metabelian, supersoluble, monomial
Aliases: C62.160D6, (C6×C12)⋊13S3, (C3×C12).201D6, C33⋊29(C4○D4), C33⋊15D4⋊7C2, C33⋊8Q8⋊11C2, C33⋊12D4⋊11C2, C3⋊5(C12.59D6), C32⋊27(C4○D12), (C3×C62).69C22, (C32×C6).98C23, C33⋊5C4.20C22, (C32×C12).101C22, (C3×C6×C12)⋊6C2, (C2×C12)⋊4(C3⋊S3), C12.78(C2×C3⋊S3), (C4×C33⋊C2)⋊9C2, C6.42(C22×C3⋊S3), (C2×C4)⋊3(C33⋊C2), C4.16(C2×C33⋊C2), (C3×C6).187(C22×S3), C22.2(C2×C33⋊C2), C2.5(C22×C33⋊C2), (C2×C33⋊C2).18C22, (C2×C6).49(C2×C3⋊S3), SmallGroup(432,723)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C62.160D6
G = < a,b,c,d | a6=b6=1, c6=d2=b3, ab=ba, ac=ca, dad-1=a-1b3, bc=cb, dbd-1=b-1, dcd-1=c5 >
Subgroups: 2984 in 560 conjugacy classes, 179 normal (15 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C2×C4, C2×C4, D4, Q8, C32, Dic3, C12, D6, C2×C6, C4○D4, C3⋊S3, C3×C6, C3×C6, Dic6, C4×S3, D12, C3⋊D4, C2×C12, C33, C3⋊Dic3, C3×C12, C2×C3⋊S3, C62, C4○D12, C33⋊C2, C32×C6, C32×C6, C32⋊4Q8, C4×C3⋊S3, C12⋊S3, C32⋊7D4, C6×C12, C33⋊5C4, C32×C12, C2×C33⋊C2, C3×C62, C12.59D6, C33⋊8Q8, C4×C33⋊C2, C33⋊12D4, C33⋊15D4, C3×C6×C12, C62.160D6
Quotients: C1, C2, C22, S3, C23, D6, C4○D4, C3⋊S3, C22×S3, C2×C3⋊S3, C4○D12, C33⋊C2, C22×C3⋊S3, C2×C33⋊C2, C12.59D6, C22×C33⋊C2, C62.160D6
►On 216 points
Generators in S216
(1 67 98)(2 68 99)(3 69 100)(4 70 101)(5 71 102)(6 72 103)(7 61 104)(8 62 105)(9 63 106)(10 64 107)(11 65 108)(12 66 97)(13 210 194 19 216 200)(14 211 195 20 205 201)(15 212 196 21 206 202)(16 213 197 22 207 203)(17 214 198 23 208 204)(18 215 199 24 209 193)(25 90 148 31 96 154)(26 91 149 32 85 155)(27 92 150 33 86 156)(28 93 151 34 87 145)(29 94 152 35 88 146)(30 95 153 36 89 147)(37 191 140 43 185 134)(38 192 141 44 186 135)(39 181 142 45 187 136)(40 182 143 46 188 137)(41 183 144 47 189 138)(42 184 133 48 190 139)(49 117 160)(50 118 161)(51 119 162)(52 120 163)(53 109 164)(54 110 165)(55 111 166)(56 112 167)(57 113 168)(58 114 157)(59 115 158)(60 116 159)(73 169 132)(74 170 121)(75 171 122)(76 172 123)(77 173 124)(78 174 125)(79 175 126)(80 176 127)(81 177 128)(82 178 129)(83 179 130)(84 180 131)
(1 121 109 7 127 115)(2 122 110 8 128 116)(3 123 111 9 129 117)(4 124 112 10 130 118)(5 125 113 11 131 119)(6 126 114 12 132 120)(13 42 146 19 48 152)(14 43 147 20 37 153)(15 44 148 21 38 154)(16 45 149 22 39 155)(17 46 150 23 40 156)(18 47 151 24 41 145)(25 212 186 31 206 192)(26 213 187 32 207 181)(27 214 188 33 208 182)(28 215 189 34 209 183)(29 216 190 35 210 184)(30 205 191 36 211 185)(49 100 172 55 106 178)(50 101 173 56 107 179)(51 102 174 57 108 180)(52 103 175 58 97 169)(53 104 176 59 98 170)(54 105 177 60 99 171)(61 80 158 67 74 164)(62 81 159 68 75 165)(63 82 160 69 76 166)(64 83 161 70 77 167)(65 84 162 71 78 168)(66 73 163 72 79 157)(85 203 142 91 197 136)(86 204 143 92 198 137)(87 193 144 93 199 138)(88 194 133 94 200 139)(89 195 134 95 201 140)(90 196 135 96 202 141)
(1 2 3 4 5 6 7 8 9 10 11 12)(13 14 15 16 17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32 33 34 35 36)(37 38 39 40 41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104 105 106 107 108)(109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132)(133 134 135 136 137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152 153 154 155 156)(157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180)(181 182 183 184 185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200 201 202 203 204)(205 206 207 208 209 210 211 212 213 214 215 216)
(1 16 7 22)(2 21 8 15)(3 14 9 20)(4 19 10 13)(5 24 11 18)(6 17 12 23)(25 177 31 171)(26 170 32 176)(27 175 33 169)(28 180 34 174)(29 173 35 179)(30 178 36 172)(37 117 43 111)(38 110 44 116)(39 115 45 109)(40 120 46 114)(41 113 47 119)(42 118 48 112)(49 191 55 185)(50 184 56 190)(51 189 57 183)(52 182 58 188)(53 187 59 181)(54 192 60 186)(61 203 67 197)(62 196 68 202)(63 201 69 195)(64 194 70 200)(65 199 71 193)(66 204 72 198)(73 86 79 92)(74 91 80 85)(75 96 81 90)(76 89 82 95)(77 94 83 88)(78 87 84 93)(97 214 103 208)(98 207 104 213)(99 212 105 206)(100 205 106 211)(101 210 107 216)(102 215 108 209)(121 155 127 149)(122 148 128 154)(123 153 129 147)(124 146 130 152)(125 151 131 145)(126 156 132 150)(133 161 139 167)(134 166 140 160)(135 159 141 165)(136 164 142 158)(137 157 143 163)(138 162 144 168)
G:=sub<Sym(216)| (1,67,98)(2,68,99)(3,69,100)(4,70,101)(5,71,102)(6,72,103)(7,61,104)(8,62,105)(9,63,106)(10,64,107)(11,65,108)(12,66,97)(13,210,194,19,216,200)(14,211,195,20,205,201)(15,212,196,21,206,202)(16,213,197,22,207,203)(17,214,198,23,208,204)(18,215,199,24,209,193)(25,90,148,31,96,154)(26,91,149,32,85,155)(27,92,150,33,86,156)(28,93,151,34,87,145)(29,94,152,35,88,146)(30,95,153,36,89,147)(37,191,140,43,185,134)(38,192,141,44,186,135)(39,181,142,45,187,136)(40,182,143,46,188,137)(41,183,144,47,189,138)(42,184,133,48,190,139)(49,117,160)(50,118,161)(51,119,162)(52,120,163)(53,109,164)(54,110,165)(55,111,166)(56,112,167)(57,113,168)(58,114,157)(59,115,158)(60,116,159)(73,169,132)(74,170,121)(75,171,122)(76,172,123)(77,173,124)(78,174,125)(79,175,126)(80,176,127)(81,177,128)(82,178,129)(83,179,130)(84,180,131), (1,121,109,7,127,115)(2,122,110,8,128,116)(3,123,111,9,129,117)(4,124,112,10,130,118)(5,125,113,11,131,119)(6,126,114,12,132,120)(13,42,146,19,48,152)(14,43,147,20,37,153)(15,44,148,21,38,154)(16,45,149,22,39,155)(17,46,150,23,40,156)(18,47,151,24,41,145)(25,212,186,31,206,192)(26,213,187,32,207,181)(27,214,188,33,208,182)(28,215,189,34,209,183)(29,216,190,35,210,184)(30,205,191,36,211,185)(49,100,172,55,106,178)(50,101,173,56,107,179)(51,102,174,57,108,180)(52,103,175,58,97,169)(53,104,176,59,98,170)(54,105,177,60,99,171)(61,80,158,67,74,164)(62,81,159,68,75,165)(63,82,160,69,76,166)(64,83,161,70,77,167)(65,84,162,71,78,168)(66,73,163,72,79,157)(85,203,142,91,197,136)(86,204,143,92,198,137)(87,193,144,93,199,138)(88,194,133,94,200,139)(89,195,134,95,201,140)(90,196,135,96,202,141), (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108)(109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132)(133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204)(205,206,207,208,209,210,211,212,213,214,215,216), (1,16,7,22)(2,21,8,15)(3,14,9,20)(4,19,10,13)(5,24,11,18)(6,17,12,23)(25,177,31,171)(26,170,32,176)(27,175,33,169)(28,180,34,174)(29,173,35,179)(30,178,36,172)(37,117,43,111)(38,110,44,116)(39,115,45,109)(40,120,46,114)(41,113,47,119)(42,118,48,112)(49,191,55,185)(50,184,56,190)(51,189,57,183)(52,182,58,188)(53,187,59,181)(54,192,60,186)(61,203,67,197)(62,196,68,202)(63,201,69,195)(64,194,70,200)(65,199,71,193)(66,204,72,198)(73,86,79,92)(74,91,80,85)(75,96,81,90)(76,89,82,95)(77,94,83,88)(78,87,84,93)(97,214,103,208)(98,207,104,213)(99,212,105,206)(100,205,106,211)(101,210,107,216)(102,215,108,209)(121,155,127,149)(122,148,128,154)(123,153,129,147)(124,146,130,152)(125,151,131,145)(126,156,132,150)(133,161,139,167)(134,166,140,160)(135,159,141,165)(136,164,142,158)(137,157,143,163)(138,162,144,168)>;
G:=Group( (1,67,98)(2,68,99)(3,69,100)(4,70,101)(5,71,102)(6,72,103)(7,61,104)(8,62,105)(9,63,106)(10,64,107)(11,65,108)(12,66,97)(13,210,194,19,216,200)(14,211,195,20,205,201)(15,212,196,21,206,202)(16,213,197,22,207,203)(17,214,198,23,208,204)(18,215,199,24,209,193)(25,90,148,31,96,154)(26,91,149,32,85,155)(27,92,150,33,86,156)(28,93,151,34,87,145)(29,94,152,35,88,146)(30,95,153,36,89,147)(37,191,140,43,185,134)(38,192,141,44,186,135)(39,181,142,45,187,136)(40,182,143,46,188,137)(41,183,144,47,189,138)(42,184,133,48,190,139)(49,117,160)(50,118,161)(51,119,162)(52,120,163)(53,109,164)(54,110,165)(55,111,166)(56,112,167)(57,113,168)(58,114,157)(59,115,158)(60,116,159)(73,169,132)(74,170,121)(75,171,122)(76,172,123)(77,173,124)(78,174,125)(79,175,126)(80,176,127)(81,177,128)(82,178,129)(83,179,130)(84,180,131), (1,121,109,7,127,115)(2,122,110,8,128,116)(3,123,111,9,129,117)(4,124,112,10,130,118)(5,125,113,11,131,119)(6,126,114,12,132,120)(13,42,146,19,48,152)(14,43,147,20,37,153)(15,44,148,21,38,154)(16,45,149,22,39,155)(17,46,150,23,40,156)(18,47,151,24,41,145)(25,212,186,31,206,192)(26,213,187,32,207,181)(27,214,188,33,208,182)(28,215,189,34,209,183)(29,216,190,35,210,184)(30,205,191,36,211,185)(49,100,172,55,106,178)(50,101,173,56,107,179)(51,102,174,57,108,180)(52,103,175,58,97,169)(53,104,176,59,98,170)(54,105,177,60,99,171)(61,80,158,67,74,164)(62,81,159,68,75,165)(63,82,160,69,76,166)(64,83,161,70,77,167)(65,84,162,71,78,168)(66,73,163,72,79,157)(85,203,142,91,197,136)(86,204,143,92,198,137)(87,193,144,93,199,138)(88,194,133,94,200,139)(89,195,134,95,201,140)(90,196,135,96,202,141), (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108)(109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132)(133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204)(205,206,207,208,209,210,211,212,213,214,215,216), (1,16,7,22)(2,21,8,15)(3,14,9,20)(4,19,10,13)(5,24,11,18)(6,17,12,23)(25,177,31,171)(26,170,32,176)(27,175,33,169)(28,180,34,174)(29,173,35,179)(30,178,36,172)(37,117,43,111)(38,110,44,116)(39,115,45,109)(40,120,46,114)(41,113,47,119)(42,118,48,112)(49,191,55,185)(50,184,56,190)(51,189,57,183)(52,182,58,188)(53,187,59,181)(54,192,60,186)(61,203,67,197)(62,196,68,202)(63,201,69,195)(64,194,70,200)(65,199,71,193)(66,204,72,198)(73,86,79,92)(74,91,80,85)(75,96,81,90)(76,89,82,95)(77,94,83,88)(78,87,84,93)(97,214,103,208)(98,207,104,213)(99,212,105,206)(100,205,106,211)(101,210,107,216)(102,215,108,209)(121,155,127,149)(122,148,128,154)(123,153,129,147)(124,146,130,152)(125,151,131,145)(126,156,132,150)(133,161,139,167)(134,166,140,160)(135,159,141,165)(136,164,142,158)(137,157,143,163)(138,162,144,168) );
G=PermutationGroup([[(1,67,98),(2,68,99),(3,69,100),(4,70,101),(5,71,102),(6,72,103),(7,61,104),(8,62,105),(9,63,106),(10,64,107),(11,65,108),(12,66,97),(13,210,194,19,216,200),(14,211,195,20,205,201),(15,212,196,21,206,202),(16,213,197,22,207,203),(17,214,198,23,208,204),(18,215,199,24,209,193),(25,90,148,31,96,154),(26,91,149,32,85,155),(27,92,150,33,86,156),(28,93,151,34,87,145),(29,94,152,35,88,146),(30,95,153,36,89,147),(37,191,140,43,185,134),(38,192,141,44,186,135),(39,181,142,45,187,136),(40,182,143,46,188,137),(41,183,144,47,189,138),(42,184,133,48,190,139),(49,117,160),(50,118,161),(51,119,162),(52,120,163),(53,109,164),(54,110,165),(55,111,166),(56,112,167),(57,113,168),(58,114,157),(59,115,158),(60,116,159),(73,169,132),(74,170,121),(75,171,122),(76,172,123),(77,173,124),(78,174,125),(79,175,126),(80,176,127),(81,177,128),(82,178,129),(83,179,130),(84,180,131)], [(1,121,109,7,127,115),(2,122,110,8,128,116),(3,123,111,9,129,117),(4,124,112,10,130,118),(5,125,113,11,131,119),(6,126,114,12,132,120),(13,42,146,19,48,152),(14,43,147,20,37,153),(15,44,148,21,38,154),(16,45,149,22,39,155),(17,46,150,23,40,156),(18,47,151,24,41,145),(25,212,186,31,206,192),(26,213,187,32,207,181),(27,214,188,33,208,182),(28,215,189,34,209,183),(29,216,190,35,210,184),(30,205,191,36,211,185),(49,100,172,55,106,178),(50,101,173,56,107,179),(51,102,174,57,108,180),(52,103,175,58,97,169),(53,104,176,59,98,170),(54,105,177,60,99,171),(61,80,158,67,74,164),(62,81,159,68,75,165),(63,82,160,69,76,166),(64,83,161,70,77,167),(65,84,162,71,78,168),(66,73,163,72,79,157),(85,203,142,91,197,136),(86,204,143,92,198,137),(87,193,144,93,199,138),(88,194,133,94,200,139),(89,195,134,95,201,140),(90,196,135,96,202,141)], [(1,2,3,4,5,6,7,8,9,10,11,12),(13,14,15,16,17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32,33,34,35,36),(37,38,39,40,41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104,105,106,107,108),(109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132),(133,134,135,136,137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152,153,154,155,156),(157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180),(181,182,183,184,185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200,201,202,203,204),(205,206,207,208,209,210,211,212,213,214,215,216)], [(1,16,7,22),(2,21,8,15),(3,14,9,20),(4,19,10,13),(5,24,11,18),(6,17,12,23),(25,177,31,171),(26,170,32,176),(27,175,33,169),(28,180,34,174),(29,173,35,179),(30,178,36,172),(37,117,43,111),(38,110,44,116),(39,115,45,109),(40,120,46,114),(41,113,47,119),(42,118,48,112),(49,191,55,185),(50,184,56,190),(51,189,57,183),(52,182,58,188),(53,187,59,181),(54,192,60,186),(61,203,67,197),(62,196,68,202),(63,201,69,195),(64,194,70,200),(65,199,71,193),(66,204,72,198),(73,86,79,92),(74,91,80,85),(75,96,81,90),(76,89,82,95),(77,94,83,88),(78,87,84,93),(97,214,103,208),(98,207,104,213),(99,212,105,206),(100,205,106,211),(101,210,107,216),(102,215,108,209),(121,155,127,149),(122,148,128,154),(123,153,129,147),(124,146,130,152),(125,151,131,145),(126,156,132,150),(133,161,139,167),(134,166,140,160),(135,159,141,165),(136,164,142,158),(137,157,143,163),(138,162,144,168)]])
114 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3A | ··· | 3M | 4A | 4B | 4C | 4D | 4E | 6A | ··· | 6AM | 12A | ··· | 12AZ |
| order | 1 | 2 | 2 | 2 | 2 | 3 | ··· | 3 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | 2 | 54 | 54 | 2 | ··· | 2 | 1 | 1 | 2 | 54 | 54 | 2 | ··· | 2 | 2 | ··· | 2 |
114 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D6 | D6 | C4○D4 | C4○D12 |
| kernel | C62.160D6 | C33⋊8Q8 | C4×C33⋊C2 | C33⋊12D4 | C33⋊15D4 | C3×C6×C12 | C6×C12 | C3×C12 | C62 | C33 | C32 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 13 | 26 | 13 | 2 | 52 |
Matrix representation of C62.160D6 ►in GL6(𝔽13)
| 3 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 10 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 |
| 6 | 0 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 |
| 0 | 2 | 0 | 0 | 0 | 0 |
| 6 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 |
| 0 | 0 | 0 | 0 | 5 | 0 |
G:=sub<GL(6,GF(13))| [3,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,12],[10,0,0,0,0,0,0,4,0,0,0,0,0,0,10,0,0,0,0,0,0,4,0,0,0,0,0,0,10,0,0,0,0,0,0,4],[6,0,0,0,0,0,0,2,0,0,0,0,0,0,6,0,0,0,0,0,0,2,0,0,0,0,0,0,5,0,0,0,0,0,0,5],[0,6,0,0,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,2,0,0,0,0,0,0,0,0,5,0,0,0,0,5,0] >;
C62.160D6 in GAP, Magma, Sage, TeX
C_6^2._{160}D_6 % in TeX
G:=Group("C6^2.160D6"); // GroupNames label
G:=SmallGroup(432,723);
// by ID
G=gap.SmallGroup(432,723);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,64,254,1124,4037,14118]);
// Polycyclic
G:=Group<a,b,c,d|a^6=b^6=1,c^6=d^2=b^3,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1*b^3,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^5>;
// generators/relations