direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C23×C3⋊C8, C12.73C24, C24.8Dic3, C3⋊2(C23×C8), C6⋊2(C22×C8), (C22×C6)⋊5C8, C6.40(C23×C4), (C23×C4).20S3, (C23×C6).10C4, C4.72(S3×C23), (C23×C12).20C2, (C22×C12).34C4, (C22×C4).487D6, C2.1(C23×Dic3), C12.179(C22×C4), (C2×C12).883C23, C4.37(C22×Dic3), C23.48(C2×Dic3), (C22×C4).24Dic3, (C22×C12).568C22, C22.27(C22×Dic3), (C2×C6)⋊9(C2×C8), (C2×C12).321(C2×C4), (C2×C4).826(C22×S3), (C2×C6).204(C22×C4), (C22×C6).139(C2×C4), (C2×C4).105(C2×Dic3), SmallGroup(192,1339)
Series: Derived ►Chief ►Lower central ►Upper central
| C3 — C23×C3⋊C8 |
Generators and relations for C23×C3⋊C8
G = < a,b,c,d,e | a2=b2=c2=d3=e8=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 440 in 338 conjugacy classes, 287 normal (11 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C8, C2×C4, C23, C12, C12, C2×C6, C2×C8, C22×C4, C24, C3⋊C8, C2×C12, C22×C6, C22×C8, C23×C4, C2×C3⋊C8, C22×C12, C23×C6, C23×C8, C22×C3⋊C8, C23×C12, C23×C3⋊C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, C23, Dic3, D6, C2×C8, C22×C4, C24, C3⋊C8, C2×Dic3, C22×S3, C22×C8, C23×C4, C2×C3⋊C8, C22×Dic3, S3×C23, C23×C8, C22×C3⋊C8, C23×Dic3, C23×C3⋊C8
►Regular action on 192 points
Generators in S192
(1 15)(2 16)(3 9)(4 10)(5 11)(6 12)(7 13)(8 14)(17 57)(18 58)(19 59)(20 60)(21 61)(22 62)(23 63)(24 64)(25 133)(26 134)(27 135)(28 136)(29 129)(30 130)(31 131)(32 132)(33 182)(34 183)(35 184)(36 177)(37 178)(38 179)(39 180)(40 181)(41 71)(42 72)(43 65)(44 66)(45 67)(46 68)(47 69)(48 70)(49 101)(50 102)(51 103)(52 104)(53 97)(54 98)(55 99)(56 100)(73 121)(74 122)(75 123)(76 124)(77 125)(78 126)(79 127)(80 128)(81 96)(82 89)(83 90)(84 91)(85 92)(86 93)(87 94)(88 95)(105 187)(106 188)(107 189)(108 190)(109 191)(110 192)(111 185)(112 186)(113 156)(114 157)(115 158)(116 159)(117 160)(118 153)(119 154)(120 155)(137 175)(138 176)(139 169)(140 170)(141 171)(142 172)(143 173)(144 174)(145 162)(146 163)(147 164)(148 165)(149 166)(150 167)(151 168)(152 161)
(1 43)(2 44)(3 45)(4 46)(5 47)(6 48)(7 41)(8 42)(9 67)(10 68)(11 69)(12 70)(13 71)(14 72)(15 65)(16 66)(17 149)(18 150)(19 151)(20 152)(21 145)(22 146)(23 147)(24 148)(25 109)(26 110)(27 111)(28 112)(29 105)(30 106)(31 107)(32 108)(33 79)(34 80)(35 73)(36 74)(37 75)(38 76)(39 77)(40 78)(49 156)(50 157)(51 158)(52 159)(53 160)(54 153)(55 154)(56 155)(57 166)(58 167)(59 168)(60 161)(61 162)(62 163)(63 164)(64 165)(81 142)(82 143)(83 144)(84 137)(85 138)(86 139)(87 140)(88 141)(89 173)(90 174)(91 175)(92 176)(93 169)(94 170)(95 171)(96 172)(97 117)(98 118)(99 119)(100 120)(101 113)(102 114)(103 115)(104 116)(121 184)(122 177)(123 178)(124 179)(125 180)(126 181)(127 182)(128 183)(129 187)(130 188)(131 189)(132 190)(133 191)(134 192)(135 185)(136 186)
(1 173)(2 174)(3 175)(4 176)(5 169)(6 170)(7 171)(8 172)(9 137)(10 138)(11 139)(12 140)(13 141)(14 142)(15 143)(16 144)(17 132)(18 133)(19 134)(20 135)(21 136)(22 129)(23 130)(24 131)(25 58)(26 59)(27 60)(28 61)(29 62)(30 63)(31 64)(32 57)(33 158)(34 159)(35 160)(36 153)(37 154)(38 155)(39 156)(40 157)(41 95)(42 96)(43 89)(44 90)(45 91)(46 92)(47 93)(48 94)(49 77)(50 78)(51 79)(52 80)(53 73)(54 74)(55 75)(56 76)(65 82)(66 83)(67 84)(68 85)(69 86)(70 87)(71 88)(72 81)(97 121)(98 122)(99 123)(100 124)(101 125)(102 126)(103 127)(104 128)(105 163)(106 164)(107 165)(108 166)(109 167)(110 168)(111 161)(112 162)(113 180)(114 181)(115 182)(116 183)(117 184)(118 177)(119 178)(120 179)(145 186)(146 187)(147 188)(148 189)(149 190)(150 191)(151 192)(152 185)
(1 51 29)(2 30 52)(3 53 31)(4 32 54)(5 55 25)(6 26 56)(7 49 27)(8 28 50)(9 97 131)(10 132 98)(11 99 133)(12 134 100)(13 101 135)(14 136 102)(15 103 129)(16 130 104)(17 122 138)(18 139 123)(19 124 140)(20 141 125)(21 126 142)(22 143 127)(23 128 144)(24 137 121)(33 163 89)(34 90 164)(35 165 91)(36 92 166)(37 167 93)(38 94 168)(39 161 95)(40 96 162)(41 156 111)(42 112 157)(43 158 105)(44 106 159)(45 160 107)(46 108 153)(47 154 109)(48 110 155)(57 74 176)(58 169 75)(59 76 170)(60 171 77)(61 78 172)(62 173 79)(63 80 174)(64 175 73)(65 115 187)(66 188 116)(67 117 189)(68 190 118)(69 119 191)(70 192 120)(71 113 185)(72 186 114)(81 145 181)(82 182 146)(83 147 183)(84 184 148)(85 149 177)(86 178 150)(87 151 179)(88 180 152)
(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)| (1,15)(2,16)(3,9)(4,10)(5,11)(6,12)(7,13)(8,14)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,133)(26,134)(27,135)(28,136)(29,129)(30,130)(31,131)(32,132)(33,182)(34,183)(35,184)(36,177)(37,178)(38,179)(39,180)(40,181)(41,71)(42,72)(43,65)(44,66)(45,67)(46,68)(47,69)(48,70)(49,101)(50,102)(51,103)(52,104)(53,97)(54,98)(55,99)(56,100)(73,121)(74,122)(75,123)(76,124)(77,125)(78,126)(79,127)(80,128)(81,96)(82,89)(83,90)(84,91)(85,92)(86,93)(87,94)(88,95)(105,187)(106,188)(107,189)(108,190)(109,191)(110,192)(111,185)(112,186)(113,156)(114,157)(115,158)(116,159)(117,160)(118,153)(119,154)(120,155)(137,175)(138,176)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,162)(146,163)(147,164)(148,165)(149,166)(150,167)(151,168)(152,161), (1,43)(2,44)(3,45)(4,46)(5,47)(6,48)(7,41)(8,42)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,65)(16,66)(17,149)(18,150)(19,151)(20,152)(21,145)(22,146)(23,147)(24,148)(25,109)(26,110)(27,111)(28,112)(29,105)(30,106)(31,107)(32,108)(33,79)(34,80)(35,73)(36,74)(37,75)(38,76)(39,77)(40,78)(49,156)(50,157)(51,158)(52,159)(53,160)(54,153)(55,154)(56,155)(57,166)(58,167)(59,168)(60,161)(61,162)(62,163)(63,164)(64,165)(81,142)(82,143)(83,144)(84,137)(85,138)(86,139)(87,140)(88,141)(89,173)(90,174)(91,175)(92,176)(93,169)(94,170)(95,171)(96,172)(97,117)(98,118)(99,119)(100,120)(101,113)(102,114)(103,115)(104,116)(121,184)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,185)(136,186), (1,173)(2,174)(3,175)(4,176)(5,169)(6,170)(7,171)(8,172)(9,137)(10,138)(11,139)(12,140)(13,141)(14,142)(15,143)(16,144)(17,132)(18,133)(19,134)(20,135)(21,136)(22,129)(23,130)(24,131)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,57)(33,158)(34,159)(35,160)(36,153)(37,154)(38,155)(39,156)(40,157)(41,95)(42,96)(43,89)(44,90)(45,91)(46,92)(47,93)(48,94)(49,77)(50,78)(51,79)(52,80)(53,73)(54,74)(55,75)(56,76)(65,82)(66,83)(67,84)(68,85)(69,86)(70,87)(71,88)(72,81)(97,121)(98,122)(99,123)(100,124)(101,125)(102,126)(103,127)(104,128)(105,163)(106,164)(107,165)(108,166)(109,167)(110,168)(111,161)(112,162)(113,180)(114,181)(115,182)(116,183)(117,184)(118,177)(119,178)(120,179)(145,186)(146,187)(147,188)(148,189)(149,190)(150,191)(151,192)(152,185), (1,51,29)(2,30,52)(3,53,31)(4,32,54)(5,55,25)(6,26,56)(7,49,27)(8,28,50)(9,97,131)(10,132,98)(11,99,133)(12,134,100)(13,101,135)(14,136,102)(15,103,129)(16,130,104)(17,122,138)(18,139,123)(19,124,140)(20,141,125)(21,126,142)(22,143,127)(23,128,144)(24,137,121)(33,163,89)(34,90,164)(35,165,91)(36,92,166)(37,167,93)(38,94,168)(39,161,95)(40,96,162)(41,156,111)(42,112,157)(43,158,105)(44,106,159)(45,160,107)(46,108,153)(47,154,109)(48,110,155)(57,74,176)(58,169,75)(59,76,170)(60,171,77)(61,78,172)(62,173,79)(63,80,174)(64,175,73)(65,115,187)(66,188,116)(67,117,189)(68,190,118)(69,119,191)(70,192,120)(71,113,185)(72,186,114)(81,145,181)(82,182,146)(83,147,183)(84,184,148)(85,149,177)(86,178,150)(87,151,179)(88,180,152), (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( (1,15)(2,16)(3,9)(4,10)(5,11)(6,12)(7,13)(8,14)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,133)(26,134)(27,135)(28,136)(29,129)(30,130)(31,131)(32,132)(33,182)(34,183)(35,184)(36,177)(37,178)(38,179)(39,180)(40,181)(41,71)(42,72)(43,65)(44,66)(45,67)(46,68)(47,69)(48,70)(49,101)(50,102)(51,103)(52,104)(53,97)(54,98)(55,99)(56,100)(73,121)(74,122)(75,123)(76,124)(77,125)(78,126)(79,127)(80,128)(81,96)(82,89)(83,90)(84,91)(85,92)(86,93)(87,94)(88,95)(105,187)(106,188)(107,189)(108,190)(109,191)(110,192)(111,185)(112,186)(113,156)(114,157)(115,158)(116,159)(117,160)(118,153)(119,154)(120,155)(137,175)(138,176)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,162)(146,163)(147,164)(148,165)(149,166)(150,167)(151,168)(152,161), (1,43)(2,44)(3,45)(4,46)(5,47)(6,48)(7,41)(8,42)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,65)(16,66)(17,149)(18,150)(19,151)(20,152)(21,145)(22,146)(23,147)(24,148)(25,109)(26,110)(27,111)(28,112)(29,105)(30,106)(31,107)(32,108)(33,79)(34,80)(35,73)(36,74)(37,75)(38,76)(39,77)(40,78)(49,156)(50,157)(51,158)(52,159)(53,160)(54,153)(55,154)(56,155)(57,166)(58,167)(59,168)(60,161)(61,162)(62,163)(63,164)(64,165)(81,142)(82,143)(83,144)(84,137)(85,138)(86,139)(87,140)(88,141)(89,173)(90,174)(91,175)(92,176)(93,169)(94,170)(95,171)(96,172)(97,117)(98,118)(99,119)(100,120)(101,113)(102,114)(103,115)(104,116)(121,184)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,185)(136,186), (1,173)(2,174)(3,175)(4,176)(5,169)(6,170)(7,171)(8,172)(9,137)(10,138)(11,139)(12,140)(13,141)(14,142)(15,143)(16,144)(17,132)(18,133)(19,134)(20,135)(21,136)(22,129)(23,130)(24,131)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,57)(33,158)(34,159)(35,160)(36,153)(37,154)(38,155)(39,156)(40,157)(41,95)(42,96)(43,89)(44,90)(45,91)(46,92)(47,93)(48,94)(49,77)(50,78)(51,79)(52,80)(53,73)(54,74)(55,75)(56,76)(65,82)(66,83)(67,84)(68,85)(69,86)(70,87)(71,88)(72,81)(97,121)(98,122)(99,123)(100,124)(101,125)(102,126)(103,127)(104,128)(105,163)(106,164)(107,165)(108,166)(109,167)(110,168)(111,161)(112,162)(113,180)(114,181)(115,182)(116,183)(117,184)(118,177)(119,178)(120,179)(145,186)(146,187)(147,188)(148,189)(149,190)(150,191)(151,192)(152,185), (1,51,29)(2,30,52)(3,53,31)(4,32,54)(5,55,25)(6,26,56)(7,49,27)(8,28,50)(9,97,131)(10,132,98)(11,99,133)(12,134,100)(13,101,135)(14,136,102)(15,103,129)(16,130,104)(17,122,138)(18,139,123)(19,124,140)(20,141,125)(21,126,142)(22,143,127)(23,128,144)(24,137,121)(33,163,89)(34,90,164)(35,165,91)(36,92,166)(37,167,93)(38,94,168)(39,161,95)(40,96,162)(41,156,111)(42,112,157)(43,158,105)(44,106,159)(45,160,107)(46,108,153)(47,154,109)(48,110,155)(57,74,176)(58,169,75)(59,76,170)(60,171,77)(61,78,172)(62,173,79)(63,80,174)(64,175,73)(65,115,187)(66,188,116)(67,117,189)(68,190,118)(69,119,191)(70,192,120)(71,113,185)(72,186,114)(81,145,181)(82,182,146)(83,147,183)(84,184,148)(85,149,177)(86,178,150)(87,151,179)(88,180,152), (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([[(1,15),(2,16),(3,9),(4,10),(5,11),(6,12),(7,13),(8,14),(17,57),(18,58),(19,59),(20,60),(21,61),(22,62),(23,63),(24,64),(25,133),(26,134),(27,135),(28,136),(29,129),(30,130),(31,131),(32,132),(33,182),(34,183),(35,184),(36,177),(37,178),(38,179),(39,180),(40,181),(41,71),(42,72),(43,65),(44,66),(45,67),(46,68),(47,69),(48,70),(49,101),(50,102),(51,103),(52,104),(53,97),(54,98),(55,99),(56,100),(73,121),(74,122),(75,123),(76,124),(77,125),(78,126),(79,127),(80,128),(81,96),(82,89),(83,90),(84,91),(85,92),(86,93),(87,94),(88,95),(105,187),(106,188),(107,189),(108,190),(109,191),(110,192),(111,185),(112,186),(113,156),(114,157),(115,158),(116,159),(117,160),(118,153),(119,154),(120,155),(137,175),(138,176),(139,169),(140,170),(141,171),(142,172),(143,173),(144,174),(145,162),(146,163),(147,164),(148,165),(149,166),(150,167),(151,168),(152,161)], [(1,43),(2,44),(3,45),(4,46),(5,47),(6,48),(7,41),(8,42),(9,67),(10,68),(11,69),(12,70),(13,71),(14,72),(15,65),(16,66),(17,149),(18,150),(19,151),(20,152),(21,145),(22,146),(23,147),(24,148),(25,109),(26,110),(27,111),(28,112),(29,105),(30,106),(31,107),(32,108),(33,79),(34,80),(35,73),(36,74),(37,75),(38,76),(39,77),(40,78),(49,156),(50,157),(51,158),(52,159),(53,160),(54,153),(55,154),(56,155),(57,166),(58,167),(59,168),(60,161),(61,162),(62,163),(63,164),(64,165),(81,142),(82,143),(83,144),(84,137),(85,138),(86,139),(87,140),(88,141),(89,173),(90,174),(91,175),(92,176),(93,169),(94,170),(95,171),(96,172),(97,117),(98,118),(99,119),(100,120),(101,113),(102,114),(103,115),(104,116),(121,184),(122,177),(123,178),(124,179),(125,180),(126,181),(127,182),(128,183),(129,187),(130,188),(131,189),(132,190),(133,191),(134,192),(135,185),(136,186)], [(1,173),(2,174),(3,175),(4,176),(5,169),(6,170),(7,171),(8,172),(9,137),(10,138),(11,139),(12,140),(13,141),(14,142),(15,143),(16,144),(17,132),(18,133),(19,134),(20,135),(21,136),(22,129),(23,130),(24,131),(25,58),(26,59),(27,60),(28,61),(29,62),(30,63),(31,64),(32,57),(33,158),(34,159),(35,160),(36,153),(37,154),(38,155),(39,156),(40,157),(41,95),(42,96),(43,89),(44,90),(45,91),(46,92),(47,93),(48,94),(49,77),(50,78),(51,79),(52,80),(53,73),(54,74),(55,75),(56,76),(65,82),(66,83),(67,84),(68,85),(69,86),(70,87),(71,88),(72,81),(97,121),(98,122),(99,123),(100,124),(101,125),(102,126),(103,127),(104,128),(105,163),(106,164),(107,165),(108,166),(109,167),(110,168),(111,161),(112,162),(113,180),(114,181),(115,182),(116,183),(117,184),(118,177),(119,178),(120,179),(145,186),(146,187),(147,188),(148,189),(149,190),(150,191),(151,192),(152,185)], [(1,51,29),(2,30,52),(3,53,31),(4,32,54),(5,55,25),(6,26,56),(7,49,27),(8,28,50),(9,97,131),(10,132,98),(11,99,133),(12,134,100),(13,101,135),(14,136,102),(15,103,129),(16,130,104),(17,122,138),(18,139,123),(19,124,140),(20,141,125),(21,126,142),(22,143,127),(23,128,144),(24,137,121),(33,163,89),(34,90,164),(35,165,91),(36,92,166),(37,167,93),(38,94,168),(39,161,95),(40,96,162),(41,156,111),(42,112,157),(43,158,105),(44,106,159),(45,160,107),(46,108,153),(47,154,109),(48,110,155),(57,74,176),(58,169,75),(59,76,170),(60,171,77),(61,78,172),(62,173,79),(63,80,174),(64,175,73),(65,115,187),(66,188,116),(67,117,189),(68,190,118),(69,119,191),(70,192,120),(71,113,185),(72,186,114),(81,145,181),(82,182,146),(83,147,183),(84,184,148),(85,149,177),(86,178,150),(87,151,179),(88,180,152)], [(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)]])
96 conjugacy classes
| class | 1 | 2A | ··· | 2O | 3 | 4A | ··· | 4P | 6A | ··· | 6O | 8A | ··· | 8AF | 12A | ··· | 12P |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 6 | ··· | 6 | 8 | ··· | 8 | 12 | ··· | 12 |
| size | 1 | 1 | ··· | 1 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 3 | ··· | 3 | 2 | ··· | 2 |
96 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | S3 | Dic3 | D6 | Dic3 | C3⋊C8 |
| kernel | C23×C3⋊C8 | C22×C3⋊C8 | C23×C12 | C22×C12 | C23×C6 | C22×C6 | C23×C4 | C22×C4 | C22×C4 | C24 | C23 |
| # reps | 1 | 14 | 1 | 14 | 2 | 32 | 1 | 7 | 7 | 1 | 16 |
Matrix representation of C23×C3⋊C8 ►in GL5(𝔽73)
| 72 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 72 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 0 | 72 |
| 72 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 0 | 72 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 |
| 0 | 0 | 0 | 1 | 72 |
| 51 | 0 | 0 | 0 | 0 |
| 0 | 27 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 22 | 41 |
| 0 | 0 | 0 | 63 | 51 |
G:=sub<GL(5,GF(73))| [72,0,0,0,0,0,72,0,0,0,0,0,72,0,0,0,0,0,1,0,0,0,0,0,1],[72,0,0,0,0,0,1,0,0,0,0,0,72,0,0,0,0,0,72,0,0,0,0,0,72],[72,0,0,0,0,0,72,0,0,0,0,0,72,0,0,0,0,0,72,0,0,0,0,0,72],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,72,72],[51,0,0,0,0,0,27,0,0,0,0,0,72,0,0,0,0,0,22,63,0,0,0,41,51] >;
C23×C3⋊C8 in GAP, Magma, Sage, TeX
C_2^3\times C_3\rtimes C_8
% in TeX
G:=Group("C2^3xC3:C8"); // GroupNames label
G:=SmallGroup(192,1339);
// by ID
G=gap.SmallGroup(192,1339);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,102,6278]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^3=e^8=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,e*d*e^-1=d^-1>;
// generators/relations