71, 252)(72, 251)(73, 278)(74, 277)(75, 280)(76, 279)(77, 274)(78, 273)(79, 276)(80, 275)(81, 270)(82, 269)(83, 272)(84, 271)(85, 266)(86, 265)(87, 268)(88, 267)(89, 286)(90, 285)(91, 288)(92, 287)(93, 282)(94, 281)(95, 284)(96, 283)(97, 218)(98, 220)(99, 222)(100, 217)(101, 196)(102, 194)(103, 193)(104, 198)(105, 215)(106, 214)(107, 221)(108, 213)(109, 208)(110, 216)(111, 200)(112, 199)(113, 232)(114, 240)(115, 223)(116, 224)(117, 230)(118, 231)(119, 229)(120, 197)(121, 227)(122, 219)(123, 236)(124, 235)(125, 225)(126, 228)(127, 226)(128, 202)(129, 212)(130, 209)(131, 234)(132, 210)(133, 195)(134, 211)(135, 203)(136, 204)(137, 237)(138, 239)(139, 233)(140, 238)(141, 207)(142, 205)(143, 206)(144, 201) MAP : A2.7 NOTES : type II, reflexible, isomorphic to DBar({4,6}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 121)(27, 127)(28, 125)(29, 124)(30, 136)(31, 123)(32, 130)(33, 142)(34, 128)(35, 139)(36, 134)(37, 144)(38, 132)(39, 143)(40, 126)(41, 138)(42, 137)(43, 131)(44, 141)(45, 140)(46, 129)(47, 135)(48, 133)(49, 102)(50, 99)(51, 108)(52, 97)(53, 105)(54, 120)(55, 104)(56, 107)(57, 114)(58, 101)(59, 117)(60, 119)(61, 115)(62, 100)(63, 118)(64, 106)(65, 110)(66, 116)(67, 98)(68, 112)(69, 111)(70, 103)(71, 109)(72, 113) MAP : A2.8 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 126)(26, 123)(27, 132)(28, 121)(29, 129)(30, 144)(31, 128)(32, 131)(33, 138)(34, 125)(35, 141)(36, 143)(37, 139)(38, 124)(39, 142)(40, 130)(41, 134)(42, 140)(43, 122)(44, 136)(45, 135)(46, 127)(47, 133)(48, 137)(49, 99)(50, 102)(51, 104)(52, 105)(53, 97)(54, 106)(55, 108)(56, 101)(57, 103)(58, 107)(59, 98)(60, 100)(61, 113)(62, 119)(63, 109)(64, 120)(65, 116)(66, 110)(67, 117)(68, 111)(69, 112)(70, 114)(71, 118)(72, 115) MAP : A2.9 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 126)(27, 128)(28, 129)(29, 121)(30, 130)(31, 132)(32, 125)(33, 127)(34, 131)(35, 122)(36, 124)(37, 137)(38, 143)(39, 133)(40, 144)(41, 140)(42, 134)(43, 141)(44, 135)(45, 136)(46, 138)(47, 142)(48, 139)(49, 98)(50, 97)(51, 103)(52, 101)(53, 100)(54, 112)(55, 99)(56, 106)(57, 118)(58, 104)(59, 115)(60, 110)(61, 120)(62, 108)(63, 119)(64, 102)(65, 114)(66, 113)(67, 107)(68, 117)(69, 116)(70, 105)(71, 111)(72, 109) MAP : A2.10 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 126)(27, 128)(28, 129)(29, 121)(30, 130)(31, 132)(32, 125)(33, 127)(34, 131)(35, 122)(36, 124)(37, 137)(38, 143)(39, 133)(40, 144)(41, 140)(42, 134)(43, 141)(44, 135)(45, 136)(46, 138)(47, 142)(48, 139)(49, 108)(50, 120)(51, 107)(52, 114)(53, 102)(54, 101)(55, 119)(56, 105)(57, 104)(58, 117)(59, 99)(60, 97)(61, 110)(62, 109)(63, 115)(64, 113)(65, 112)(66, 100)(67, 111)(68, 118)(69, 106)(70, 116)(71, 103)(72, 98) MAP : A2.11 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 124)(26, 139)(27, 122)(28, 134)(29, 130)(30, 121)(31, 142)(32, 127)(33, 125)(34, 136)(35, 128)(36, 123)(37, 143)(38, 137)(39, 141)(40, 140)(41, 144)(42, 129)(43, 133)(44, 138)(45, 131)(46, 135)(47, 132)(48, 126)(49, 99)(50, 102)(51, 104)(52, 105)(53, 97)(54, 106)(55, 108)(56, 101)(57, 103)(58, 107)(59, 98)(60, 100)(61, 113)(62, 119)(63, 109)(64, 120)(65, 116)(66, 110)(67, 117)(68, 111)(69, 112)(70, 114)(71, 118)(72, 115) MAP : A2.12 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 121)(27, 127)(28, 125)(29, 124)(30, 136)(31, 123)(32, 130)(33, 142)(34, 128)(35, 139)(36, 134)(37, 144)(38, 132)(39, 143)(40, 126)(41, 138)(42, 137)(43, 131)(44, 141)(45, 140)(46, 129)(47, 135)(48, 133)(49, 100)(50, 115)(51, 98)(52, 110)(53, 106)(54, 97)(55, 118)(56, 103)(57, 101)(58, 112)(59, 104)(60, 99)(61, 119)(62, 113)(63, 117)(64, 116)(65, 120)(66, 105)(67, 109)(68, 114)(69, 107)(70, 111)(71, 108)(72, 102) MAP : A2.13 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 126)(27, 128)(28, 129)(29, 121)(30, 130)(31, 132)(32, 125)(33, 127)(34, 131)(35, 122)(36, 124)(37, 137)(38, 143)(39, 133)(40, 144)(41, 140)(42, 134)(43, 141)(44, 135)(45, 136)(46, 138)(47, 142)(48, 139)(49, 102)(50, 99)(51, 108)(52, 97)(53, 105)(54, 120)(55, 104)(56, 107)(57, 114)(58, 101)(59, 117)(60, 119)(61, 115)(62, 100)(63, 118)(64, 106)(65, 110)(66, 116)(67, 98)(68, 112)(69, 111)(70, 103)(71, 109)(72, 113) MAP : A2.14 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 124)(26, 139)(27, 122)(28, 134)(29, 130)(30, 121)(31, 142)(32, 127)(33, 125)(34, 136)(35, 128)(36, 123)(37, 143)(38, 137)(39, 141)(40, 140)(41, 144)(42, 129)(43, 133)(44, 138)(45, 131)(46, 135)(47, 132)(48, 126)(49, 98)(50, 97)(51, 103)(52, 101)(53, 100)(54, 112)(55, 99)(56, 106)(57, 118)(58, 104)(59, 115)(60, 110)(61, 120)(62, 108)(63, 119)(64, 102)(65, 114)(66, 113)(67, 107)(68, 117)(69, 116)(70, 105)(71, 111)(72, 109) MAP : A2.15 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 126)(26, 123)(27, 132)(28, 121)(29, 129)(30, 144)(31, 128)(32, 131)(33, 138)(34, 125)(35, 141)(36, 143)(37, 139)(38, 124)(39, 142)(40, 130)(41, 134)(42, 140)(43, 122)(44, 136)(45, 135)(46, 127)(47, 133)(48, 137)(49, 98)(50, 97)(51, 103)(52, 101)(53, 100)(54, 112)(55, 99)(56, 106)(57, 118)(58, 104)(59, 115)(60, 110)(61, 120)(62, 108)(63, 119)(64, 102)(65, 114)(66, 113)(67, 107)(68, 117)(69, 116)(70, 105)(71, 111)(72, 109) MAP : A2.16 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 6, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 121)(27, 127)(28, 125)(29, 124)(30, 136)(31, 123)(32, 130)(33, 142)(34, 128)(35, 139)(36, 134)(37, 144)(38, 132)(39, 143)(40, 126)(41, 138)(42, 137)(43, 131)(44, 141)(45, 140)(46, 129)(47, 135)(48, 133)(49, 99)(50, 102)(51, 104)(52, 105)(53, 97)(54, 106)(55, 108)(56, 101)(57, 103)(58, 107)(59, 98)(60, 100)(61, 113)(62, 119)(63, 109)(64, 120)(65, 116)(66, 110)(67, 117)(68, 111)(69, 112)(70, 114)(71, 118)(72, 115) MAP : A2.17 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 6, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 121)(27, 127)(28, 125)(29, 124)(30, 136)(31, 123)(32, 130)(33, 142)(34, 128)(35, 139)(36, 134)(37, 144)(38, 132)(39, 143)(40, 126)(41, 138)(42, 137)(43, 131)(44, 141)(45, 140)(46, 129)(47, 135)(48, 133)(49, 115)(50, 100)(51, 118)(52, 106)(53, 110)(54, 116)(55, 98)(56, 112)(57, 111)(58, 103)(59, 109)(60, 113)(61, 102)(62, 99)(63, 108)(64, 97)(65, 105)(66, 120)(67, 104)(68, 107)(69, 114)(70, 101)(71, 117)(72, 119) MAP : A2.18 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A2.7. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 126)(27, 128)(28, 129)(29, 121)(30, 130)(31, 132)(32, 125)(33, 127)(34, 131)(35, 122)(36, 124)(37, 137)(38, 143)(39, 133)(40, 144)(41, 140)(42, 134)(43, 141)(44, 135)(45, 136)(46, 138)(47, 142)(48, 139)(49, 100)(50, 115)(51, 98)(52, 110)(53, 106)(54, 97)(55, 118)(56, 103)(57, 101)(58, 112)(59, 104)(60, 99)(61, 119)(62, 113)(63, 117)(64, 116)(65, 120)(66, 105)(67, 109)(68, 114)(69, 107)(70, 111)(71, 108)(72, 102) MAP : A2.19 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, (x.2 * x.3)^3, x.3 * x.2^3 * x.3 * x.2^3 * x.3 * x.2^-1, x.3 * x.2 * x.3 * x.2^-3 * x.3 * x.2^-3, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 251)(51, 260)(52, 259)(53, 241)(54, 244)(55, 242)(56, 266)(57, 261)(58, 263)(59, 257)(60, 262)(61, 271)(62, 269)(63, 270)(64, 265)(65, 284)(66, 281)(67, 258)(68, 282)(69, 275)(70, 283)(71, 267)(72, 268)(73, 250)(74, 252)(75, 254)(76, 249)(77, 276)(78, 274)(79, 273)(80, 278)(81, 248)(82, 264)(83, 255)(84, 256)(85, 246)(86, 247)(87, 245)(88, 277)(89, 287)(90, 286)(91, 253)(92, 285)(93, 272)(94, 288)(95, 280)(96, 279)(97, 198)(98, 197)(99, 200)(100, 199)(101, 194)(102, 193)(103, 196)(104, 195)(105, 214)(106, 213)(107, 216)(108, 215)(109, 210)(110, 209)(111, 212)(112, 211)(113, 206)(114, 205)(115, 208)(116, 207)(117, 202)(118, 201)(119, 204)(120, 203)(121, 230)(122, 229)(123, 232)(124, 231)(125, 226)(126, 225)(127, 228)(128, 227)(129, 222)(130, 221)(131, 224)(132, 223)(133, 218)(134, 217)(135, 220)(136, 219)(137, 238)(138, 237)(139, 240)(140, 239)(141, 234)(142, 233)(143, 236)(144, 235) MAP : A2.20 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-3)^2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 244)(51, 246)(52, 241)(53, 268)(54, 266)(55, 265)(56, 270)(57, 279)(58, 278)(59, 245)(60, 277)(61, 288)(62, 280)(63, 272)(64, 271)(65, 264)(66, 256)(67, 247)(68, 248)(69, 262)(70, 263)(71, 261)(72, 269)(73, 259)(74, 243)(75, 252)(76, 251)(77, 257)(78, 260)(79, 258)(80, 282)(81, 276)(82, 273)(83, 250)(84, 274)(85, 267)(86, 275)(87, 283)(88, 284)(89, 253)(90, 255)(91, 249)(92, 254)(93, 287)(94, 285)(95, 286)(96, 281)(97, 211)(98, 195)(99, 204)(100, 203)(101, 209)(102, 212)(103, 210)(104, 234)(105, 205)(106, 207)(107, 201)(108, 206)(109, 239)(110, 237)(111, 238)(112, 233)(113, 228)(114, 225)(115, 202)(116, 226)(117, 219)(118, 227)(119, 235)(120, 236)(121, 194)(122, 196)(123, 198)(124, 193)(125, 220)(126, 218)(127, 217)(128, 222)(129, 216)(130, 208)(131, 199)(132, 200)(133, 214)(134, 215)(135, 213)(136, 221)(137, 231)(138, 230)(139, 197)(140, 229)(141, 240)(142, 232)(143, 224)(144, 223) MAP : A2.21 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 245)(51, 248)(52, 247)(53, 242)(54, 241)(55, 244)(56, 243)(57, 262)(58, 261)(59, 264)(60, 263)(61, 258)(62, 257)(63, 260)(64, 259)(65, 254)(66, 253)(67, 256)(68, 255)(69, 250)(70, 249)(71, 252)(72, 251)(73, 278)(74, 277)(75, 280)(76, 279)(77, 274)(78, 273)(79, 276)(80, 275)(81, 270)(82, 269)(83, 272)(84, 271)(85, 266)(86, 265)(87, 268)(88, 267)(89, 286)(90, 285)(91, 288)(92, 287)(93, 282)(94, 281)(95, 284)(96, 283)(97, 194)(98, 196)(99, 198)(100, 193)(101, 220)(102, 218)(103, 217)(104, 222)(105, 231)(106, 230)(107, 197)(108, 229)(109, 240)(110, 232)(111, 224)(112, 223)(113, 216)(114, 208)(115, 199)(116, 200)(117, 214)(118, 215)(119, 213)(120, 221)(121, 211)(122, 195)(123, 204)(124, 203)(125, 209)(126, 212)(127, 210)(128, 234)(129, 228)(130, 225)(131, 202)(132, 226)(133, 219)(134, 227)(135, 235)(136, 236)(137, 205)(138, 207)(139, 201)(140, 206)(141, 239)(142, 237)(143, 238)(144, 233) MAP : A2.22 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, (x.2 * x.3)^3, x.3 * x.2^3 * x.3 * x.2^3 * x.3 * x.2^-1, x.3 * x.2 * x.3 * x.2^-3 * x.3 * x.2^-3, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 288)(50, 272)(51, 279)(52, 280)(53, 286)(54, 287)(55, 285)(56, 253)(57, 274)(58, 276)(59, 278)(60, 273)(61, 252)(62, 250)(63, 249)(64, 254)(65, 247)(66, 246)(67, 277)(68, 245)(69, 264)(70, 248)(71, 256)(72, 255)(73, 269)(74, 271)(75, 265)(76, 270)(77, 263)(78, 261)(79, 262)(80, 257)(81, 283)(82, 275)(83, 268)(84, 267)(85, 281)(86, 284)(87, 282)(88, 258)(89, 244)(90, 241)(91, 266)(92, 242)(93, 251)(94, 243)(95, 259)(96, 260)(97, 214)(98, 213)(99, 216)(100, 215)(101, 210)(102, 209)(103, 212)(104, 211)(105, 206)(106, 205)(107, 208)(108, 207)(109, 202)(110, 201)(111, 204)(112, 203)(113, 198)(114, 197)(115, 200)(116, 199)(117, 194)(118, 193)(119, 196)(120, 195)(121, 222)(122, 221)(123, 224)(124, 223)(125, 218)(126, 217)(127, 220)(128, 219)(129, 238)(130, 237)(131, 240)(132, 239)(133, 234)(134, 233)(135, 236)(136, 235)(137, 230)(138, 229)(139, 232)(140, 231)(141, 226)(142, 225)(143, 228)(144, 227) MAP : A2.23 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-3)^2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 244)(51, 246)(52, 241)(53, 268)(54, 266)(55, 265)(56, 270)(57, 279)(58, 278)(59, 245)(60, 277)(61, 288)(62, 280)(63, 272)(64, 271)(65, 264)(66, 256)(67, 247)(68, 248)(69, 262)(70, 263)(71, 261)(72, 269)(73, 259)(74, 243)(75, 252)(76, 251)(77, 257)(78, 260)(79, 258)(80, 282)(81, 276)(82, 273)(83, 250)(84, 274)(85, 267)(86, 275)(87, 283)(88, 284)(89, 253)(90, 255)(91, 249)(92, 254)(93, 287)(94, 285)(95, 286)(96, 281)(97, 232)(98, 240)(99, 223)(100, 224)(101, 230)(102, 231)(103, 229)(104, 197)(105, 218)(106, 220)(107, 222)(108, 217)(109, 196)(110, 194)(111, 193)(112, 198)(113, 215)(114, 214)(115, 221)(116, 213)(117, 208)(118, 216)(119, 200)(120, 199)(121, 237)(122, 239)(123, 233)(124, 238)(125, 207)(126, 205)(127, 206)(128, 201)(129, 227)(130, 219)(131, 236)(132, 235)(133, 225)(134, 228)(135, 226)(136, 202)(137, 212)(138, 209)(139, 234)(140, 210)(141, 195)(142, 211)(143, 203)(144, 204) MAP : A2.24 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A2.1. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 245)(51, 248)(52, 247)(53, 242)(54, 241)(55, 244)(56, 243)(57, 262)(58, 261)(59, 264)(60, 263)(61, 258)(62, 257)(63, 260)(64, 259)(65, 254)(66, 253)(67, 256)(68, 255)(69, 250)(70, 249)(71, 252)(72, 251)(73, 278)(74, 277)(75, 280)(76, 279)(77, 274)(78, 273)(79, 276)(80, 275)(81, 270)(82, 269)(83, 272)(84, 271)(85, 266)(86, 265)(87, 268)(88, 267)(89, 286)(90, 285)(91, 288)(92, 287)(93, 282)(94, 281)(95, 284)(96, 283)(97, 200)(98, 216)(99, 207)(100, 208)(101, 198)(102, 199)(103, 197)(104, 229)(105, 202)(106, 204)(107, 206)(108, 201)(109, 228)(110, 226)(111, 225)(112, 230)(113, 239)(114, 238)(115, 205)(116, 237)(117, 224)(118, 240)(119, 232)(120, 231)(121, 213)(122, 215)(123, 209)(124, 214)(125, 223)(126, 221)(127, 222)(128, 217)(129, 195)(130, 203)(131, 212)(132, 211)(133, 193)(134, 196)(135, 194)(136, 218)(137, 236)(138, 233)(139, 210)(140, 234)(141, 227)(142, 235)(143, 219)(144, 220) MAP : A2.25 NOTES : type I, reflexible, isomorphic to TDual({3,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, x.2^-1 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 137)(27, 124)(28, 121)(29, 138)(30, 139)(31, 129)(32, 122)(33, 134)(34, 135)(35, 141)(36, 130)(37, 140)(38, 127)(39, 132)(40, 133)(41, 128)(42, 142)(43, 144)(44, 136)(45, 143)(46, 125)(47, 131)(48, 126)(49, 102)(50, 103)(51, 109)(52, 98)(53, 108)(54, 119)(55, 100)(56, 101)(57, 120)(58, 110)(59, 112)(60, 104)(61, 111)(62, 117)(63, 99)(64, 118)(65, 115)(66, 105)(67, 116)(68, 113)(69, 106)(70, 107)(71, 97)(72, 114) MAP : A2.26 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, x.2^-1 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 124)(26, 128)(27, 121)(28, 123)(29, 142)(30, 144)(31, 134)(32, 137)(33, 127)(34, 132)(35, 143)(36, 135)(37, 136)(38, 129)(39, 130)(40, 140)(41, 122)(42, 125)(43, 126)(44, 133)(45, 131)(46, 138)(47, 141)(48, 139)(49, 119)(50, 100)(51, 111)(52, 103)(53, 104)(54, 97)(55, 98)(56, 108)(57, 114)(58, 117)(59, 118)(60, 101)(61, 99)(62, 106)(63, 109)(64, 107)(65, 116)(66, 120)(67, 113)(68, 115)(69, 110)(70, 112)(71, 102)(72, 105) MAP : A2.27 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^8, (x.2^3 * x.1 * x.2)^2, (x.2^-2 * x.1 * x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 99)(50, 107)(51, 116)(52, 115)(53, 97)(54, 100)(55, 98)(56, 122)(57, 117)(58, 119)(59, 113)(60, 118)(61, 127)(62, 125)(63, 126)(64, 121)(65, 140)(66, 137)(67, 114)(68, 138)(69, 131)(70, 139)(71, 123)(72, 124)(73, 106)(74, 108)(75, 110)(76, 105)(77, 132)(78, 130)(79, 129)(80, 134)(81, 104)(82, 120)(83, 111)(84, 112)(85, 102)(86, 103)(87, 101)(88, 133)(89, 143)(90, 142)(91, 109)(92, 141)(93, 128)(94, 144)(95, 136)(96, 135) MAP : A2.28 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^8, (x.2^3 * x.1 * x.2)^2, (x.2^-2 * x.1 * x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 122)(50, 124)(51, 126)(52, 121)(53, 100)(54, 98)(55, 97)(56, 102)(57, 119)(58, 118)(59, 125)(60, 117)(61, 112)(62, 120)(63, 104)(64, 103)(65, 136)(66, 144)(67, 127)(68, 128)(69, 134)(70, 135)(71, 133)(72, 101)(73, 131)(74, 123)(75, 140)(76, 139)(77, 129)(78, 132)(79, 130)(80, 106)(81, 116)(82, 113)(83, 138)(84, 114)(85, 99)(86, 115)(87, 107)(88, 108)(89, 141)(90, 143)(91, 137)(92, 142)(93, 111)(94, 109)(95, 110)(96, 105) MAP : A2.29 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^4, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 125)(27, 126)(28, 133)(29, 131)(30, 138)(31, 141)(32, 139)(33, 124)(34, 128)(35, 121)(36, 123)(37, 142)(38, 144)(39, 134)(40, 137)(41, 127)(42, 132)(43, 143)(44, 135)(45, 136)(46, 129)(47, 130)(48, 140)(49, 102)(50, 103)(51, 109)(52, 98)(53, 108)(54, 119)(55, 100)(56, 101)(57, 120)(58, 110)(59, 112)(60, 104)(61, 111)(62, 117)(63, 99)(64, 118)(65, 115)(66, 105)(67, 116)(68, 113)(69, 106)(70, 107)(71, 97)(72, 114) MAP : A2.30 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^4, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 125)(27, 126)(28, 133)(29, 131)(30, 138)(31, 141)(32, 139)(33, 124)(34, 128)(35, 121)(36, 123)(37, 142)(38, 144)(39, 134)(40, 137)(41, 127)(42, 132)(43, 143)(44, 135)(45, 136)(46, 129)(47, 130)(48, 140)(49, 100)(50, 104)(51, 97)(52, 99)(53, 118)(54, 120)(55, 110)(56, 113)(57, 103)(58, 108)(59, 119)(60, 111)(61, 112)(62, 105)(63, 106)(64, 116)(65, 98)(66, 101)(67, 102)(68, 109)(69, 107)(70, 114)(71, 117)(72, 115) MAP : A2.31 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, x.2 * x.3^2 * x.2^-1 * x.3^-2, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 137)(27, 124)(28, 121)(29, 138)(30, 139)(31, 129)(32, 122)(33, 134)(34, 135)(35, 141)(36, 130)(37, 140)(38, 127)(39, 132)(40, 133)(41, 128)(42, 142)(43, 144)(44, 136)(45, 143)(46, 125)(47, 131)(48, 126)(49, 111)(50, 116)(51, 103)(52, 119)(53, 120)(54, 113)(55, 114)(56, 100)(57, 106)(58, 109)(59, 110)(60, 117)(61, 115)(62, 98)(63, 101)(64, 99)(65, 108)(66, 112)(67, 105)(68, 107)(69, 102)(70, 104)(71, 118)(72, 97) MAP : A2.32 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A2.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, x.2 * x.3^2 * x.2^-1 * x.3^-2, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 124)(26, 128)(27, 121)(28, 123)(29, 142)(30, 144)(31, 134)(32, 137)(33, 127)(34, 132)(35, 143)(36, 135)(37, 136)(38, 129)(39, 130)(40, 140)(41, 122)(42, 125)(43, 126)(44, 133)(45, 131)(46, 138)(47, 141)(48, 139)(49, 98)(50, 101)(51, 102)(52, 109)(53, 107)(54, 114)(55, 117)(56, 115)(57, 100)(58, 104)(59, 97)(60, 99)(61, 118)(62, 120)(63, 110)(64, 113)(65, 103)(66, 108)(67, 119)(68, 111)(69, 112)(70, 105)(71, 106)(72, 116) MAP : A2.33 NOTES : type I, reflexible, isomorphic to Med2({3,8}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^8, (x.1^-1 * x.2 * x.1^-2)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 59)(3, 68)(4, 67)(5, 49)(6, 52)(7, 50)(8, 74)(9, 69)(10, 71)(11, 65)(12, 70)(13, 79)(14, 77)(15, 78)(16, 73)(17, 92)(18, 89)(19, 66)(20, 90)(21, 83)(22, 91)(23, 75)(24, 76)(25, 58)(26, 60)(27, 62)(28, 57)(29, 84)(30, 82)(31, 81)(32, 86)(33, 56)(34, 72)(35, 63)(36, 64)(37, 54)(38, 55)(39, 53)(40, 85)(41, 95)(42, 94)(43, 61)(44, 93)(45, 80)(46, 96)(47, 88)(48, 87)(97, 146)(98, 148)(99, 150)(100, 145)(101, 172)(102, 170)(103, 169)(104, 174)(105, 183)(106, 182)(107, 149)(108, 181)(109, 192)(110, 184)(111, 176)(112, 175)(113, 168)(114, 160)(115, 151)(116, 152)(117, 166)(118, 167)(119, 165)(120, 173)(121, 163)(122, 147)(123, 156)(124, 155)(125, 161)(126, 164)(127, 162)(128, 186)(129, 180)(130, 177)(131, 154)(132, 178)(133, 171)(134, 179)(135, 187)(136, 188)(137, 157)(138, 159)(139, 153)(140, 158)(141, 191)(142, 189)(143, 190)(144, 185) MAP : A2.34 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A2.33. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^8, (x.1^-1 * x.2 * x.1^-2)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 96)(2, 80)(3, 87)(4, 88)(5, 94)(6, 95)(7, 93)(8, 61)(9, 82)(10, 84)(11, 86)(12, 81)(13, 60)(14, 58)(15, 57)(16, 62)(17, 55)(18, 54)(19, 85)(20, 53)(21, 72)(22, 56)(23, 64)(24, 63)(25, 77)(26, 79)(27, 73)(28, 78)(29, 71)(30, 69)(31, 70)(32, 65)(33, 91)(34, 83)(35, 76)(36, 75)(37, 89)(38, 92)(39, 90)(40, 66)(41, 52)(42, 49)(43, 74)(44, 50)(45, 59)(46, 51)(47, 67)(48, 68)(97, 146)(98, 148)(99, 150)(100, 145)(101, 172)(102, 170)(103, 169)(104, 174)(105, 183)(106, 182)(107, 149)(108, 181)(109, 192)(110, 184)(111, 176)(112, 175)(113, 168)(114, 160)(115, 151)(116, 152)(117, 166)(118, 167)(119, 165)(120, 173)(121, 163)(122, 147)(123, 156)(124, 155)(125, 161)(126, 164)(127, 162)(128, 186)(129, 180)(130, 177)(131, 154)(132, 178)(133, 171)(134, 179)(135, 187)(136, 188)(137, 157)(138, 159)(139, 153)(140, 158)(141, 191)(142, 189)(143, 190)(144, 185) MAP : A2.35 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A2.33. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2^3, x.4^3, x.2 * x.4^-1 * x.3^-1 * x.2 * x.3^-1, x.2 * x.3^2 * x.4 * x.3^-1, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 51)(26, 65)(27, 52)(28, 49)(29, 66)(30, 67)(31, 57)(32, 50)(33, 62)(34, 63)(35, 69)(36, 58)(37, 68)(38, 55)(39, 60)(40, 61)(41, 56)(42, 70)(43, 72)(44, 64)(45, 71)(46, 53)(47, 59)(48, 54)(73, 122)(74, 125)(75, 126)(76, 133)(77, 131)(78, 138)(79, 141)(80, 139)(81, 124)(82, 128)(83, 121)(84, 123)(85, 142)(86, 144)(87, 134)(88, 137)(89, 127)(90, 132)(91, 143)(92, 135)(93, 136)(94, 129)(95, 130)(96, 140)(145, 191)(146, 172)(147, 183)(148, 175)(149, 176)(150, 169)(151, 170)(152, 180)(153, 186)(154, 189)(155, 190)(156, 173)(157, 171)(158, 178)(159, 181)(160, 179)(161, 188)(162, 192)(163, 185)(164, 187)(165, 182)(166, 184)(167, 174)(168, 177) MAP : A2.36 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A2.33. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2^3, x.4^3, x.2 * x.4^-1 * x.3^-1 * x.2 * x.3^-1, x.2 * x.3^2 * x.4 * x.3^-1, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 71)(26, 52)(27, 63)(28, 55)(29, 56)(30, 49)(31, 50)(32, 60)(33, 66)(34, 69)(35, 70)(36, 53)(37, 51)(38, 58)(39, 61)(40, 59)(41, 68)(42, 72)(43, 65)(44, 67)(45, 62)(46, 64)(47, 54)(48, 57)(73, 122)(74, 125)(75, 126)(76, 133)(77, 131)(78, 138)(79, 141)(80, 139)(81, 124)(82, 128)(83, 121)(84, 123)(85, 142)(86, 144)(87, 134)(88, 137)(89, 127)(90, 132)(91, 143)(92, 135)(93, 136)(94, 129)(95, 130)(96, 140)(145, 184)(146, 174)(147, 176)(148, 192)(149, 175)(150, 181)(151, 187)(152, 182)(153, 179)(154, 169)(155, 180)(156, 177)(157, 170)(158, 171)(159, 185)(160, 178)(161, 190)(162, 191)(163, 173)(164, 186)(165, 172)(166, 183)(167, 188)(168, 189) MAP : A2.37 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A2.33. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^8, (x.2^3 * x.1^-1)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 52)(3, 54)(4, 49)(5, 76)(6, 74)(7, 73)(8, 78)(9, 87)(10, 86)(11, 53)(12, 85)(13, 96)(14, 88)(15, 80)(16, 79)(17, 72)(18, 64)(19, 55)(20, 56)(21, 70)(22, 71)(23, 69)(24, 77)(25, 67)(26, 51)(27, 60)(28, 59)(29, 65)(30, 68)(31, 66)(32, 90)(33, 84)(34, 81)(35, 58)(36, 82)(37, 75)(38, 83)(39, 91)(40, 92)(41, 61)(42, 63)(43, 57)(44, 62)(45, 95)(46, 93)(47, 94)(48, 89)(97, 147)(98, 155)(99, 164)(100, 163)(101, 145)(102, 148)(103, 146)(104, 170)(105, 165)(106, 167)(107, 161)(108, 166)(109, 175)(110, 173)(111, 174)(112, 169)(113, 188)(114, 185)(115, 162)(116, 186)(117, 179)(118, 187)(119, 171)(120, 172)(121, 154)(122, 156)(123, 158)(124, 153)(125, 180)(126, 178)(127, 177)(128, 182)(129, 152)(130, 168)(131, 159)(132, 160)(133, 150)(134, 151)(135, 149)(136, 181)(137, 191)(138, 190)(139, 157)(140, 189)(141, 176)(142, 192)(143, 184)(144, 183) MAP : A2.38 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A2.33. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^8, (x.2^3 * x.1^-1)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 52)(3, 54)(4, 49)(5, 76)(6, 74)(7, 73)(8, 78)(9, 87)(10, 86)(11, 53)(12, 85)(13, 96)(14, 88)(15, 80)(16, 79)(17, 72)(18, 64)(19, 55)(20, 56)(21, 70)(22, 71)(23, 69)(24, 77)(25, 67)(26, 51)(27, 60)(28, 59)(29, 65)(30, 68)(31, 66)(32, 90)(33, 84)(34, 81)(35, 58)(36, 82)(37, 75)(38, 83)(39, 91)(40, 92)(41, 61)(42, 63)(43, 57)(44, 62)(45, 95)(46, 93)(47, 94)(48, 89)(97, 192)(98, 176)(99, 183)(100, 184)(101, 190)(102, 191)(103, 189)(104, 157)(105, 178)(106, 180)(107, 182)(108, 177)(109, 156)(110, 154)(111, 153)(112, 158)(113, 151)(114, 150)(115, 181)(116, 149)(117, 168)(118, 152)(119, 160)(120, 159)(121, 173)(122, 175)(123, 169)(124, 174)(125, 167)(126, 165)(127, 166)(128, 161)(129, 187)(130, 179)(131, 172)(132, 171)(133, 185)(134, 188)(135, 186)(136, 162)(137, 148)(138, 145)(139, 170)(140, 146)(141, 155)(142, 147)(143, 163)(144, 164) MAP : A2.39 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1^-1, x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1^-1, x.1^-2 * x.2 * x.1^-2 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 29)(3, 30)(4, 37)(5, 35)(6, 42)(7, 45)(8, 43)(9, 28)(10, 32)(11, 25)(12, 27)(13, 46)(14, 48)(15, 38)(16, 41)(17, 31)(18, 36)(19, 47)(20, 39)(21, 40)(22, 33)(23, 34)(24, 44)(49, 75)(50, 89)(51, 76)(52, 73)(53, 90)(54, 91)(55, 81)(56, 74)(57, 86)(58, 87)(59, 93)(60, 82)(61, 92)(62, 79)(63, 84)(64, 85)(65, 80)(66, 94)(67, 96)(68, 88)(69, 95)(70, 77)(71, 83)(72, 78) MAP : A2.40 NOTES : type I, reflexible, isomorphic to A2.39. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1^-1, x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1^-1, x.1^-2 * x.2 * x.1^-2 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 29)(3, 30)(4, 37)(5, 35)(6, 42)(7, 45)(8, 43)(9, 28)(10, 32)(11, 25)(12, 27)(13, 46)(14, 48)(15, 38)(16, 41)(17, 31)(18, 36)(19, 47)(20, 39)(21, 40)(22, 33)(23, 34)(24, 44)(49, 95)(50, 76)(51, 87)(52, 79)(53, 80)(54, 73)(55, 74)(56, 84)(57, 90)(58, 93)(59, 94)(60, 77)(61, 75)(62, 82)(63, 85)(64, 83)(65, 92)(66, 96)(67, 89)(68, 91)(69, 86)(70, 88)(71, 78)(72, 81) MAP : A2.41 NOTES : type I, reflexible, isomorphic to A2.39. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, x.1 * x.2^-1 * x.1 * x.2^-1 * x.1 * x.2, x.2^-1 * x.1 * x.2^-2 * x.1^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 28)(2, 32)(3, 25)(4, 27)(5, 46)(6, 48)(7, 38)(8, 41)(9, 31)(10, 36)(11, 47)(12, 39)(13, 40)(14, 33)(15, 34)(16, 44)(17, 26)(18, 29)(19, 30)(20, 37)(21, 35)(22, 42)(23, 45)(24, 43)(49, 87)(50, 92)(51, 79)(52, 95)(53, 96)(54, 89)(55, 90)(56, 76)(57, 82)(58, 85)(59, 86)(60, 93)(61, 91)(62, 74)(63, 77)(64, 75)(65, 84)(66, 88)(67, 81)(68, 83)(69, 78)(70, 80)(71, 94)(72, 73) MAP : A2.42 NOTES : type I, reflexible, isomorphic to A2.39. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, x.1 * x.2^-1 * x.1 * x.2^-1 * x.1 * x.2, x.2^-1 * x.1 * x.2^-2 * x.1^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 27)(2, 41)(3, 28)(4, 25)(5, 42)(6, 43)(7, 33)(8, 26)(9, 38)(10, 39)(11, 45)(12, 34)(13, 44)(14, 31)(15, 36)(16, 37)(17, 32)(18, 46)(19, 48)(20, 40)(21, 47)(22, 29)(23, 35)(24, 30)(49, 74)(50, 77)(51, 78)(52, 85)(53, 83)(54, 90)(55, 93)(56, 91)(57, 76)(58, 80)(59, 73)(60, 75)(61, 94)(62, 96)(63, 86)(64, 89)(65, 79)(66, 84)(67, 95)(68, 87)(69, 88)(70, 81)(71, 82)(72, 92) MAP : A2.43 NOTES : type I, reflexible, isomorphic to Med2({4,6}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 30)(2, 27)(3, 36)(4, 25)(5, 33)(6, 48)(7, 32)(8, 35)(9, 42)(10, 29)(11, 45)(12, 47)(13, 43)(14, 28)(15, 46)(16, 34)(17, 38)(18, 44)(19, 26)(20, 40)(21, 39)(22, 31)(23, 37)(24, 41)(49, 75)(50, 78)(51, 80)(52, 81)(53, 73)(54, 82)(55, 84)(56, 77)(57, 79)(58, 83)(59, 74)(60, 76)(61, 89)(62, 95)(63, 85)(64, 96)(65, 92)(66, 86)(67, 93)(68, 87)(69, 88)(70, 90)(71, 94)(72, 91) MAP : A2.44 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 27)(2, 30)(3, 32)(4, 33)(5, 25)(6, 34)(7, 36)(8, 29)(9, 31)(10, 35)(11, 26)(12, 28)(13, 41)(14, 47)(15, 37)(16, 48)(17, 44)(18, 38)(19, 45)(20, 39)(21, 40)(22, 42)(23, 46)(24, 43)(49, 76)(50, 91)(51, 74)(52, 86)(53, 82)(54, 73)(55, 94)(56, 79)(57, 77)(58, 88)(59, 80)(60, 75)(61, 95)(62, 89)(63, 93)(64, 92)(65, 96)(66, 81)(67, 85)(68, 90)(69, 83)(70, 87)(71, 84)(72, 78) MAP : A2.45 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 28)(2, 43)(3, 26)(4, 38)(5, 34)(6, 25)(7, 46)(8, 31)(9, 29)(10, 40)(11, 32)(12, 27)(13, 47)(14, 41)(15, 45)(16, 44)(17, 48)(18, 33)(19, 37)(20, 42)(21, 35)(22, 39)(23, 36)(24, 30)(49, 75)(50, 78)(51, 80)(52, 81)(53, 73)(54, 82)(55, 84)(56, 77)(57, 79)(58, 83)(59, 74)(60, 76)(61, 89)(62, 95)(63, 85)(64, 96)(65, 92)(66, 86)(67, 93)(68, 87)(69, 88)(70, 90)(71, 94)(72, 91) MAP : A2.46 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.1)^2, x.4 * x.5 * x.1 * x.2, x.4^-1 * x.5 * x.4 * x.5, (x.2 * x.5)^2, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70)(73, 75)(74, 83)(76, 80)(77, 84)(78, 79)(81, 82) MAP : A2.47 NOTES : type II, reflexible, isomorphic to A2.46. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.2 * x.5 * x.4 * x.1, (x.5 * x.2)^2, (x.5 * x.1)^2, (x.5 * x.3^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 27)(26, 35)(28, 32)(29, 36)(30, 31)(33, 34)(37, 65)(38, 69)(39, 68)(40, 61)(41, 64)(42, 62)(43, 70)(44, 72)(45, 66)(46, 71)(47, 67)(48, 63)(73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84) MAP : A2.48 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 27)(2, 30)(3, 32)(4, 33)(5, 25)(6, 34)(7, 36)(8, 29)(9, 31)(10, 35)(11, 26)(12, 28)(13, 41)(14, 47)(15, 37)(16, 48)(17, 44)(18, 38)(19, 45)(20, 39)(21, 40)(22, 42)(23, 46)(24, 43)(49, 78)(50, 75)(51, 84)(52, 73)(53, 81)(54, 96)(55, 80)(56, 83)(57, 90)(58, 77)(59, 93)(60, 95)(61, 91)(62, 76)(63, 94)(64, 82)(65, 86)(66, 92)(67, 74)(68, 88)(69, 87)(70, 79)(71, 85)(72, 89) MAP : A2.49 NOTES : type II, reflexible, isomorphic to A2.46. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.1)^2, x.4 * x.5 * x.1 * x.2, x.4^-1 * x.5 * x.4 * x.5, (x.2 * x.5)^2, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 27)(26, 35)(28, 32)(29, 36)(30, 31)(33, 34)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70)(73, 82)(74, 84)(75, 78)(76, 83)(77, 79)(80, 81) MAP : A2.50 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 75)(26, 83)(27, 73)(28, 80)(29, 84)(30, 79)(31, 78)(32, 76)(33, 82)(34, 81)(35, 74)(36, 77)(37, 71)(38, 63)(39, 62)(40, 67)(41, 70)(42, 68)(43, 64)(44, 66)(45, 72)(46, 65)(47, 61)(48, 69) MAP : A2.51 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.52 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 68)(38, 67)(39, 65)(40, 72)(41, 63)(42, 70)(43, 62)(44, 61)(45, 71)(46, 66)(47, 69)(48, 64) MAP : A2.53 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 63)(38, 71)(39, 61)(40, 68)(41, 72)(42, 67)(43, 66)(44, 64)(45, 70)(46, 69)(47, 62)(48, 65) MAP : A2.54 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66) MAP : A2.55 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 75)(26, 83)(27, 73)(28, 80)(29, 84)(30, 79)(31, 78)(32, 76)(33, 82)(34, 81)(35, 74)(36, 77)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68) MAP : A2.56 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68) MAP : A2.57 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 95)(15, 85)(16, 92)(17, 96)(18, 91)(19, 90)(20, 88)(21, 94)(22, 93)(23, 86)(24, 89)(25, 83)(26, 75)(27, 74)(28, 79)(29, 82)(30, 80)(31, 76)(32, 78)(33, 84)(34, 77)(35, 73)(36, 81)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68) MAP : A2.58 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.4, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 95)(15, 85)(16, 92)(17, 96)(18, 91)(19, 90)(20, 88)(21, 94)(22, 93)(23, 86)(24, 89)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68) MAP : A2.59 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 80)(26, 79)(27, 77)(28, 84)(29, 75)(30, 82)(31, 74)(32, 73)(33, 83)(34, 78)(35, 81)(36, 76)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68) MAP : A2.60 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.4, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68) MAP : A2.61 NOTES : type II, reflexible, isomorphic to A2.46. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.2 * x.5 * x.4 * x.1, (x.5 * x.2)^2, (x.5 * x.1)^2, (x.5 * x.3^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 64)(38, 66)(39, 72)(40, 65)(41, 61)(42, 69)(43, 71)(44, 63)(45, 62)(46, 67)(47, 70)(48, 68)(73, 75)(74, 83)(76, 80)(77, 84)(78, 79)(81, 82) MAP : A2.62 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 75)(26, 83)(27, 73)(28, 80)(29, 84)(30, 79)(31, 78)(32, 76)(33, 82)(34, 81)(35, 74)(36, 77)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.63 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 95)(15, 85)(16, 92)(17, 96)(18, 91)(19, 90)(20, 88)(21, 94)(22, 93)(23, 86)(24, 89)(25, 84)(26, 82)(27, 76)(28, 75)(29, 80)(30, 83)(31, 81)(32, 77)(33, 79)(34, 74)(35, 78)(36, 73)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.64 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4 * x.2^-1, (x.2 * x.3)^3, x.3 * x.2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 95)(15, 85)(16, 92)(17, 96)(18, 91)(19, 90)(20, 88)(21, 94)(22, 93)(23, 86)(24, 89)(25, 84)(26, 82)(27, 76)(28, 75)(29, 80)(30, 83)(31, 81)(32, 77)(33, 79)(34, 74)(35, 78)(36, 73)(37, 70)(38, 72)(39, 66)(40, 71)(41, 67)(42, 63)(43, 65)(44, 69)(45, 68)(46, 61)(47, 64)(48, 62) MAP : A2.65 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 82)(26, 84)(27, 78)(28, 83)(29, 79)(30, 75)(31, 77)(32, 81)(33, 80)(34, 73)(35, 76)(36, 74)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.66 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4 * x.2^-1, (x.2 * x.3)^3, x.3 * x.2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 82)(26, 84)(27, 78)(28, 83)(29, 79)(30, 75)(31, 77)(32, 81)(33, 80)(34, 73)(35, 76)(36, 74)(37, 72)(38, 70)(39, 64)(40, 63)(41, 68)(42, 71)(43, 69)(44, 65)(45, 67)(46, 62)(47, 66)(48, 61) MAP : A2.67 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 75)(26, 83)(27, 73)(28, 80)(29, 84)(30, 79)(31, 78)(32, 76)(33, 82)(34, 81)(35, 74)(36, 77)(37, 72)(38, 70)(39, 64)(40, 63)(41, 68)(42, 71)(43, 69)(44, 65)(45, 67)(46, 62)(47, 66)(48, 61) MAP : A2.68 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 70)(38, 72)(39, 66)(40, 71)(41, 67)(42, 63)(43, 65)(44, 69)(45, 68)(46, 61)(47, 64)(48, 62) MAP : A2.69 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, x.2 * x.4^-1 * x.3 * x.4^-1 * x.2 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 95)(15, 85)(16, 92)(17, 96)(18, 91)(19, 90)(20, 88)(21, 94)(22, 93)(23, 86)(24, 89)(25, 83)(26, 75)(27, 74)(28, 79)(29, 82)(30, 80)(31, 76)(32, 78)(33, 84)(34, 77)(35, 73)(36, 81)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66) MAP : A2.70 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^-3 * x.4, x.3^-2 * x.4 * x.3^-1, x.4 * x.2 * x.4 * x.2^-1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 95)(15, 85)(16, 92)(17, 96)(18, 91)(19, 90)(20, 88)(21, 94)(22, 93)(23, 86)(24, 89)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.71 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, x.2 * x.4^-1 * x.3 * x.4^-1 * x.2 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 80)(26, 79)(27, 77)(28, 84)(29, 75)(30, 82)(31, 74)(32, 73)(33, 83)(34, 78)(35, 81)(36, 76)(37, 63)(38, 71)(39, 61)(40, 68)(41, 72)(42, 67)(43, 66)(44, 64)(45, 70)(46, 69)(47, 62)(48, 65) MAP : A2.72 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^-3 * x.4, x.3^-2 * x.4 * x.3^-1, x.4 * x.2 * x.4 * x.2^-1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.73 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3 > CTG (small) : <12, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 26)(14, 32)(15, 28)(16, 30)(17, 25)(18, 33)(19, 34)(20, 29)(21, 27)(22, 36)(23, 31)(24, 35)(37, 64)(38, 70)(39, 65)(40, 67)(41, 71)(42, 62)(43, 61)(44, 69)(45, 72)(46, 66)(47, 63)(48, 68)(73, 95)(74, 88)(75, 96)(76, 89)(77, 93)(78, 91)(79, 87)(80, 94)(81, 86)(82, 85)(83, 92)(84, 90) MAP : A2.74 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.3^-3 * x.2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 63)(38, 71)(39, 61)(40, 68)(41, 72)(42, 67)(43, 66)(44, 64)(45, 70)(46, 69)(47, 62)(48, 65) MAP : A2.75 NOTES : type II, reflexible, isomorphic to A2.51. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.3^-3 * x.2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 85)(15, 95)(16, 90)(17, 93)(18, 88)(19, 92)(20, 91)(21, 89)(22, 96)(23, 87)(24, 94)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66) MAP : A2.76 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 29)(14, 28)(15, 25)(16, 34)(17, 33)(18, 26)(19, 27)(20, 30)(21, 35)(22, 36)(23, 31)(24, 32)(37, 62)(38, 61)(39, 66)(40, 65)(41, 64)(42, 63)(43, 68)(44, 67)(45, 70)(46, 69)(47, 72)(48, 71)(73, 90)(74, 87)(75, 92)(76, 85)(77, 86)(78, 91)(79, 96)(80, 95)(81, 88)(82, 89)(83, 94)(84, 93) MAP : A2.77 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 28)(14, 29)(15, 26)(16, 33)(17, 34)(18, 25)(19, 30)(20, 27)(21, 36)(22, 35)(23, 32)(24, 31)(37, 62)(38, 61)(39, 66)(40, 65)(41, 64)(42, 63)(43, 68)(44, 67)(45, 70)(46, 69)(47, 72)(48, 71)(73, 87)(74, 90)(75, 91)(76, 86)(77, 85)(78, 92)(79, 95)(80, 96)(81, 89)(82, 88)(83, 93)(84, 94) MAP : A2.78 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 30)(14, 27)(15, 32)(16, 25)(17, 26)(18, 31)(19, 36)(20, 35)(21, 28)(22, 29)(23, 34)(24, 33)(37, 62)(38, 61)(39, 66)(40, 65)(41, 64)(42, 63)(43, 68)(44, 67)(45, 70)(46, 69)(47, 72)(48, 71)(73, 89)(74, 88)(75, 85)(76, 94)(77, 93)(78, 86)(79, 87)(80, 90)(81, 95)(82, 96)(83, 91)(84, 92) MAP : A2.79 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 28)(14, 29)(15, 26)(16, 33)(17, 34)(18, 25)(19, 30)(20, 27)(21, 36)(22, 35)(23, 32)(24, 31)(37, 71)(38, 72)(39, 69)(40, 68)(41, 67)(42, 70)(43, 65)(44, 64)(45, 63)(46, 66)(47, 61)(48, 62)(73, 94)(74, 93)(75, 88)(76, 95)(77, 96)(78, 89)(79, 86)(80, 85)(81, 92)(82, 91)(83, 90)(84, 87) MAP : A2.80 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 30)(14, 27)(15, 32)(16, 25)(17, 26)(18, 31)(19, 36)(20, 35)(21, 28)(22, 29)(23, 34)(24, 33)(37, 71)(38, 72)(39, 69)(40, 68)(41, 67)(42, 70)(43, 65)(44, 64)(45, 63)(46, 66)(47, 61)(48, 62)(73, 92)(74, 91)(75, 96)(76, 87)(77, 90)(78, 95)(79, 94)(80, 93)(81, 86)(82, 85)(83, 88)(84, 89) MAP : A2.81 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 32)(14, 31)(15, 36)(16, 27)(17, 30)(18, 35)(19, 34)(20, 33)(21, 26)(22, 25)(23, 28)(24, 29)(37, 71)(38, 72)(39, 69)(40, 68)(41, 67)(42, 70)(43, 65)(44, 64)(45, 63)(46, 66)(47, 61)(48, 62)(73, 90)(74, 87)(75, 92)(76, 85)(77, 86)(78, 91)(79, 96)(80, 95)(81, 88)(82, 89)(83, 94)(84, 93) MAP : A2.82 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 34)(14, 33)(15, 28)(16, 35)(17, 36)(18, 29)(19, 26)(20, 25)(21, 32)(22, 31)(23, 30)(24, 27)(37, 71)(38, 72)(39, 69)(40, 68)(41, 67)(42, 70)(43, 65)(44, 64)(45, 63)(46, 66)(47, 61)(48, 62)(73, 88)(74, 89)(75, 86)(76, 93)(77, 94)(78, 85)(79, 90)(80, 87)(81, 96)(82, 95)(83, 92)(84, 91) MAP : A2.83 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 27)(14, 30)(15, 31)(16, 26)(17, 25)(18, 32)(19, 35)(20, 36)(21, 29)(22, 28)(23, 33)(24, 34)(37, 72)(38, 71)(39, 70)(40, 67)(41, 68)(42, 69)(43, 64)(44, 65)(45, 66)(46, 63)(47, 62)(48, 61)(73, 92)(74, 91)(75, 96)(76, 87)(77, 90)(78, 95)(79, 94)(80, 93)(81, 86)(82, 85)(83, 88)(84, 89) MAP : A2.84 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 29)(14, 28)(15, 25)(16, 34)(17, 33)(18, 26)(19, 27)(20, 30)(21, 35)(22, 36)(23, 31)(24, 32)(37, 72)(38, 71)(39, 70)(40, 67)(41, 68)(42, 69)(43, 64)(44, 65)(45, 66)(46, 63)(47, 62)(48, 61)(73, 94)(74, 93)(75, 88)(76, 95)(77, 96)(78, 89)(79, 86)(80, 85)(81, 92)(82, 91)(83, 90)(84, 87) MAP : A2.85 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 32)(14, 31)(15, 36)(16, 27)(17, 30)(18, 35)(19, 34)(20, 33)(21, 26)(22, 25)(23, 28)(24, 29)(37, 72)(38, 71)(39, 70)(40, 67)(41, 68)(42, 69)(43, 64)(44, 65)(45, 66)(46, 63)(47, 62)(48, 61)(73, 87)(74, 90)(75, 91)(76, 86)(77, 85)(78, 92)(79, 95)(80, 96)(81, 89)(82, 88)(83, 93)(84, 94) MAP : A2.86 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 34)(14, 33)(15, 28)(16, 35)(17, 36)(18, 29)(19, 26)(20, 25)(21, 32)(22, 31)(23, 30)(24, 27)(37, 72)(38, 71)(39, 70)(40, 67)(41, 68)(42, 69)(43, 64)(44, 65)(45, 66)(46, 63)(47, 62)(48, 61)(73, 89)(74, 88)(75, 85)(76, 94)(77, 93)(78, 86)(79, 87)(80, 90)(81, 95)(82, 96)(83, 91)(84, 92) MAP : A2.87 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3 > CTG (small) : <12, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 29)(14, 25)(15, 33)(16, 27)(17, 32)(18, 28)(19, 35)(20, 26)(21, 30)(22, 31)(23, 36)(24, 34)(37, 64)(38, 70)(39, 65)(40, 67)(41, 71)(42, 62)(43, 61)(44, 69)(45, 72)(46, 66)(47, 63)(48, 68)(73, 94)(74, 93)(75, 91)(76, 86)(77, 88)(78, 96)(79, 90)(80, 95)(81, 89)(82, 92)(83, 85)(84, 87) MAP : A2.88 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A2.43. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <12, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 27)(14, 30)(15, 31)(16, 26)(17, 25)(18, 32)(19, 35)(20, 36)(21, 29)(22, 28)(23, 33)(24, 34)(37, 62)(38, 61)(39, 66)(40, 65)(41, 64)(42, 63)(43, 68)(44, 67)(45, 70)(46, 69)(47, 72)(48, 71)(73, 88)(74, 89)(75, 86)(76, 93)(77, 94)(78, 85)(79, 90)(80, 87)(81, 96)(82, 95)(83, 92)(84, 91) MAP : A2.89 NOTES : type I, chiral, isomorphic to Snub({3,8}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^8, x.3 * x.2^-2 * x.1 * x.3^-1 * x.2^-3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 99)(50, 107)(51, 116)(52, 115)(53, 97)(54, 100)(55, 98)(56, 122)(57, 117)(58, 119)(59, 113)(60, 118)(61, 127)(62, 125)(63, 126)(64, 121)(65, 140)(66, 137)(67, 114)(68, 138)(69, 131)(70, 139)(71, 123)(72, 124)(73, 106)(74, 108)(75, 110)(76, 105)(77, 132)(78, 130)(79, 129)(80, 134)(81, 104)(82, 120)(83, 111)(84, 112)(85, 102)(86, 103)(87, 101)(88, 133)(89, 143)(90, 142)(91, 109)(92, 141)(93, 128)(94, 144)(95, 136)(96, 135)(145, 194)(146, 196)(147, 198)(148, 193)(149, 220)(150, 218)(151, 217)(152, 222)(153, 231)(154, 230)(155, 197)(156, 229)(157, 240)(158, 232)(159, 224)(160, 223)(161, 216)(162, 208)(163, 199)(164, 200)(165, 214)(166, 215)(167, 213)(168, 221)(169, 211)(170, 195)(171, 204)(172, 203)(173, 209)(174, 212)(175, 210)(176, 234)(177, 228)(178, 225)(179, 202)(180, 226)(181, 219)(182, 227)(183, 235)(184, 236)(185, 205)(186, 207)(187, 201)(188, 206)(189, 239)(190, 237)(191, 238)(192, 233) MAP : A2.90 NOTES : type I, chiral, isomorphic to Snub({3,8}), isomorphic to A2.89. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^8, x.3 * x.2^-2 * x.1 * x.3^-1 * x.2^-3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 122)(50, 124)(51, 126)(52, 121)(53, 100)(54, 98)(55, 97)(56, 102)(57, 119)(58, 118)(59, 125)(60, 117)(61, 112)(62, 120)(63, 104)(64, 103)(65, 136)(66, 144)(67, 127)(68, 128)(69, 134)(70, 135)(71, 133)(72, 101)(73, 131)(74, 123)(75, 140)(76, 139)(77, 129)(78, 132)(79, 130)(80, 106)(81, 116)(82, 113)(83, 138)(84, 114)(85, 99)(86, 115)(87, 107)(88, 108)(89, 141)(90, 143)(91, 137)(92, 142)(93, 111)(94, 109)(95, 110)(96, 105)(145, 196)(146, 193)(147, 218)(148, 194)(149, 203)(150, 195)(151, 211)(152, 212)(153, 235)(154, 227)(155, 220)(156, 219)(157, 233)(158, 236)(159, 234)(160, 210)(161, 221)(162, 223)(163, 217)(164, 222)(165, 215)(166, 213)(167, 214)(168, 209)(169, 199)(170, 198)(171, 229)(172, 197)(173, 216)(174, 200)(175, 208)(176, 207)(177, 226)(178, 228)(179, 230)(180, 225)(181, 204)(182, 202)(183, 201)(184, 206)(185, 240)(186, 224)(187, 231)(188, 232)(189, 238)(190, 239)(191, 237)(192, 205) MAP : A2.91 NOTES : type I, chiral, isomorphic to Snub({3,8}), isomorphic to A2.89. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^8, x.3 * x.1 * x.2 * x.3^2 * x.1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 98)(50, 100)(51, 102)(52, 97)(53, 124)(54, 122)(55, 121)(56, 126)(57, 135)(58, 134)(59, 101)(60, 133)(61, 144)(62, 136)(63, 128)(64, 127)(65, 120)(66, 112)(67, 103)(68, 104)(69, 118)(70, 119)(71, 117)(72, 125)(73, 115)(74, 99)(75, 108)(76, 107)(77, 113)(78, 116)(79, 114)(80, 138)(81, 132)(82, 129)(83, 106)(84, 130)(85, 123)(86, 131)(87, 139)(88, 140)(89, 109)(90, 111)(91, 105)(92, 110)(93, 143)(94, 141)(95, 142)(96, 137)(145, 199)(146, 198)(147, 229)(148, 197)(149, 216)(150, 200)(151, 208)(152, 207)(153, 240)(154, 224)(155, 231)(156, 232)(157, 238)(158, 239)(159, 237)(160, 205)(161, 226)(162, 228)(163, 230)(164, 225)(165, 204)(166, 202)(167, 201)(168, 206)(169, 196)(170, 193)(171, 218)(172, 194)(173, 203)(174, 195)(175, 211)(176, 212)(177, 221)(178, 223)(179, 217)(180, 222)(181, 215)(182, 213)(183, 214)(184, 209)(185, 235)(186, 227)(187, 220)(188, 219)(189, 233)(190, 236)(191, 234)(192, 210) MAP : A2.92 NOTES : type I, chiral, isomorphic to Snub({3,8}), isomorphic to A2.89. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^8, x.3 * x.1 * x.2 * x.3^2 * x.1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 104)(50, 120)(51, 111)(52, 112)(53, 102)(54, 103)(55, 101)(56, 133)(57, 106)(58, 108)(59, 110)(60, 105)(61, 132)(62, 130)(63, 129)(64, 134)(65, 143)(66, 142)(67, 109)(68, 141)(69, 128)(70, 144)(71, 136)(72, 135)(73, 117)(74, 119)(75, 113)(76, 118)(77, 127)(78, 125)(79, 126)(80, 121)(81, 99)(82, 107)(83, 116)(84, 115)(85, 97)(86, 100)(87, 98)(88, 122)(89, 140)(90, 137)(91, 114)(92, 138)(93, 131)(94, 139)(95, 123)(96, 124)(145, 218)(146, 220)(147, 222)(148, 217)(149, 196)(150, 194)(151, 193)(152, 198)(153, 215)(154, 214)(155, 221)(156, 213)(157, 208)(158, 216)(159, 200)(160, 199)(161, 232)(162, 240)(163, 223)(164, 224)(165, 230)(166, 231)(167, 229)(168, 197)(169, 227)(170, 219)(171, 236)(172, 235)(173, 225)(174, 228)(175, 226)(176, 202)(177, 212)(178, 209)(179, 234)(180, 210)(181, 195)(182, 211)(183, 203)(184, 204)(185, 237)(186, 239)(187, 233)(188, 238)(189, 207)(190, 205)(191, 206)(192, 201) MAP : A2.93 NOTES : type I, chiral, isomorphic to Snub({4,6}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, (x.3^-1 * x.2)^2, x.3^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 2)(3, 7)(4, 5)(6, 16)(8, 10)(9, 22)(11, 19)(12, 14)(13, 24)(15, 23)(17, 18)(20, 21)(25, 51)(26, 54)(27, 56)(28, 57)(29, 49)(30, 58)(31, 60)(32, 53)(33, 55)(34, 59)(35, 50)(36, 52)(37, 65)(38, 71)(39, 61)(40, 72)(41, 68)(42, 62)(43, 69)(44, 63)(45, 64)(46, 66)(47, 70)(48, 67)(73, 100)(74, 115)(75, 98)(76, 110)(77, 106)(78, 97)(79, 118)(80, 103)(81, 101)(82, 112)(83, 104)(84, 99)(85, 119)(86, 113)(87, 117)(88, 116)(89, 120)(90, 105)(91, 109)(92, 114)(93, 107)(94, 111)(95, 108)(96, 102) MAP : A2.94 NOTES : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A2.93. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, (x.3^-1 * x.2)^2, x.3^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 2)(3, 7)(4, 5)(6, 16)(8, 10)(9, 22)(11, 19)(12, 14)(13, 24)(15, 23)(17, 18)(20, 21)(25, 67)(26, 52)(27, 70)(28, 58)(29, 62)(30, 68)(31, 50)(32, 64)(33, 63)(34, 55)(35, 61)(36, 65)(37, 54)(38, 51)(39, 60)(40, 49)(41, 57)(42, 72)(43, 56)(44, 59)(45, 66)(46, 53)(47, 69)(48, 71)(73, 102)(74, 99)(75, 108)(76, 97)(77, 105)(78, 120)(79, 104)(80, 107)(81, 114)(82, 101)(83, 117)(84, 119)(85, 115)(86, 100)(87, 118)(88, 106)(89, 110)(90, 116)(91, 98)(92, 112)(93, 111)(94, 103)(95, 109)(96, 113) MAP : A2.95 NOTES : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A2.93. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^4, (x.3^-1 * x.2)^2, x.2^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 6, 3, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 2)(3, 7)(4, 5)(6, 16)(8, 10)(9, 22)(11, 19)(12, 14)(13, 24)(15, 23)(17, 18)(20, 21)(25, 52)(26, 67)(27, 50)(28, 62)(29, 58)(30, 49)(31, 70)(32, 55)(33, 53)(34, 64)(35, 56)(36, 51)(37, 71)(38, 65)(39, 69)(40, 68)(41, 72)(42, 57)(43, 61)(44, 66)(45, 59)(46, 63)(47, 60)(48, 54)(73, 112)(74, 103)(75, 110)(76, 98)(77, 118)(78, 109)(79, 106)(80, 115)(81, 113)(82, 100)(83, 116)(84, 111)(85, 107)(86, 101)(87, 105)(88, 104)(89, 108)(90, 117)(91, 97)(92, 102)(93, 119)(94, 99)(95, 120)(96, 114) MAP : A2.96 NOTES : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A2.93. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^4, (x.3^-1 * x.2)^2, x.2^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 6, 3, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 2)(3, 7)(4, 5)(6, 16)(8, 10)(9, 22)(11, 19)(12, 14)(13, 24)(15, 23)(17, 18)(20, 21)(25, 54)(26, 51)(27, 60)(28, 49)(29, 57)(30, 72)(31, 56)(32, 59)(33, 66)(34, 53)(35, 69)(36, 71)(37, 67)(38, 52)(39, 70)(40, 58)(41, 62)(42, 68)(43, 50)(44, 64)(45, 63)(46, 55)(47, 61)(48, 65)(73, 101)(74, 107)(75, 97)(76, 108)(77, 104)(78, 98)(79, 105)(80, 99)(81, 100)(82, 102)(83, 106)(84, 103)(85, 111)(86, 114)(87, 116)(88, 117)(89, 109)(90, 118)(91, 120)(92, 113)(93, 115)(94, 119)(95, 110)(96, 112) MAP : A2.97 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.5^3, u.6^3, u.4 * u.5^-1 * u.1 * u.3^-1, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.5^3, x.6^3, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 60 R = (1, 7, 13, 19, 25)(2, 8, 14, 20, 26)(3, 9, 15, 21, 27)(4, 10, 16, 22, 28)(5, 11, 17, 23, 29)(6, 12, 18, 24, 30)(31, 37, 43, 49, 55)(32, 38, 44, 50, 56)(33, 39, 45, 51, 57)(34, 40, 46, 52, 58)(35, 41, 47, 53, 59)(36, 42, 48, 54, 60) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 35)(8, 33)(9, 36)(10, 32)(11, 34)(12, 31)(13, 21)(14, 23)(15, 22)(16, 19)(17, 24)(18, 20)(25, 26)(27, 29)(28, 30)(37, 38)(39, 41)(40, 42)(43, 52)(44, 54)(45, 49)(46, 51)(47, 50)(48, 53) MAP : A2.98 NOTES : type II, reflexible, isomorphic to A2.97. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.5^3, u.6^3, u.4 * u.5^-1 * u.1 * u.3^-1, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.5^3, x.6^3, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 60 R = (1, 7, 13, 19, 25)(2, 8, 14, 20, 26)(3, 9, 15, 21, 27)(4, 10, 16, 22, 28)(5, 11, 17, 23, 29)(6, 12, 18, 24, 30)(31, 37, 43, 49, 55)(32, 38, 44, 50, 56)(33, 39, 45, 51, 57)(34, 40, 46, 52, 58)(35, 41, 47, 53, 59)(36, 42, 48, 54, 60) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 36)(8, 34)(9, 32)(10, 35)(11, 31)(12, 33)(13, 22)(14, 24)(15, 19)(16, 21)(17, 20)(18, 23)(25, 26)(27, 29)(28, 30)(37, 38)(39, 41)(40, 42)(43, 51)(44, 53)(45, 52)(46, 49)(47, 54)(48, 50) MAP : A2.99 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.1 * x.2^-2 * x.3 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 27)(2, 41)(3, 28)(4, 25)(5, 42)(6, 43)(7, 33)(8, 26)(9, 38)(10, 39)(11, 45)(12, 34)(13, 44)(14, 31)(15, 36)(16, 37)(17, 32)(18, 46)(19, 48)(20, 40)(21, 47)(22, 29)(23, 35)(24, 30)(49, 74)(50, 77)(51, 78)(52, 85)(53, 83)(54, 90)(55, 93)(56, 91)(57, 76)(58, 80)(59, 73)(60, 75)(61, 94)(62, 96)(63, 86)(64, 89)(65, 79)(66, 84)(67, 95)(68, 87)(69, 88)(70, 81)(71, 82)(72, 92)(97, 143)(98, 124)(99, 135)(100, 127)(101, 128)(102, 121)(103, 122)(104, 132)(105, 138)(106, 141)(107, 142)(108, 125)(109, 123)(110, 130)(111, 133)(112, 131)(113, 140)(114, 144)(115, 137)(116, 139)(117, 134)(118, 136)(119, 126)(120, 129) MAP : A2.100 NOTES : type I, reflexible, isomorphic to A2.99. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.1 * x.2^-2 * x.3 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 28)(2, 32)(3, 25)(4, 27)(5, 46)(6, 48)(7, 38)(8, 41)(9, 31)(10, 36)(11, 47)(12, 39)(13, 40)(14, 33)(15, 34)(16, 44)(17, 26)(18, 29)(19, 30)(20, 37)(21, 35)(22, 42)(23, 45)(24, 43)(49, 87)(50, 92)(51, 79)(52, 95)(53, 96)(54, 89)(55, 90)(56, 76)(57, 82)(58, 85)(59, 86)(60, 93)(61, 91)(62, 74)(63, 77)(64, 75)(65, 84)(66, 88)(67, 81)(68, 83)(69, 78)(70, 80)(71, 94)(72, 73)(97, 126)(98, 127)(99, 133)(100, 122)(101, 132)(102, 143)(103, 124)(104, 125)(105, 144)(106, 134)(107, 136)(108, 128)(109, 135)(110, 141)(111, 123)(112, 142)(113, 139)(114, 129)(115, 140)(116, 137)(117, 130)(118, 131)(119, 121)(120, 138) MAP : A2.101 NOTES : type I, reflexible, isomorphic to A2.99. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.1^-1 * x.2 * x.1^-1 * x.3 * x.1^-1, x.2 * x.3 * x.1^-1 * x.3^-1 * x.2^-1 * x.1^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 26)(2, 29)(3, 30)(4, 37)(5, 35)(6, 42)(7, 45)(8, 43)(9, 28)(10, 32)(11, 25)(12, 27)(13, 46)(14, 48)(15, 38)(16, 41)(17, 31)(18, 36)(19, 47)(20, 39)(21, 40)(22, 33)(23, 34)(24, 44)(49, 75)(50, 89)(51, 76)(52, 73)(53, 90)(54, 91)(55, 81)(56, 74)(57, 86)(58, 87)(59, 93)(60, 82)(61, 92)(62, 79)(63, 84)(64, 85)(65, 80)(66, 94)(67, 96)(68, 88)(69, 95)(70, 77)(71, 83)(72, 78)(97, 129)(98, 130)(99, 131)(100, 132)(101, 133)(102, 134)(103, 135)(104, 136)(105, 137)(106, 138)(107, 139)(108, 140)(109, 141)(110, 142)(111, 143)(112, 144)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128) MAP : A2.102 NOTES : type I, reflexible, isomorphic to A2.99. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.1^-1 * x.2 * x.1^-1 * x.3 * x.1^-1, x.2 * x.3 * x.1^-1 * x.3^-1 * x.2^-1 * x.1^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 26)(2, 29)(3, 30)(4, 37)(5, 35)(6, 42)(7, 45)(8, 43)(9, 28)(10, 32)(11, 25)(12, 27)(13, 46)(14, 48)(15, 38)(16, 41)(17, 31)(18, 36)(19, 47)(20, 39)(21, 40)(22, 33)(23, 34)(24, 44)(49, 95)(50, 76)(51, 87)(52, 79)(53, 80)(54, 73)(55, 74)(56, 84)(57, 90)(58, 93)(59, 94)(60, 77)(61, 75)(62, 82)(63, 85)(64, 83)(65, 92)(66, 96)(67, 89)(68, 91)(69, 86)(70, 88)(71, 78)(72, 81)(97, 123)(98, 137)(99, 124)(100, 121)(101, 138)(102, 139)(103, 129)(104, 122)(105, 134)(106, 135)(107, 141)(108, 130)(109, 140)(110, 127)(111, 132)(112, 133)(113, 128)(114, 142)(115, 144)(116, 136)(117, 143)(118, 125)(119, 131)(120, 126) MAP : A2.103 NOTES : type I, reflexible, isomorphic to A2.99. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.1 * x.3^-1 * x.2 * x.3^-2, x.1 * x.2 * x.1^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 27)(2, 41)(3, 28)(4, 25)(5, 42)(6, 43)(7, 33)(8, 26)(9, 38)(10, 39)(11, 45)(12, 34)(13, 44)(14, 31)(15, 36)(16, 37)(17, 32)(18, 46)(19, 48)(20, 40)(21, 47)(22, 29)(23, 35)(24, 30)(49, 95)(50, 76)(51, 87)(52, 79)(53, 80)(54, 73)(55, 74)(56, 84)(57, 90)(58, 93)(59, 94)(60, 77)(61, 75)(62, 82)(63, 85)(64, 83)(65, 92)(66, 96)(67, 89)(68, 91)(69, 86)(70, 88)(71, 78)(72, 81)(97, 144)(98, 134)(99, 136)(100, 128)(101, 135)(102, 141)(103, 123)(104, 142)(105, 139)(106, 129)(107, 140)(108, 137)(109, 130)(110, 131)(111, 121)(112, 138)(113, 126)(114, 127)(115, 133)(116, 122)(117, 132)(118, 143)(119, 124)(120, 125) MAP : A2.104 NOTES : type I, reflexible, isomorphic to A2.99. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.1 * x.3^-1 * x.2 * x.3^-2, x.1 * x.2 * x.1^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 28)(2, 32)(3, 25)(4, 27)(5, 46)(6, 48)(7, 38)(8, 41)(9, 31)(10, 36)(11, 47)(12, 39)(13, 40)(14, 33)(15, 34)(16, 44)(17, 26)(18, 29)(19, 30)(20, 37)(21, 35)(22, 42)(23, 45)(24, 43)(49, 78)(50, 79)(51, 85)(52, 74)(53, 84)(54, 95)(55, 76)(56, 77)(57, 96)(58, 86)(59, 88)(60, 80)(61, 87)(62, 93)(63, 75)(64, 94)(65, 91)(66, 81)(67, 92)(68, 89)(69, 82)(70, 83)(71, 73)(72, 90)(97, 131)(98, 121)(99, 132)(100, 129)(101, 122)(102, 123)(103, 137)(104, 130)(105, 142)(106, 143)(107, 125)(108, 138)(109, 124)(110, 135)(111, 140)(112, 141)(113, 136)(114, 126)(115, 128)(116, 144)(117, 127)(118, 133)(119, 139)(120, 134) MAP : A2.105 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, x.3 * x.4^-2, x.1 * x.3 * x.4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 72 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72) L = (1, 2)(3, 11)(4, 6)(5, 9)(7, 8)(10, 12)(13, 29)(14, 33)(15, 32)(16, 25)(17, 28)(18, 26)(19, 34)(20, 36)(21, 30)(22, 35)(23, 31)(24, 27)(37, 66)(38, 64)(39, 70)(40, 69)(41, 62)(42, 65)(43, 63)(44, 71)(45, 61)(46, 68)(47, 72)(48, 67)(49, 51)(50, 59)(52, 56)(53, 60)(54, 55)(57, 58) MAP : A2.106 NOTES : type I, chiral, isomorphic to A2.105. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, x.3 * x.4^-2, x.1 * x.3 * x.4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 72 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72) L = (1, 2)(3, 11)(4, 6)(5, 9)(7, 8)(10, 12)(13, 29)(14, 33)(15, 32)(16, 25)(17, 28)(18, 26)(19, 34)(20, 36)(21, 30)(22, 35)(23, 31)(24, 27)(37, 66)(38, 64)(39, 70)(40, 69)(41, 62)(42, 65)(43, 63)(44, 71)(45, 61)(46, 68)(47, 72)(48, 67)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60) MAP : A2.107 NOTES : type I, chiral, isomorphic to A2.105. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3 * x.1 * x.4^-1, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 72 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72) L = (1, 54)(2, 52)(3, 58)(4, 57)(5, 50)(6, 53)(7, 51)(8, 59)(9, 49)(10, 56)(11, 60)(12, 55)(13, 28)(14, 30)(15, 36)(16, 29)(17, 25)(18, 33)(19, 35)(20, 27)(21, 26)(22, 31)(23, 34)(24, 32)(37, 38)(39, 47)(40, 42)(41, 45)(43, 44)(46, 48)(61, 63)(62, 71)(64, 68)(65, 72)(66, 67)(69, 70) MAP : A2.108 NOTES : type I, chiral, isomorphic to A2.105. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3 * x.1 * x.4^-1, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 72 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72) L = (1, 54)(2, 52)(3, 58)(4, 57)(5, 50)(6, 53)(7, 51)(8, 59)(9, 49)(10, 56)(11, 60)(12, 55)(13, 28)(14, 30)(15, 36)(16, 29)(17, 25)(18, 33)(19, 35)(20, 27)(21, 26)(22, 31)(23, 34)(24, 32)(37, 38)(39, 47)(40, 42)(41, 45)(43, 44)(46, 48)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72) MAP : A2.109 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^3, u.6^3, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.2 * x.1, x.6 * x.3^-1, x.3 * x.7 * x.4^-1, x.6^3, x.3^3, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 72 R = (1, 7, 13, 19, 25, 31)(2, 8, 14, 20, 26, 32)(3, 9, 15, 21, 27, 33)(4, 10, 16, 22, 28, 34)(5, 11, 17, 23, 29, 35)(6, 12, 18, 24, 30, 36)(37, 43, 49, 55, 61, 67)(38, 44, 50, 56, 62, 68)(39, 45, 51, 57, 63, 69)(40, 46, 52, 58, 64, 70)(41, 47, 53, 59, 65, 71)(42, 48, 54, 60, 66, 72) L = (1, 9)(2, 11)(3, 10)(4, 7)(5, 12)(6, 8)(13, 30)(14, 28)(15, 26)(16, 29)(17, 25)(18, 27)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(31, 32)(33, 35)(34, 36)(37, 69)(38, 71)(39, 70)(40, 67)(41, 72)(42, 68)(43, 44)(45, 47)(46, 48)(49, 65)(50, 63)(51, 66)(52, 62)(53, 64)(54, 61) MAP : A2.110 NOTES : type II, reflexible, isomorphic to A2.109. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^3, u.6^3, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.2 * x.1, x.6 * x.3^-1, x.3 * x.7 * x.4^-1, x.6^3, x.3^3, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 72 R = (1, 7, 13, 19, 25, 31)(2, 8, 14, 20, 26, 32)(3, 9, 15, 21, 27, 33)(4, 10, 16, 22, 28, 34)(5, 11, 17, 23, 29, 35)(6, 12, 18, 24, 30, 36)(37, 43, 49, 55, 61, 67)(38, 44, 50, 56, 62, 68)(39, 45, 51, 57, 63, 69)(40, 46, 52, 58, 64, 70)(41, 47, 53, 59, 65, 71)(42, 48, 54, 60, 66, 72) L = (1, 10)(2, 12)(3, 7)(4, 9)(5, 8)(6, 11)(13, 29)(14, 27)(15, 30)(16, 26)(17, 28)(18, 25)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(31, 32)(33, 35)(34, 36)(37, 70)(38, 72)(39, 67)(40, 69)(41, 68)(42, 71)(43, 44)(45, 47)(46, 48)(49, 66)(50, 64)(51, 62)(52, 65)(53, 61)(54, 63) MAP : A2.111 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4 * x.5^-2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, (x.3 * x.1)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 16)(2, 18)(3, 24)(4, 17)(5, 13)(6, 21)(7, 23)(8, 15)(9, 14)(10, 19)(11, 22)(12, 20)(25, 69)(26, 65)(27, 67)(28, 62)(29, 66)(30, 61)(31, 72)(32, 70)(33, 64)(34, 63)(35, 68)(36, 71)(37, 39)(38, 47)(40, 44)(41, 48)(42, 43)(45, 46)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(73, 74)(75, 83)(76, 78)(77, 81)(79, 80)(82, 84) MAP : A2.112 NOTES : type I, chiral, isomorphic to A2.111. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^-1 * x.4^-2, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, (x.3 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 3)(2, 11)(4, 8)(5, 12)(6, 7)(9, 10)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 52)(38, 54)(39, 60)(40, 53)(41, 49)(42, 57)(43, 59)(44, 51)(45, 50)(46, 55)(47, 58)(48, 56)(61, 62)(63, 71)(64, 66)(65, 69)(67, 68)(70, 72) MAP : A2.113 NOTES : type I, chiral, isomorphic to A2.111. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^-1 * x.4^-2, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, (x.3 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 24)(14, 22)(15, 16)(17, 20)(18, 23)(19, 21)(25, 78)(26, 76)(27, 82)(28, 81)(29, 74)(30, 77)(31, 75)(32, 83)(33, 73)(34, 80)(35, 84)(36, 79)(37, 52)(38, 54)(39, 60)(40, 53)(41, 49)(42, 57)(43, 59)(44, 51)(45, 50)(46, 55)(47, 58)(48, 56)(61, 62)(63, 71)(64, 66)(65, 69)(67, 68)(70, 72) MAP : A2.114 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^3, u.7^3, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.2 * x.1, x.7 * x.3^-1, x.4 * x.5^-1 * x.6, x.5 * x.6^-1 * x.8, x.3^3, x.3^-1 * x.4^-1 * x.1, x.7 * x.2 * x.8^-1, x.7^3, x.3 * x.6 * x.4^-1, x.1 * x.3 * x.6^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 7, 13, 19, 25, 31, 37)(2, 8, 14, 20, 26, 32, 38)(3, 9, 15, 21, 27, 33, 39)(4, 10, 16, 22, 28, 34, 40)(5, 11, 17, 23, 29, 35, 41)(6, 12, 18, 24, 30, 36, 42)(43, 49, 55, 61, 67, 73, 79)(44, 50, 56, 62, 68, 74, 80)(45, 51, 57, 63, 69, 75, 81)(46, 52, 58, 64, 70, 76, 82)(47, 53, 59, 65, 71, 77, 83)(48, 54, 60, 66, 72, 78, 84) L = (1, 9)(2, 11)(3, 10)(4, 7)(5, 12)(6, 8)(13, 36)(14, 34)(15, 32)(16, 35)(17, 31)(18, 33)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 71)(26, 69)(27, 72)(28, 68)(29, 70)(30, 67)(37, 38)(39, 41)(40, 42)(43, 81)(44, 83)(45, 82)(46, 79)(47, 84)(48, 80)(49, 50)(51, 53)(52, 54)(55, 77)(56, 75)(57, 78)(58, 74)(59, 76)(60, 73) MAP : A2.115 NOTES : type II, reflexible, isomorphic to A2.114. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^3, u.7^3, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.2 * x.1, x.7 * x.3^-1, x.4 * x.5^-1 * x.6, x.5 * x.6^-1 * x.8, x.3^3, x.3^-1 * x.4^-1 * x.1, x.7 * x.2 * x.8^-1, x.7^3, x.3 * x.6 * x.4^-1, x.1 * x.3 * x.6^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 7, 13, 19, 25, 31, 37)(2, 8, 14, 20, 26, 32, 38)(3, 9, 15, 21, 27, 33, 39)(4, 10, 16, 22, 28, 34, 40)(5, 11, 17, 23, 29, 35, 41)(6, 12, 18, 24, 30, 36, 42)(43, 49, 55, 61, 67, 73, 79)(44, 50, 56, 62, 68, 74, 80)(45, 51, 57, 63, 69, 75, 81)(46, 52, 58, 64, 70, 76, 82)(47, 53, 59, 65, 71, 77, 83)(48, 54, 60, 66, 72, 78, 84) L = (1, 10)(2, 12)(3, 7)(4, 9)(5, 8)(6, 11)(13, 35)(14, 33)(15, 36)(16, 32)(17, 34)(18, 31)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 72)(26, 70)(27, 68)(28, 71)(29, 67)(30, 69)(37, 38)(39, 41)(40, 42)(43, 82)(44, 84)(45, 79)(46, 81)(47, 80)(48, 83)(49, 50)(51, 53)(52, 54)(55, 78)(56, 76)(57, 74)(58, 77)(59, 73)(60, 75) MAP : A2.116 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.6^3, u.8^3, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6 * x.4^-1, x.6^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.6^3, x.5 * x.6^-1 * x.7^-1, x.8^3, x.4 * x.2 * x.5^-1, x.3 * x.4^-1 * x.8^-1 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 7, 13, 19, 25, 31, 37)(2, 8, 14, 20, 26, 32, 38)(3, 9, 15, 21, 27, 33, 39)(4, 10, 16, 22, 28, 34, 40)(5, 11, 17, 23, 29, 35, 41)(6, 12, 18, 24, 30, 36, 42)(43, 49, 55, 61, 67, 73, 79)(44, 50, 56, 62, 68, 74, 80)(45, 51, 57, 63, 69, 75, 81)(46, 52, 58, 64, 70, 76, 82)(47, 53, 59, 65, 71, 77, 83)(48, 54, 60, 66, 72, 78, 84) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 51)(8, 53)(9, 52)(10, 49)(11, 54)(12, 50)(13, 14)(15, 17)(16, 18)(19, 47)(20, 45)(21, 48)(22, 44)(23, 46)(24, 43)(25, 33)(26, 35)(27, 34)(28, 31)(29, 36)(30, 32)(37, 80)(38, 79)(39, 83)(40, 84)(41, 81)(42, 82)(55, 64)(56, 66)(57, 61)(58, 63)(59, 62)(60, 65)(73, 74)(75, 77)(76, 78) MAP : A2.117 NOTES : type II, reflexible, isomorphic to A2.116. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.6^3, u.8^3, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1 > CTG (small) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6 * x.4^-1, x.6^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.6^3, x.5 * x.6^-1 * x.7^-1, x.8^3, x.4 * x.2 * x.5^-1, x.3 * x.4^-1 * x.8^-1 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 84 R = (1, 7, 13, 19, 25, 31, 37)(2, 8, 14, 20, 26, 32, 38)(3, 9, 15, 21, 27, 33, 39)(4, 10, 16, 22, 28, 34, 40)(5, 11, 17, 23, 29, 35, 41)(6, 12, 18, 24, 30, 36, 42)(43, 49, 55, 61, 67, 73, 79)(44, 50, 56, 62, 68, 74, 80)(45, 51, 57, 63, 69, 75, 81)(46, 52, 58, 64, 70, 76, 82)(47, 53, 59, 65, 71, 77, 83)(48, 54, 60, 66, 72, 78, 84) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 52)(8, 54)(9, 49)(10, 51)(11, 50)(12, 53)(13, 14)(15, 17)(16, 18)(19, 48)(20, 46)(21, 44)(22, 47)(23, 43)(24, 45)(25, 34)(26, 36)(27, 31)(28, 33)(29, 32)(30, 35)(37, 80)(38, 79)(39, 83)(40, 84)(41, 81)(42, 82)(55, 63)(56, 65)(57, 64)(58, 61)(59, 66)(60, 62)(73, 74)(75, 77)(76, 78)