metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C4×Dic3)⋊9C4, C12.17(C4⋊C4), (C2×C12).19Q8, C3⋊3(C42⋊8C4), (C2×C12).139D4, (C2×C4).30Dic6, (C22×C4).55D6, C4.17(Dic3⋊C4), C6.49(C4.4D4), C2.4(C4.Dic6), C6.17(C42.C2), C22.28(C2×Dic6), C6.35(C42⋊C2), C2.3(C23.12D6), C2.1(C12.23D4), C6.C42.17C2, C23.301(C22×S3), (C22×C6).341C23, C22.55(D4⋊2S3), (C22×C12).142C22, C22.23(Q8⋊3S3), (C22×Dic3).189C22, C6.37(C2×C4⋊C4), (C6×C4⋊C4).13C2, (C2×C4⋊C4).14S3, (C2×C6).36(C2×Q8), (C2×C4×Dic3).7C2, (C2×C12).84(C2×C4), (C2×C4).153(C4×S3), (C2×C6).446(C2×D4), C22.134(S3×C2×C4), (C2×C4⋊Dic3).34C2, C2.12(C2×Dic3⋊C4), C2.11(C4⋊C4⋊7S3), C22.64(C2×C3⋊D4), (C2×C6).152(C4○D4), (C2×C4).128(C3⋊D4), (C2×C6).117(C22×C4), (C2×Dic3).95(C2×C4), SmallGroup(192,536)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C4×Dic3)⋊9C4
G = < a,b,c,d | a4=b6=d4=1, c2=b3, ab=ba, ac=ca, dad-1=a-1, cbc-1=b-1, bd=db, dcd-1=a2b3c >
Subgroups: 344 in 154 conjugacy classes, 79 normal (23 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C2×C4, C2×C4, C23, Dic3, C12, C12, C2×C6, C2×C6, C42, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×C6, C2.C42, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C4×Dic3, C4⋊Dic3, C3×C4⋊C4, C22×Dic3, C22×C12, C22×C12, C42⋊8C4, C6.C42, C2×C4×Dic3, C2×C4⋊Dic3, C6×C4⋊C4, (C4×Dic3)⋊9C4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, Q8, C23, D6, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic6, C4×S3, C3⋊D4, C22×S3, C2×C4⋊C4, C42⋊C2, C4.4D4, C42.C2, Dic3⋊C4, C2×Dic6, S3×C2×C4, D4⋊2S3, Q8⋊3S3, C2×C3⋊D4, C42⋊8C4, C4.Dic6, C4⋊C4⋊7S3, C2×Dic3⋊C4, C23.12D6, C12.23D4, (C4×Dic3)⋊9C4
►Regular action on 192 points
Generators in S192
(1 65 17 58)(2 66 18 59)(3 61 13 60)(4 62 14 55)(5 63 15 56)(6 64 16 57)(7 148 188 140)(8 149 189 141)(9 150 190 142)(10 145 191 143)(11 146 192 144)(12 147 187 139)(19 74 26 67)(20 75 27 68)(21 76 28 69)(22 77 29 70)(23 78 30 71)(24 73 25 72)(31 86 38 79)(32 87 39 80)(33 88 40 81)(34 89 41 82)(35 90 42 83)(36 85 37 84)(43 99 50 91)(44 100 51 92)(45 101 52 93)(46 102 53 94)(47 97 54 95)(48 98 49 96)(103 159 111 151)(104 160 112 152)(105 161 113 153)(106 162 114 154)(107 157 109 155)(108 158 110 156)(115 171 123 163)(116 172 124 164)(117 173 125 165)(118 174 126 166)(119 169 121 167)(120 170 122 168)(127 183 135 175)(128 184 136 176)(129 185 137 177)(130 186 138 178)(131 181 133 179)(132 182 134 180)
(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)
(1 121 4 124)(2 126 5 123)(3 125 6 122)(7 82 10 79)(8 81 11 84)(9 80 12 83)(13 117 16 120)(14 116 17 119)(15 115 18 118)(19 112 22 109)(20 111 23 114)(21 110 24 113)(25 105 28 108)(26 104 29 107)(27 103 30 106)(31 148 34 145)(32 147 35 150)(33 146 36 149)(37 141 40 144)(38 140 41 143)(39 139 42 142)(43 136 46 133)(44 135 47 138)(45 134 48 137)(49 129 52 132)(50 128 53 131)(51 127 54 130)(55 172 58 169)(56 171 59 174)(57 170 60 173)(61 165 64 168)(62 164 65 167)(63 163 66 166)(67 160 70 157)(68 159 71 162)(69 158 72 161)(73 153 76 156)(74 152 77 155)(75 151 78 154)(85 189 88 192)(86 188 89 191)(87 187 90 190)(91 184 94 181)(92 183 95 186)(93 182 96 185)(97 178 100 175)(98 177 101 180)(99 176 102 179)
(1 46 22 34)(2 47 23 35)(3 48 24 36)(4 43 19 31)(5 44 20 32)(6 45 21 33)(7 169 184 157)(8 170 185 158)(9 171 186 159)(10 172 181 160)(11 173 182 161)(12 174 183 162)(13 49 25 37)(14 50 26 38)(15 51 27 39)(16 52 28 40)(17 53 29 41)(18 54 30 42)(55 99 67 86)(56 100 68 87)(57 101 69 88)(58 102 70 89)(59 97 71 90)(60 98 72 85)(61 96 73 84)(62 91 74 79)(63 92 75 80)(64 93 76 81)(65 94 77 82)(66 95 78 83)(103 150 115 138)(104 145 116 133)(105 146 117 134)(106 147 118 135)(107 148 119 136)(108 149 120 137)(109 140 121 128)(110 141 122 129)(111 142 123 130)(112 143 124 131)(113 144 125 132)(114 139 126 127)(151 190 163 178)(152 191 164 179)(153 192 165 180)(154 187 166 175)(155 188 167 176)(156 189 168 177)
G:=sub<Sym(192)| (1,65,17,58)(2,66,18,59)(3,61,13,60)(4,62,14,55)(5,63,15,56)(6,64,16,57)(7,148,188,140)(8,149,189,141)(9,150,190,142)(10,145,191,143)(11,146,192,144)(12,147,187,139)(19,74,26,67)(20,75,27,68)(21,76,28,69)(22,77,29,70)(23,78,30,71)(24,73,25,72)(31,86,38,79)(32,87,39,80)(33,88,40,81)(34,89,41,82)(35,90,42,83)(36,85,37,84)(43,99,50,91)(44,100,51,92)(45,101,52,93)(46,102,53,94)(47,97,54,95)(48,98,49,96)(103,159,111,151)(104,160,112,152)(105,161,113,153)(106,162,114,154)(107,157,109,155)(108,158,110,156)(115,171,123,163)(116,172,124,164)(117,173,125,165)(118,174,126,166)(119,169,121,167)(120,170,122,168)(127,183,135,175)(128,184,136,176)(129,185,137,177)(130,186,138,178)(131,181,133,179)(132,182,134,180), (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), (1,121,4,124)(2,126,5,123)(3,125,6,122)(7,82,10,79)(8,81,11,84)(9,80,12,83)(13,117,16,120)(14,116,17,119)(15,115,18,118)(19,112,22,109)(20,111,23,114)(21,110,24,113)(25,105,28,108)(26,104,29,107)(27,103,30,106)(31,148,34,145)(32,147,35,150)(33,146,36,149)(37,141,40,144)(38,140,41,143)(39,139,42,142)(43,136,46,133)(44,135,47,138)(45,134,48,137)(49,129,52,132)(50,128,53,131)(51,127,54,130)(55,172,58,169)(56,171,59,174)(57,170,60,173)(61,165,64,168)(62,164,65,167)(63,163,66,166)(67,160,70,157)(68,159,71,162)(69,158,72,161)(73,153,76,156)(74,152,77,155)(75,151,78,154)(85,189,88,192)(86,188,89,191)(87,187,90,190)(91,184,94,181)(92,183,95,186)(93,182,96,185)(97,178,100,175)(98,177,101,180)(99,176,102,179), (1,46,22,34)(2,47,23,35)(3,48,24,36)(4,43,19,31)(5,44,20,32)(6,45,21,33)(7,169,184,157)(8,170,185,158)(9,171,186,159)(10,172,181,160)(11,173,182,161)(12,174,183,162)(13,49,25,37)(14,50,26,38)(15,51,27,39)(16,52,28,40)(17,53,29,41)(18,54,30,42)(55,99,67,86)(56,100,68,87)(57,101,69,88)(58,102,70,89)(59,97,71,90)(60,98,72,85)(61,96,73,84)(62,91,74,79)(63,92,75,80)(64,93,76,81)(65,94,77,82)(66,95,78,83)(103,150,115,138)(104,145,116,133)(105,146,117,134)(106,147,118,135)(107,148,119,136)(108,149,120,137)(109,140,121,128)(110,141,122,129)(111,142,123,130)(112,143,124,131)(113,144,125,132)(114,139,126,127)(151,190,163,178)(152,191,164,179)(153,192,165,180)(154,187,166,175)(155,188,167,176)(156,189,168,177)>;
G:=Group( (1,65,17,58)(2,66,18,59)(3,61,13,60)(4,62,14,55)(5,63,15,56)(6,64,16,57)(7,148,188,140)(8,149,189,141)(9,150,190,142)(10,145,191,143)(11,146,192,144)(12,147,187,139)(19,74,26,67)(20,75,27,68)(21,76,28,69)(22,77,29,70)(23,78,30,71)(24,73,25,72)(31,86,38,79)(32,87,39,80)(33,88,40,81)(34,89,41,82)(35,90,42,83)(36,85,37,84)(43,99,50,91)(44,100,51,92)(45,101,52,93)(46,102,53,94)(47,97,54,95)(48,98,49,96)(103,159,111,151)(104,160,112,152)(105,161,113,153)(106,162,114,154)(107,157,109,155)(108,158,110,156)(115,171,123,163)(116,172,124,164)(117,173,125,165)(118,174,126,166)(119,169,121,167)(120,170,122,168)(127,183,135,175)(128,184,136,176)(129,185,137,177)(130,186,138,178)(131,181,133,179)(132,182,134,180), (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), (1,121,4,124)(2,126,5,123)(3,125,6,122)(7,82,10,79)(8,81,11,84)(9,80,12,83)(13,117,16,120)(14,116,17,119)(15,115,18,118)(19,112,22,109)(20,111,23,114)(21,110,24,113)(25,105,28,108)(26,104,29,107)(27,103,30,106)(31,148,34,145)(32,147,35,150)(33,146,36,149)(37,141,40,144)(38,140,41,143)(39,139,42,142)(43,136,46,133)(44,135,47,138)(45,134,48,137)(49,129,52,132)(50,128,53,131)(51,127,54,130)(55,172,58,169)(56,171,59,174)(57,170,60,173)(61,165,64,168)(62,164,65,167)(63,163,66,166)(67,160,70,157)(68,159,71,162)(69,158,72,161)(73,153,76,156)(74,152,77,155)(75,151,78,154)(85,189,88,192)(86,188,89,191)(87,187,90,190)(91,184,94,181)(92,183,95,186)(93,182,96,185)(97,178,100,175)(98,177,101,180)(99,176,102,179), (1,46,22,34)(2,47,23,35)(3,48,24,36)(4,43,19,31)(5,44,20,32)(6,45,21,33)(7,169,184,157)(8,170,185,158)(9,171,186,159)(10,172,181,160)(11,173,182,161)(12,174,183,162)(13,49,25,37)(14,50,26,38)(15,51,27,39)(16,52,28,40)(17,53,29,41)(18,54,30,42)(55,99,67,86)(56,100,68,87)(57,101,69,88)(58,102,70,89)(59,97,71,90)(60,98,72,85)(61,96,73,84)(62,91,74,79)(63,92,75,80)(64,93,76,81)(65,94,77,82)(66,95,78,83)(103,150,115,138)(104,145,116,133)(105,146,117,134)(106,147,118,135)(107,148,119,136)(108,149,120,137)(109,140,121,128)(110,141,122,129)(111,142,123,130)(112,143,124,131)(113,144,125,132)(114,139,126,127)(151,190,163,178)(152,191,164,179)(153,192,165,180)(154,187,166,175)(155,188,167,176)(156,189,168,177) );
G=PermutationGroup([[(1,65,17,58),(2,66,18,59),(3,61,13,60),(4,62,14,55),(5,63,15,56),(6,64,16,57),(7,148,188,140),(8,149,189,141),(9,150,190,142),(10,145,191,143),(11,146,192,144),(12,147,187,139),(19,74,26,67),(20,75,27,68),(21,76,28,69),(22,77,29,70),(23,78,30,71),(24,73,25,72),(31,86,38,79),(32,87,39,80),(33,88,40,81),(34,89,41,82),(35,90,42,83),(36,85,37,84),(43,99,50,91),(44,100,51,92),(45,101,52,93),(46,102,53,94),(47,97,54,95),(48,98,49,96),(103,159,111,151),(104,160,112,152),(105,161,113,153),(106,162,114,154),(107,157,109,155),(108,158,110,156),(115,171,123,163),(116,172,124,164),(117,173,125,165),(118,174,126,166),(119,169,121,167),(120,170,122,168),(127,183,135,175),(128,184,136,176),(129,185,137,177),(130,186,138,178),(131,181,133,179),(132,182,134,180)], [(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)], [(1,121,4,124),(2,126,5,123),(3,125,6,122),(7,82,10,79),(8,81,11,84),(9,80,12,83),(13,117,16,120),(14,116,17,119),(15,115,18,118),(19,112,22,109),(20,111,23,114),(21,110,24,113),(25,105,28,108),(26,104,29,107),(27,103,30,106),(31,148,34,145),(32,147,35,150),(33,146,36,149),(37,141,40,144),(38,140,41,143),(39,139,42,142),(43,136,46,133),(44,135,47,138),(45,134,48,137),(49,129,52,132),(50,128,53,131),(51,127,54,130),(55,172,58,169),(56,171,59,174),(57,170,60,173),(61,165,64,168),(62,164,65,167),(63,163,66,166),(67,160,70,157),(68,159,71,162),(69,158,72,161),(73,153,76,156),(74,152,77,155),(75,151,78,154),(85,189,88,192),(86,188,89,191),(87,187,90,190),(91,184,94,181),(92,183,95,186),(93,182,96,185),(97,178,100,175),(98,177,101,180),(99,176,102,179)], [(1,46,22,34),(2,47,23,35),(3,48,24,36),(4,43,19,31),(5,44,20,32),(6,45,21,33),(7,169,184,157),(8,170,185,158),(9,171,186,159),(10,172,181,160),(11,173,182,161),(12,174,183,162),(13,49,25,37),(14,50,26,38),(15,51,27,39),(16,52,28,40),(17,53,29,41),(18,54,30,42),(55,99,67,86),(56,100,68,87),(57,101,69,88),(58,102,70,89),(59,97,71,90),(60,98,72,85),(61,96,73,84),(62,91,74,79),(63,92,75,80),(64,93,76,81),(65,94,77,82),(66,95,78,83),(103,150,115,138),(104,145,116,133),(105,146,117,134),(106,147,118,135),(107,148,119,136),(108,149,120,137),(109,140,121,128),(110,141,122,129),(111,142,123,130),(112,143,124,131),(113,144,125,132),(114,139,126,127),(151,190,163,178),(152,191,164,179),(153,192,165,180),(154,187,166,175),(155,188,167,176),(156,189,168,177)]])
48 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 4S | 4T | 6A | ··· | 6G | 12A | ··· | 12L |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 12 | 12 | 12 | 12 | 2 | ··· | 2 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | - | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | Q8 | D6 | C4○D4 | Dic6 | C4×S3 | C3⋊D4 | D4⋊2S3 | Q8⋊3S3 |
| kernel | (C4×Dic3)⋊9C4 | C6.C42 | C2×C4×Dic3 | C2×C4⋊Dic3 | C6×C4⋊C4 | C4×Dic3 | C2×C4⋊C4 | C2×C12 | C2×C12 | C22×C4 | C2×C6 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 3 | 8 | 4 | 4 | 4 | 2 | 2 |
Matrix representation of (C4×Dic3)⋊9C4 ►in GL7(𝔽13)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 2 | 0 | 0 | 0 | 0 |
| 0 | 12 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 0 | 1 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 8 | 10 | 0 | 0 | 0 | 0 |
| 0 | 8 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 6 | 8 | 0 | 0 |
| 0 | 0 | 0 | 10 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 11 | 0 | 0 |
| 0 | 0 | 0 | 1 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(7,GF(13))| [1,0,0,0,0,0,0,0,12,12,0,0,0,0,0,2,1,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,12,12],[1,0,0,0,0,0,0,0,8,8,0,0,0,0,0,10,5,0,0,0,0,0,0,0,6,10,0,0,0,0,0,8,7,0,0,0,0,0,0,0,12,0,0,0,0,0,0,1,1],[5,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,12,0,0,0,0,0,0,0,1,1,0,0,0,0,0,11,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1] >;
(C4×Dic3)⋊9C4 in GAP, Magma, Sage, TeX
(C_4\times {\rm Dic}_3)\rtimes_9C_4 % in TeX
G:=Group("(C4xDic3):9C4"); // GroupNames label
G:=SmallGroup(192,536);
// by ID
G=gap.SmallGroup(192,536);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,232,1094,387,58,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^6=d^4=1,c^2=b^3,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=a^2*b^3*c>;
// generators/relations