direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic6⋊C4, C6⋊2(C4×Q8), C4⋊C4.304D6, Dic3⋊6(C2×Q8), Dic6⋊21(C2×C4), (C2×Dic6)⋊17C4, (C2×Dic3)⋊11Q8, C6.10(C23×C4), (C2×C6).40C24, C6.21(C22×Q8), C22.29(S3×Q8), C12.87(C22×C4), (C22×C4).331D6, (C2×C12).576C23, C22.20(S3×C23), Dic3.4(C22×C4), (C22×C6).389C23, C23.330(C22×S3), (C22×Dic6).16C2, C22.70(D4⋊2S3), Dic3⋊C4.128C22, (C22×C12).213C22, (C2×Dic3).304C23, (C4×Dic3).289C22, (C2×Dic6).280C22, (C22×Dic3).205C22, C3⋊2(C2×C4×Q8), C2.1(C2×S3×Q8), C4.56(S3×C2×C4), (C6×C4⋊C4).16C2, (C2×C4⋊C4).29S3, (C2×C4).86(C4×S3), C6.69(C2×C4○D4), C22.70(S3×C2×C4), C2.12(S3×C22×C4), (C2×C6).90(C2×Q8), C2.3(C2×D4⋊2S3), (C2×C4×Dic3).40C2, (C2×C12).127(C2×C4), (C2×C6).169(C4○D4), (C3×C4⋊C4).289C22, (C2×Dic3⋊C4).28C2, (C2×C6).149(C22×C4), (C2×C4).263(C22×S3), (C2×Dic3).70(C2×C4), SmallGroup(192,1055)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 536 in 298 conjugacy classes, 175 normal (21 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×4], C4 [×18], C22, C22 [×6], C6 [×3], C6 [×4], C2×C4 [×10], C2×C4 [×26], Q8 [×16], C23, Dic3 [×12], Dic3 [×2], C12 [×4], C12 [×4], C2×C6, C2×C6 [×6], C42 [×12], C4⋊C4 [×4], C4⋊C4 [×8], C22×C4, C22×C4 [×2], C22×C4 [×4], C2×Q8 [×12], Dic6 [×16], C2×Dic3 [×20], C2×Dic3 [×2], C2×C12 [×10], C2×C12 [×4], C22×C6, C2×C42 [×3], C2×C4⋊C4, C2×C4⋊C4 [×2], C4×Q8 [×8], C22×Q8, C4×Dic3 [×12], Dic3⋊C4 [×8], C3×C4⋊C4 [×4], C2×Dic6 [×12], C22×Dic3 [×2], C22×Dic3 [×2], C22×C12, C22×C12 [×2], C2×C4×Q8, Dic6⋊C4 [×8], C2×C4×Dic3, C2×C4×Dic3 [×2], C2×Dic3⋊C4 [×2], C6×C4⋊C4, C22×Dic6, C2×Dic6⋊C4
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], S3, C2×C4 [×28], Q8 [×4], C23 [×15], D6 [×7], C22×C4 [×14], C2×Q8 [×6], C4○D4 [×2], C24, C4×S3 [×4], C22×S3 [×7], C4×Q8 [×4], C23×C4, C22×Q8, C2×C4○D4, S3×C2×C4 [×6], D4⋊2S3 [×2], S3×Q8 [×2], S3×C23, C2×C4×Q8, Dic6⋊C4 [×4], S3×C22×C4, C2×D4⋊2S3, C2×S3×Q8, C2×Dic6⋊C4
Generators and relations
G = < a,b,c,d | a2=b12=d4=1, c2=b6, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b7, cd=dc >
►Regular action on 192 points
Generators in S192
(1 102)(2 103)(3 104)(4 105)(5 106)(6 107)(7 108)(8 97)(9 98)(10 99)(11 100)(12 101)(13 152)(14 153)(15 154)(16 155)(17 156)(18 145)(19 146)(20 147)(21 148)(22 149)(23 150)(24 151)(25 180)(26 169)(27 170)(28 171)(29 172)(30 173)(31 174)(32 175)(33 176)(34 177)(35 178)(36 179)(37 164)(38 165)(39 166)(40 167)(41 168)(42 157)(43 158)(44 159)(45 160)(46 161)(47 162)(48 163)(49 138)(50 139)(51 140)(52 141)(53 142)(54 143)(55 144)(56 133)(57 134)(58 135)(59 136)(60 137)(61 73)(62 74)(63 75)(64 76)(65 77)(66 78)(67 79)(68 80)(69 81)(70 82)(71 83)(72 84)(85 121)(86 122)(87 123)(88 124)(89 125)(90 126)(91 127)(92 128)(93 129)(94 130)(95 131)(96 132)(109 184)(110 185)(111 186)(112 187)(113 188)(114 189)(115 190)(116 191)(117 192)(118 181)(119 182)(120 183)
(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)
(1 172 7 178)(2 171 8 177)(3 170 9 176)(4 169 10 175)(5 180 11 174)(6 179 12 173)(13 42 19 48)(14 41 20 47)(15 40 21 46)(16 39 22 45)(17 38 23 44)(18 37 24 43)(25 100 31 106)(26 99 32 105)(27 98 33 104)(28 97 34 103)(29 108 35 102)(30 107 36 101)(49 130 55 124)(50 129 56 123)(51 128 57 122)(52 127 58 121)(53 126 59 132)(54 125 60 131)(61 110 67 116)(62 109 68 115)(63 120 69 114)(64 119 70 113)(65 118 71 112)(66 117 72 111)(73 185 79 191)(74 184 80 190)(75 183 81 189)(76 182 82 188)(77 181 83 187)(78 192 84 186)(85 141 91 135)(86 140 92 134)(87 139 93 133)(88 138 94 144)(89 137 95 143)(90 136 96 142)(145 164 151 158)(146 163 152 157)(147 162 153 168)(148 161 154 167)(149 160 155 166)(150 159 156 165)
(1 46 94 76)(2 41 95 83)(3 48 96 78)(4 43 85 73)(5 38 86 80)(6 45 87 75)(7 40 88 82)(8 47 89 77)(9 42 90 84)(10 37 91 79)(11 44 92 74)(12 39 93 81)(13 142 192 170)(14 137 181 177)(15 144 182 172)(16 139 183 179)(17 134 184 174)(18 141 185 169)(19 136 186 176)(20 143 187 171)(21 138 188 178)(22 133 189 173)(23 140 190 180)(24 135 191 175)(25 150 51 115)(26 145 52 110)(27 152 53 117)(28 147 54 112)(29 154 55 119)(30 149 56 114)(31 156 57 109)(32 151 58 116)(33 146 59 111)(34 153 60 118)(35 148 49 113)(36 155 50 120)(61 105 158 121)(62 100 159 128)(63 107 160 123)(64 102 161 130)(65 97 162 125)(66 104 163 132)(67 99 164 127)(68 106 165 122)(69 101 166 129)(70 108 167 124)(71 103 168 131)(72 98 157 126)
G:=sub<Sym(192)| (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,97)(9,98)(10,99)(11,100)(12,101)(13,152)(14,153)(15,154)(16,155)(17,156)(18,145)(19,146)(20,147)(21,148)(22,149)(23,150)(24,151)(25,180)(26,169)(27,170)(28,171)(29,172)(30,173)(31,174)(32,175)(33,176)(34,177)(35,178)(36,179)(37,164)(38,165)(39,166)(40,167)(41,168)(42,157)(43,158)(44,159)(45,160)(46,161)(47,162)(48,163)(49,138)(50,139)(51,140)(52,141)(53,142)(54,143)(55,144)(56,133)(57,134)(58,135)(59,136)(60,137)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,81)(70,82)(71,83)(72,84)(85,121)(86,122)(87,123)(88,124)(89,125)(90,126)(91,127)(92,128)(93,129)(94,130)(95,131)(96,132)(109,184)(110,185)(111,186)(112,187)(113,188)(114,189)(115,190)(116,191)(117,192)(118,181)(119,182)(120,183), (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), (1,172,7,178)(2,171,8,177)(3,170,9,176)(4,169,10,175)(5,180,11,174)(6,179,12,173)(13,42,19,48)(14,41,20,47)(15,40,21,46)(16,39,22,45)(17,38,23,44)(18,37,24,43)(25,100,31,106)(26,99,32,105)(27,98,33,104)(28,97,34,103)(29,108,35,102)(30,107,36,101)(49,130,55,124)(50,129,56,123)(51,128,57,122)(52,127,58,121)(53,126,59,132)(54,125,60,131)(61,110,67,116)(62,109,68,115)(63,120,69,114)(64,119,70,113)(65,118,71,112)(66,117,72,111)(73,185,79,191)(74,184,80,190)(75,183,81,189)(76,182,82,188)(77,181,83,187)(78,192,84,186)(85,141,91,135)(86,140,92,134)(87,139,93,133)(88,138,94,144)(89,137,95,143)(90,136,96,142)(145,164,151,158)(146,163,152,157)(147,162,153,168)(148,161,154,167)(149,160,155,166)(150,159,156,165), (1,46,94,76)(2,41,95,83)(3,48,96,78)(4,43,85,73)(5,38,86,80)(6,45,87,75)(7,40,88,82)(8,47,89,77)(9,42,90,84)(10,37,91,79)(11,44,92,74)(12,39,93,81)(13,142,192,170)(14,137,181,177)(15,144,182,172)(16,139,183,179)(17,134,184,174)(18,141,185,169)(19,136,186,176)(20,143,187,171)(21,138,188,178)(22,133,189,173)(23,140,190,180)(24,135,191,175)(25,150,51,115)(26,145,52,110)(27,152,53,117)(28,147,54,112)(29,154,55,119)(30,149,56,114)(31,156,57,109)(32,151,58,116)(33,146,59,111)(34,153,60,118)(35,148,49,113)(36,155,50,120)(61,105,158,121)(62,100,159,128)(63,107,160,123)(64,102,161,130)(65,97,162,125)(66,104,163,132)(67,99,164,127)(68,106,165,122)(69,101,166,129)(70,108,167,124)(71,103,168,131)(72,98,157,126)>;
G:=Group( (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,97)(9,98)(10,99)(11,100)(12,101)(13,152)(14,153)(15,154)(16,155)(17,156)(18,145)(19,146)(20,147)(21,148)(22,149)(23,150)(24,151)(25,180)(26,169)(27,170)(28,171)(29,172)(30,173)(31,174)(32,175)(33,176)(34,177)(35,178)(36,179)(37,164)(38,165)(39,166)(40,167)(41,168)(42,157)(43,158)(44,159)(45,160)(46,161)(47,162)(48,163)(49,138)(50,139)(51,140)(52,141)(53,142)(54,143)(55,144)(56,133)(57,134)(58,135)(59,136)(60,137)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,81)(70,82)(71,83)(72,84)(85,121)(86,122)(87,123)(88,124)(89,125)(90,126)(91,127)(92,128)(93,129)(94,130)(95,131)(96,132)(109,184)(110,185)(111,186)(112,187)(113,188)(114,189)(115,190)(116,191)(117,192)(118,181)(119,182)(120,183), (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), (1,172,7,178)(2,171,8,177)(3,170,9,176)(4,169,10,175)(5,180,11,174)(6,179,12,173)(13,42,19,48)(14,41,20,47)(15,40,21,46)(16,39,22,45)(17,38,23,44)(18,37,24,43)(25,100,31,106)(26,99,32,105)(27,98,33,104)(28,97,34,103)(29,108,35,102)(30,107,36,101)(49,130,55,124)(50,129,56,123)(51,128,57,122)(52,127,58,121)(53,126,59,132)(54,125,60,131)(61,110,67,116)(62,109,68,115)(63,120,69,114)(64,119,70,113)(65,118,71,112)(66,117,72,111)(73,185,79,191)(74,184,80,190)(75,183,81,189)(76,182,82,188)(77,181,83,187)(78,192,84,186)(85,141,91,135)(86,140,92,134)(87,139,93,133)(88,138,94,144)(89,137,95,143)(90,136,96,142)(145,164,151,158)(146,163,152,157)(147,162,153,168)(148,161,154,167)(149,160,155,166)(150,159,156,165), (1,46,94,76)(2,41,95,83)(3,48,96,78)(4,43,85,73)(5,38,86,80)(6,45,87,75)(7,40,88,82)(8,47,89,77)(9,42,90,84)(10,37,91,79)(11,44,92,74)(12,39,93,81)(13,142,192,170)(14,137,181,177)(15,144,182,172)(16,139,183,179)(17,134,184,174)(18,141,185,169)(19,136,186,176)(20,143,187,171)(21,138,188,178)(22,133,189,173)(23,140,190,180)(24,135,191,175)(25,150,51,115)(26,145,52,110)(27,152,53,117)(28,147,54,112)(29,154,55,119)(30,149,56,114)(31,156,57,109)(32,151,58,116)(33,146,59,111)(34,153,60,118)(35,148,49,113)(36,155,50,120)(61,105,158,121)(62,100,159,128)(63,107,160,123)(64,102,161,130)(65,97,162,125)(66,104,163,132)(67,99,164,127)(68,106,165,122)(69,101,166,129)(70,108,167,124)(71,103,168,131)(72,98,157,126) );
G=PermutationGroup([(1,102),(2,103),(3,104),(4,105),(5,106),(6,107),(7,108),(8,97),(9,98),(10,99),(11,100),(12,101),(13,152),(14,153),(15,154),(16,155),(17,156),(18,145),(19,146),(20,147),(21,148),(22,149),(23,150),(24,151),(25,180),(26,169),(27,170),(28,171),(29,172),(30,173),(31,174),(32,175),(33,176),(34,177),(35,178),(36,179),(37,164),(38,165),(39,166),(40,167),(41,168),(42,157),(43,158),(44,159),(45,160),(46,161),(47,162),(48,163),(49,138),(50,139),(51,140),(52,141),(53,142),(54,143),(55,144),(56,133),(57,134),(58,135),(59,136),(60,137),(61,73),(62,74),(63,75),(64,76),(65,77),(66,78),(67,79),(68,80),(69,81),(70,82),(71,83),(72,84),(85,121),(86,122),(87,123),(88,124),(89,125),(90,126),(91,127),(92,128),(93,129),(94,130),(95,131),(96,132),(109,184),(110,185),(111,186),(112,187),(113,188),(114,189),(115,190),(116,191),(117,192),(118,181),(119,182),(120,183)], [(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)], [(1,172,7,178),(2,171,8,177),(3,170,9,176),(4,169,10,175),(5,180,11,174),(6,179,12,173),(13,42,19,48),(14,41,20,47),(15,40,21,46),(16,39,22,45),(17,38,23,44),(18,37,24,43),(25,100,31,106),(26,99,32,105),(27,98,33,104),(28,97,34,103),(29,108,35,102),(30,107,36,101),(49,130,55,124),(50,129,56,123),(51,128,57,122),(52,127,58,121),(53,126,59,132),(54,125,60,131),(61,110,67,116),(62,109,68,115),(63,120,69,114),(64,119,70,113),(65,118,71,112),(66,117,72,111),(73,185,79,191),(74,184,80,190),(75,183,81,189),(76,182,82,188),(77,181,83,187),(78,192,84,186),(85,141,91,135),(86,140,92,134),(87,139,93,133),(88,138,94,144),(89,137,95,143),(90,136,96,142),(145,164,151,158),(146,163,152,157),(147,162,153,168),(148,161,154,167),(149,160,155,166),(150,159,156,165)], [(1,46,94,76),(2,41,95,83),(3,48,96,78),(4,43,85,73),(5,38,86,80),(6,45,87,75),(7,40,88,82),(8,47,89,77),(9,42,90,84),(10,37,91,79),(11,44,92,74),(12,39,93,81),(13,142,192,170),(14,137,181,177),(15,144,182,172),(16,139,183,179),(17,134,184,174),(18,141,185,169),(19,136,186,176),(20,143,187,171),(21,138,188,178),(22,133,189,173),(23,140,190,180),(24,135,191,175),(25,150,51,115),(26,145,52,110),(27,152,53,117),(28,147,54,112),(29,154,55,119),(30,149,56,114),(31,156,57,109),(32,151,58,116),(33,146,59,111),(34,153,60,118),(35,148,49,113),(36,155,50,120),(61,105,158,121),(62,100,159,128),(63,107,160,123),(64,102,161,130),(65,97,162,125),(66,104,163,132),(67,99,164,127),(68,106,165,122),(69,101,166,129),(70,108,167,124),(71,103,168,131),(72,98,157,126)])
Matrix representation ►G ⊆ GL6(𝔽13)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 10 | 0 | 0 | 0 | 0 | 0 |
| 8 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 0 | 0 | 0 |
| 0 | 0 | 1 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 4 |
| 0 | 0 | 0 | 0 | 4 | 10 |
| 9 | 3 | 0 | 0 | 0 | 0 |
| 8 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 9 | 0 | 0 |
| 0 | 0 | 6 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 0 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 12 | 0 |
G:=sub<GL(6,GF(13))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[10,8,0,0,0,0,0,4,0,0,0,0,0,0,10,1,0,0,0,0,0,4,0,0,0,0,0,0,3,4,0,0,0,0,4,10],[9,8,0,0,0,0,3,4,0,0,0,0,0,0,5,6,0,0,0,0,9,8,0,0,0,0,0,0,0,1,0,0,0,0,12,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,0,0,0,0,0,0,8,0,0,0,0,0,0,0,12,0,0,0,0,1,0] >;
60 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | ··· | 4L | 4M | ··· | 4T | 4U | ··· | 4AF | 6A | ··· | 6G | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | ··· | 2 | 3 | ··· | 3 | 6 | ··· | 6 | 2 | ··· | 2 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | Q8 | D6 | D6 | C4○D4 | C4×S3 | D4⋊2S3 | S3×Q8 |
| kernel | C2×Dic6⋊C4 | Dic6⋊C4 | C2×C4×Dic3 | C2×Dic3⋊C4 | C6×C4⋊C4 | C22×Dic6 | C2×Dic6 | C2×C4⋊C4 | C2×Dic3 | C4⋊C4 | C22×C4 | C2×C6 | C2×C4 | C22 | C22 |
| # reps | 1 | 8 | 3 | 2 | 1 | 1 | 16 | 1 | 4 | 4 | 3 | 4 | 8 | 2 | 2 |
In GAP, Magma, Sage, TeX
C_2\times Dic_6\rtimes C_4
% in TeX
G:=Group("C2xDic6:C4"); // GroupNames label
G:=SmallGroup(192,1055);
// by ID
G=gap.SmallGroup(192,1055);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,100,185,192,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^12=d^4=1,c^2=b^6,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^7,c*d=d*c>;
// generators/relations
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