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G = C24×C12  order 192 = 26·3

Abelian group of type [2,2,2,2,12]

direct product, abelian, monomial, 2-elementary

Aliases: C24×C12, SmallGroup(192,1530)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C24×C12
Chief series
C1 — C2 — C6 — C12 — C2×C12 — C22×C12 — C23×C12 — C24×C12
Lower central
C1 — C24×C12
Upper central
C1 — C24×C12

Generators and relations for C24×C12
 G = < a,b,c,d,e | a2=b2=c2=d2=e12=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 1362, all normal (8 characteristic)
C1, C2, C2, C3, C4, C22, C6, C6, C2×C4, C23, C12, C2×C6, C22×C4, C24, C2×C12, C22×C6, C23×C4, C25, C22×C12, C23×C6, C24×C4, C23×C12, C24×C6, C24×C12
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, C23, C12, C2×C6, C22×C4, C24, C2×C12, C22×C6, C23×C4, C25, C22×C12, C23×C6, C24×C4, C23×C12, C24×C6, C24×C12

Smallest permutation representation of C24×C12
►Regular action on 192 points
Generators in S192
(1 77)(2 78)(3 79)(4 80)(5 81)(6 82)(7 83)(8 84)(9 73)(10 74)(11 75)(12 76)(13 87)(14 88)(15 89)(16 90)(17 91)(18 92)(19 93)(20 94)(21 95)(22 96)(23 85)(24 86)(25 153)(26 154)(27 155)(28 156)(29 145)(30 146)(31 147)(32 148)(33 149)(34 150)(35 151)(36 152)(37 69)(38 70)(39 71)(40 72)(41 61)(42 62)(43 63)(44 64)(45 65)(46 66)(47 67)(48 68)(49 163)(50 164)(51 165)(52 166)(53 167)(54 168)(55 157)(56 158)(57 159)(58 160)(59 161)(60 162)(97 190)(98 191)(99 192)(100 181)(101 182)(102 183)(103 184)(104 185)(105 186)(106 187)(107 188)(108 189)(109 125)(110 126)(111 127)(112 128)(113 129)(114 130)(115 131)(116 132)(117 121)(118 122)(119 123)(120 124)(133 174)(134 175)(135 176)(136 177)(137 178)(138 179)(139 180)(140 169)(141 170)(142 171)(143 172)(144 173)

(1 20)(2 21)(3 22)(4 23)(5 24)(6 13)(7 14)(8 15)(9 16)(10 17)(11 18)(12 19)(25 69)(26 70)(27 71)(28 72)(29 61)(30 62)(31 63)(32 64)(33 65)(34 66)(35 67)(36 68)(37 153)(38 154)(39 155)(40 156)(41 145)(42 146)(43 147)(44 148)(45 149)(46 150)(47 151)(48 152)(49 111)(50 112)(51 113)(52 114)(53 115)(54 116)(55 117)(56 118)(57 119)(58 120)(59 109)(60 110)(73 90)(74 91)(75 92)(76 93)(77 94)(78 95)(79 96)(80 85)(81 86)(82 87)(83 88)(84 89)(97 174)(98 175)(99 176)(100 177)(101 178)(102 179)(103 180)(104 169)(105 170)(106 171)(107 172)(108 173)(121 157)(122 158)(123 159)(124 160)(125 161)(126 162)(127 163)(128 164)(129 165)(130 166)(131 167)(132 168)(133 190)(134 191)(135 192)(136 181)(137 182)(138 183)(139 184)(140 185)(141 186)(142 187)(143 188)(144 189)

(1 192)(2 181)(3 182)(4 183)(5 184)(6 185)(7 186)(8 187)(9 188)(10 189)(11 190)(12 191)(13 140)(14 141)(15 142)(16 143)(17 144)(18 133)(19 134)(20 135)(21 136)(22 137)(23 138)(24 139)(25 119)(26 120)(27 109)(28 110)(29 111)(30 112)(31 113)(32 114)(33 115)(34 116)(35 117)(36 118)(37 159)(38 160)(39 161)(40 162)(41 163)(42 164)(43 165)(44 166)(45 167)(46 168)(47 157)(48 158)(49 61)(50 62)(51 63)(52 64)(53 65)(54 66)(55 67)(56 68)(57 69)(58 70)(59 71)(60 72)(73 107)(74 108)(75 97)(76 98)(77 99)(78 100)(79 101)(80 102)(81 103)(82 104)(83 105)(84 106)(85 179)(86 180)(87 169)(88 170)(89 171)(90 172)(91 173)(92 174)(93 175)(94 176)(95 177)(96 178)(121 151)(122 152)(123 153)(124 154)(125 155)(126 156)(127 145)(128 146)(129 147)(130 148)(131 149)(132 150)

(1 148)(2 149)(3 150)(4 151)(5 152)(6 153)(7 154)(8 155)(9 156)(10 145)(11 146)(12 147)(13 37)(14 38)(15 39)(16 40)(17 41)(18 42)(19 43)(20 44)(21 45)(22 46)(23 47)(24 48)(25 82)(26 83)(27 84)(28 73)(29 74)(30 75)(31 76)(32 77)(33 78)(34 79)(35 80)(36 81)(49 173)(50 174)(51 175)(52 176)(53 177)(54 178)(55 179)(56 180)(57 169)(58 170)(59 171)(60 172)(61 91)(62 92)(63 93)(64 94)(65 95)(66 96)(67 85)(68 86)(69 87)(70 88)(71 89)(72 90)(97 112)(98 113)(99 114)(100 115)(101 116)(102 117)(103 118)(104 119)(105 120)(106 109)(107 110)(108 111)(121 183)(122 184)(123 185)(124 186)(125 187)(126 188)(127 189)(128 190)(129 191)(130 192)(131 181)(132 182)(133 164)(134 165)(135 166)(136 167)(137 168)(138 157)(139 158)(140 159)(141 160)(142 161)(143 162)(144 163)

(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)
 
G:=sub<Sym(192)| (1,77)(2,78)(3,79)(4,80)(5,81)(6,82)(7,83)(8,84)(9,73)(10,74)(11,75)(12,76)(13,87)(14,88)(15,89)(16,90)(17,91)(18,92)(19,93)(20,94)(21,95)(22,96)(23,85)(24,86)(25,153)(26,154)(27,155)(28,156)(29,145)(30,146)(31,147)(32,148)(33,149)(34,150)(35,151)(36,152)(37,69)(38,70)(39,71)(40,72)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,163)(50,164)(51,165)(52,166)(53,167)(54,168)(55,157)(56,158)(57,159)(58,160)(59,161)(60,162)(97,190)(98,191)(99,192)(100,181)(101,182)(102,183)(103,184)(104,185)(105,186)(106,187)(107,188)(108,189)(109,125)(110,126)(111,127)(112,128)(113,129)(114,130)(115,131)(116,132)(117,121)(118,122)(119,123)(120,124)(133,174)(134,175)(135,176)(136,177)(137,178)(138,179)(139,180)(140,169)(141,170)(142,171)(143,172)(144,173), (1,20)(2,21)(3,22)(4,23)(5,24)(6,13)(7,14)(8,15)(9,16)(10,17)(11,18)(12,19)(25,69)(26,70)(27,71)(28,72)(29,61)(30,62)(31,63)(32,64)(33,65)(34,66)(35,67)(36,68)(37,153)(38,154)(39,155)(40,156)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,111)(50,112)(51,113)(52,114)(53,115)(54,116)(55,117)(56,118)(57,119)(58,120)(59,109)(60,110)(73,90)(74,91)(75,92)(76,93)(77,94)(78,95)(79,96)(80,85)(81,86)(82,87)(83,88)(84,89)(97,174)(98,175)(99,176)(100,177)(101,178)(102,179)(103,180)(104,169)(105,170)(106,171)(107,172)(108,173)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,163)(128,164)(129,165)(130,166)(131,167)(132,168)(133,190)(134,191)(135,192)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(142,187)(143,188)(144,189), (1,192)(2,181)(3,182)(4,183)(5,184)(6,185)(7,186)(8,187)(9,188)(10,189)(11,190)(12,191)(13,140)(14,141)(15,142)(16,143)(17,144)(18,133)(19,134)(20,135)(21,136)(22,137)(23,138)(24,139)(25,119)(26,120)(27,109)(28,110)(29,111)(30,112)(31,113)(32,114)(33,115)(34,116)(35,117)(36,118)(37,159)(38,160)(39,161)(40,162)(41,163)(42,164)(43,165)(44,166)(45,167)(46,168)(47,157)(48,158)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)(73,107)(74,108)(75,97)(76,98)(77,99)(78,100)(79,101)(80,102)(81,103)(82,104)(83,105)(84,106)(85,179)(86,180)(87,169)(88,170)(89,171)(90,172)(91,173)(92,174)(93,175)(94,176)(95,177)(96,178)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150), (1,148)(2,149)(3,150)(4,151)(5,152)(6,153)(7,154)(8,155)(9,156)(10,145)(11,146)(12,147)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,82)(26,83)(27,84)(28,73)(29,74)(30,75)(31,76)(32,77)(33,78)(34,79)(35,80)(36,81)(49,173)(50,174)(51,175)(52,176)(53,177)(54,178)(55,179)(56,180)(57,169)(58,170)(59,171)(60,172)(61,91)(62,92)(63,93)(64,94)(65,95)(66,96)(67,85)(68,86)(69,87)(70,88)(71,89)(72,90)(97,112)(98,113)(99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(106,109)(107,110)(108,111)(121,183)(122,184)(123,185)(124,186)(125,187)(126,188)(127,189)(128,190)(129,191)(130,192)(131,181)(132,182)(133,164)(134,165)(135,166)(136,167)(137,168)(138,157)(139,158)(140,159)(141,160)(142,161)(143,162)(144,163), (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)>;
 
G:=Group( (1,77)(2,78)(3,79)(4,80)(5,81)(6,82)(7,83)(8,84)(9,73)(10,74)(11,75)(12,76)(13,87)(14,88)(15,89)(16,90)(17,91)(18,92)(19,93)(20,94)(21,95)(22,96)(23,85)(24,86)(25,153)(26,154)(27,155)(28,156)(29,145)(30,146)(31,147)(32,148)(33,149)(34,150)(35,151)(36,152)(37,69)(38,70)(39,71)(40,72)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,163)(50,164)(51,165)(52,166)(53,167)(54,168)(55,157)(56,158)(57,159)(58,160)(59,161)(60,162)(97,190)(98,191)(99,192)(100,181)(101,182)(102,183)(103,184)(104,185)(105,186)(106,187)(107,188)(108,189)(109,125)(110,126)(111,127)(112,128)(113,129)(114,130)(115,131)(116,132)(117,121)(118,122)(119,123)(120,124)(133,174)(134,175)(135,176)(136,177)(137,178)(138,179)(139,180)(140,169)(141,170)(142,171)(143,172)(144,173), (1,20)(2,21)(3,22)(4,23)(5,24)(6,13)(7,14)(8,15)(9,16)(10,17)(11,18)(12,19)(25,69)(26,70)(27,71)(28,72)(29,61)(30,62)(31,63)(32,64)(33,65)(34,66)(35,67)(36,68)(37,153)(38,154)(39,155)(40,156)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,111)(50,112)(51,113)(52,114)(53,115)(54,116)(55,117)(56,118)(57,119)(58,120)(59,109)(60,110)(73,90)(74,91)(75,92)(76,93)(77,94)(78,95)(79,96)(80,85)(81,86)(82,87)(83,88)(84,89)(97,174)(98,175)(99,176)(100,177)(101,178)(102,179)(103,180)(104,169)(105,170)(106,171)(107,172)(108,173)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,163)(128,164)(129,165)(130,166)(131,167)(132,168)(133,190)(134,191)(135,192)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(142,187)(143,188)(144,189), (1,192)(2,181)(3,182)(4,183)(5,184)(6,185)(7,186)(8,187)(9,188)(10,189)(11,190)(12,191)(13,140)(14,141)(15,142)(16,143)(17,144)(18,133)(19,134)(20,135)(21,136)(22,137)(23,138)(24,139)(25,119)(26,120)(27,109)(28,110)(29,111)(30,112)(31,113)(32,114)(33,115)(34,116)(35,117)(36,118)(37,159)(38,160)(39,161)(40,162)(41,163)(42,164)(43,165)(44,166)(45,167)(46,168)(47,157)(48,158)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)(73,107)(74,108)(75,97)(76,98)(77,99)(78,100)(79,101)(80,102)(81,103)(82,104)(83,105)(84,106)(85,179)(86,180)(87,169)(88,170)(89,171)(90,172)(91,173)(92,174)(93,175)(94,176)(95,177)(96,178)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150), (1,148)(2,149)(3,150)(4,151)(5,152)(6,153)(7,154)(8,155)(9,156)(10,145)(11,146)(12,147)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,82)(26,83)(27,84)(28,73)(29,74)(30,75)(31,76)(32,77)(33,78)(34,79)(35,80)(36,81)(49,173)(50,174)(51,175)(52,176)(53,177)(54,178)(55,179)(56,180)(57,169)(58,170)(59,171)(60,172)(61,91)(62,92)(63,93)(64,94)(65,95)(66,96)(67,85)(68,86)(69,87)(70,88)(71,89)(72,90)(97,112)(98,113)(99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(106,109)(107,110)(108,111)(121,183)(122,184)(123,185)(124,186)(125,187)(126,188)(127,189)(128,190)(129,191)(130,192)(131,181)(132,182)(133,164)(134,165)(135,166)(136,167)(137,168)(138,157)(139,158)(140,159)(141,160)(142,161)(143,162)(144,163), (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) );
 
G=PermutationGroup([[(1,77),(2,78),(3,79),(4,80),(5,81),(6,82),(7,83),(8,84),(9,73),(10,74),(11,75),(12,76),(13,87),(14,88),(15,89),(16,90),(17,91),(18,92),(19,93),(20,94),(21,95),(22,96),(23,85),(24,86),(25,153),(26,154),(27,155),(28,156),(29,145),(30,146),(31,147),(32,148),(33,149),(34,150),(35,151),(36,152),(37,69),(38,70),(39,71),(40,72),(41,61),(42,62),(43,63),(44,64),(45,65),(46,66),(47,67),(48,68),(49,163),(50,164),(51,165),(52,166),(53,167),(54,168),(55,157),(56,158),(57,159),(58,160),(59,161),(60,162),(97,190),(98,191),(99,192),(100,181),(101,182),(102,183),(103,184),(104,185),(105,186),(106,187),(107,188),(108,189),(109,125),(110,126),(111,127),(112,128),(113,129),(114,130),(115,131),(116,132),(117,121),(118,122),(119,123),(120,124),(133,174),(134,175),(135,176),(136,177),(137,178),(138,179),(139,180),(140,169),(141,170),(142,171),(143,172),(144,173)], [(1,20),(2,21),(3,22),(4,23),(5,24),(6,13),(7,14),(8,15),(9,16),(10,17),(11,18),(12,19),(25,69),(26,70),(27,71),(28,72),(29,61),(30,62),(31,63),(32,64),(33,65),(34,66),(35,67),(36,68),(37,153),(38,154),(39,155),(40,156),(41,145),(42,146),(43,147),(44,148),(45,149),(46,150),(47,151),(48,152),(49,111),(50,112),(51,113),(52,114),(53,115),(54,116),(55,117),(56,118),(57,119),(58,120),(59,109),(60,110),(73,90),(74,91),(75,92),(76,93),(77,94),(78,95),(79,96),(80,85),(81,86),(82,87),(83,88),(84,89),(97,174),(98,175),(99,176),(100,177),(101,178),(102,179),(103,180),(104,169),(105,170),(106,171),(107,172),(108,173),(121,157),(122,158),(123,159),(124,160),(125,161),(126,162),(127,163),(128,164),(129,165),(130,166),(131,167),(132,168),(133,190),(134,191),(135,192),(136,181),(137,182),(138,183),(139,184),(140,185),(141,186),(142,187),(143,188),(144,189)], [(1,192),(2,181),(3,182),(4,183),(5,184),(6,185),(7,186),(8,187),(9,188),(10,189),(11,190),(12,191),(13,140),(14,141),(15,142),(16,143),(17,144),(18,133),(19,134),(20,135),(21,136),(22,137),(23,138),(24,139),(25,119),(26,120),(27,109),(28,110),(29,111),(30,112),(31,113),(32,114),(33,115),(34,116),(35,117),(36,118),(37,159),(38,160),(39,161),(40,162),(41,163),(42,164),(43,165),(44,166),(45,167),(46,168),(47,157),(48,158),(49,61),(50,62),(51,63),(52,64),(53,65),(54,66),(55,67),(56,68),(57,69),(58,70),(59,71),(60,72),(73,107),(74,108),(75,97),(76,98),(77,99),(78,100),(79,101),(80,102),(81,103),(82,104),(83,105),(84,106),(85,179),(86,180),(87,169),(88,170),(89,171),(90,172),(91,173),(92,174),(93,175),(94,176),(95,177),(96,178),(121,151),(122,152),(123,153),(124,154),(125,155),(126,156),(127,145),(128,146),(129,147),(130,148),(131,149),(132,150)], [(1,148),(2,149),(3,150),(4,151),(5,152),(6,153),(7,154),(8,155),(9,156),(10,145),(11,146),(12,147),(13,37),(14,38),(15,39),(16,40),(17,41),(18,42),(19,43),(20,44),(21,45),(22,46),(23,47),(24,48),(25,82),(26,83),(27,84),(28,73),(29,74),(30,75),(31,76),(32,77),(33,78),(34,79),(35,80),(36,81),(49,173),(50,174),(51,175),(52,176),(53,177),(54,178),(55,179),(56,180),(57,169),(58,170),(59,171),(60,172),(61,91),(62,92),(63,93),(64,94),(65,95),(66,96),(67,85),(68,86),(69,87),(70,88),(71,89),(72,90),(97,112),(98,113),(99,114),(100,115),(101,116),(102,117),(103,118),(104,119),(105,120),(106,109),(107,110),(108,111),(121,183),(122,184),(123,185),(124,186),(125,187),(126,188),(127,189),(128,190),(129,191),(130,192),(131,181),(132,182),(133,164),(134,165),(135,166),(136,167),(137,168),(138,157),(139,158),(140,159),(141,160),(142,161),(143,162),(144,163)], [(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)]])
 

192 conjugacy classes

class 1 2A···2AE3A3B4A···4AF6A···6BJ12A···12BL
order12···2334···46···612···12
size11···1111···11···11···1

192 irreducible representations

dim11111111
type+++
imageC1C2C2C3C4C6C6C12
kernelC24×C12C23×C12C24×C6C24×C4C23×C6C23×C4C25C24
# reps130123260264

Matrix representation of C24×C12 ►in GL5(𝔽13)

10000
01000
001200
000120
000012
,
120000
012000
001200
000120
00001
,
10000
012000
00100
00010
00001
,
10000
01000
00100
00010
000012
,
30000
05000
00800
000120
000012

G:=sub<GL(5,GF(13))| [1,0,0,0,0,0,1,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,12],[12,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,1],[1,0,0,0,0,0,12,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,12],[3,0,0,0,0,0,5,0,0,0,0,0,8,0,0,0,0,0,12,0,0,0,0,0,12] >;
 

C24×C12 in GAP, Magma, Sage, TeX 

C_2^4\times C_{12}
 
% in TeX
 
G:=Group("C2^4xC12");
 
// GroupNames label
 
G:=SmallGroup(192,1530);
 
// by ID
 
G=gap.SmallGroup(192,1530);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-2,672]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^12=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,d*e=e*d>;
 
// generators/relations
 

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