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G = C24×C12order 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

C1 — C24×C12
C1C2C6C12C2×C12C22×C12C23×C12 — C24×C12
C1 — C24×C12
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 [×30], C3, C4 [×16], C22 [×155], C6, C6 [×30], C2×C4 [×120], C23 [×155], C12 [×16], C2×C6 [×155], C22×C4 [×140], C24 [×31], C2×C12 [×120], C22×C6 [×155], C23×C4 [×30], C25, C22×C12 [×140], C23×C6 [×31], C24×C4, C23×C12 [×30], C24×C6, C24×C12
Quotients: C1, C2 [×31], C3, C4 [×16], C22 [×155], C6 [×31], C2×C4 [×120], C23 [×155], C12 [×16], C2×C6 [×155], C22×C4 [×140], C24 [×31], C2×C12 [×120], C22×C6 [×155], C23×C4 [×30], C25, C22×C12 [×140], C23×C6 [×31], C24×C4, C23×C12 [×30], C24×C6, C24×C12

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