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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

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

Generators and relations
 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 >

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

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

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

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

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

Matrix representation ►G ⊆ 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] >;
 

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

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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