direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C23×C3⋊C8, C12.73C24, C24.8Dic3, C3⋊2(C23×C8), (C22×C6)⋊5C8, C6⋊2(C22×C8), C4.72(S3×C23), (C23×C6).10C4, (C23×C4).20S3, C6.40(C23×C4), (C22×C12).34C4, (C23×C12).20C2, (C22×C4).487D6, C2.1(C23×Dic3), C12.179(C22×C4), (C2×C12).883C23, (C22×C4).24Dic3, C23.48(C2×Dic3), C4.37(C22×Dic3), (C22×C12).568C22, C22.27(C22×Dic3), (C2×C6)⋊9(C2×C8), (C2×C12).321(C2×C4), (C22×C6).139(C2×C4), (C2×C6).204(C22×C4), (C2×C4).826(C22×S3), (C2×C4).105(C2×Dic3), SmallGroup(192,1339)
Series: Derived ►Chief ►Lower central ►Upper central
| C3 — C23×C3⋊C8 |
Subgroups: 440 in 338 conjugacy classes, 287 normal (11 characteristic)
C1, C2, C2 [×14], C3, C4, C4 [×7], C22 [×35], C6, C6 [×14], C8 [×8], C2×C4 [×28], C23 [×15], C12, C12 [×7], C2×C6 [×35], C2×C8 [×28], C22×C4 [×14], C24, C3⋊C8 [×8], C2×C12 [×28], C22×C6 [×15], C22×C8 [×14], C23×C4, C2×C3⋊C8 [×28], C22×C12 [×14], C23×C6, C23×C8, C22×C3⋊C8 [×14], C23×C12, C23×C3⋊C8
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], S3, C8 [×8], C2×C4 [×28], C23 [×15], Dic3 [×8], D6 [×7], C2×C8 [×28], C22×C4 [×14], C24, C3⋊C8 [×8], C2×Dic3 [×28], C22×S3 [×7], C22×C8 [×14], C23×C4, C2×C3⋊C8 [×28], C22×Dic3 [×14], S3×C23, C23×C8, C22×C3⋊C8 [×14], C23×Dic3, C23×C3⋊C8
Generators and relations
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 >
►Regular action on 192 points
Generators in S192
(1 121)(2 122)(3 123)(4 124)(5 125)(6 126)(7 127)(8 128)(9 86)(10 87)(11 88)(12 81)(13 82)(14 83)(15 84)(16 85)(17 171)(18 172)(19 173)(20 174)(21 175)(22 176)(23 169)(24 170)(25 135)(26 136)(27 129)(28 130)(29 131)(30 132)(31 133)(32 134)(33 189)(34 190)(35 191)(36 192)(37 185)(38 186)(39 187)(40 188)(41 69)(42 70)(43 71)(44 72)(45 65)(46 66)(47 67)(48 68)(49 105)(50 106)(51 107)(52 108)(53 109)(54 110)(55 111)(56 112)(57 113)(58 114)(59 115)(60 116)(61 117)(62 118)(63 119)(64 120)(73 162)(74 163)(75 164)(76 165)(77 166)(78 167)(79 168)(80 161)(89 151)(90 152)(91 145)(92 146)(93 147)(94 148)(95 149)(96 150)(97 184)(98 177)(99 178)(100 179)(101 180)(102 181)(103 182)(104 183)(137 160)(138 153)(139 154)(140 155)(141 156)(142 157)(143 158)(144 159)
(1 45)(2 46)(3 47)(4 48)(5 41)(6 42)(7 43)(8 44)(9 178)(10 179)(11 180)(12 181)(13 182)(14 183)(15 184)(16 177)(17 149)(18 150)(19 151)(20 152)(21 145)(22 146)(23 147)(24 148)(25 37)(26 38)(27 39)(28 40)(29 33)(30 34)(31 35)(32 36)(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)(65 121)(66 122)(67 123)(68 124)(69 125)(70 126)(71 127)(72 128)(73 117)(74 118)(75 119)(76 120)(77 113)(78 114)(79 115)(80 116)(81 102)(82 103)(83 104)(84 97)(85 98)(86 99)(87 100)(88 101)(89 173)(90 174)(91 175)(92 176)(93 169)(94 170)(95 171)(96 172)(105 141)(106 142)(107 143)(108 144)(109 137)(110 138)(111 139)(112 140)(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)(9 111)(10 112)(11 105)(12 106)(13 107)(14 108)(15 109)(16 110)(17 127)(18 128)(19 121)(20 122)(21 123)(22 124)(23 125)(24 126)(25 60)(26 61)(27 62)(28 63)(29 64)(30 57)(31 58)(32 59)(33 165)(34 166)(35 167)(36 168)(37 161)(38 162)(39 163)(40 164)(41 93)(42 94)(43 95)(44 96)(45 89)(46 90)(47 91)(48 92)(49 88)(50 81)(51 82)(52 83)(53 84)(54 85)(55 86)(56 87)(65 151)(66 152)(67 145)(68 146)(69 147)(70 148)(71 149)(72 150)(73 186)(74 187)(75 188)(76 189)(77 190)(78 191)(79 192)(80 185)(97 160)(98 153)(99 154)(100 155)(101 156)(102 157)(103 158)(104 159)(113 132)(114 133)(115 134)(116 135)(117 136)(118 129)(119 130)(120 131)(137 184)(138 177)(139 178)(140 179)(141 180)(142 181)(143 182)(144 183)
(1 51 27)(2 28 52)(3 53 29)(4 30 54)(5 55 31)(6 32 56)(7 49 25)(8 26 50)(9 114 23)(10 24 115)(11 116 17)(12 18 117)(13 118 19)(14 20 119)(15 120 21)(16 22 113)(33 47 160)(34 153 48)(35 41 154)(36 155 42)(37 43 156)(38 157 44)(39 45 158)(40 159 46)(57 85 176)(58 169 86)(59 87 170)(60 171 88)(61 81 172)(62 173 82)(63 83 174)(64 175 84)(65 143 187)(66 188 144)(67 137 189)(68 190 138)(69 139 191)(70 192 140)(71 141 185)(72 186 142)(73 181 150)(74 151 182)(75 183 152)(76 145 184)(77 177 146)(78 147 178)(79 179 148)(80 149 180)(89 103 163)(90 164 104)(91 97 165)(92 166 98)(93 99 167)(94 168 100)(95 101 161)(96 162 102)(105 135 127)(106 128 136)(107 129 121)(108 122 130)(109 131 123)(110 124 132)(111 133 125)(112 126 134)
(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)| (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,127)(8,128)(9,86)(10,87)(11,88)(12,81)(13,82)(14,83)(15,84)(16,85)(17,171)(18,172)(19,173)(20,174)(21,175)(22,176)(23,169)(24,170)(25,135)(26,136)(27,129)(28,130)(29,131)(30,132)(31,133)(32,134)(33,189)(34,190)(35,191)(36,192)(37,185)(38,186)(39,187)(40,188)(41,69)(42,70)(43,71)(44,72)(45,65)(46,66)(47,67)(48,68)(49,105)(50,106)(51,107)(52,108)(53,109)(54,110)(55,111)(56,112)(57,113)(58,114)(59,115)(60,116)(61,117)(62,118)(63,119)(64,120)(73,162)(74,163)(75,164)(76,165)(77,166)(78,167)(79,168)(80,161)(89,151)(90,152)(91,145)(92,146)(93,147)(94,148)(95,149)(96,150)(97,184)(98,177)(99,178)(100,179)(101,180)(102,181)(103,182)(104,183)(137,160)(138,153)(139,154)(140,155)(141,156)(142,157)(143,158)(144,159), (1,45)(2,46)(3,47)(4,48)(5,41)(6,42)(7,43)(8,44)(9,178)(10,179)(11,180)(12,181)(13,182)(14,183)(15,184)(16,177)(17,149)(18,150)(19,151)(20,152)(21,145)(22,146)(23,147)(24,148)(25,37)(26,38)(27,39)(28,40)(29,33)(30,34)(31,35)(32,36)(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)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,117)(74,118)(75,119)(76,120)(77,113)(78,114)(79,115)(80,116)(81,102)(82,103)(83,104)(84,97)(85,98)(86,99)(87,100)(88,101)(89,173)(90,174)(91,175)(92,176)(93,169)(94,170)(95,171)(96,172)(105,141)(106,142)(107,143)(108,144)(109,137)(110,138)(111,139)(112,140)(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)(9,111)(10,112)(11,105)(12,106)(13,107)(14,108)(15,109)(16,110)(17,127)(18,128)(19,121)(20,122)(21,123)(22,124)(23,125)(24,126)(25,60)(26,61)(27,62)(28,63)(29,64)(30,57)(31,58)(32,59)(33,165)(34,166)(35,167)(36,168)(37,161)(38,162)(39,163)(40,164)(41,93)(42,94)(43,95)(44,96)(45,89)(46,90)(47,91)(48,92)(49,88)(50,81)(51,82)(52,83)(53,84)(54,85)(55,86)(56,87)(65,151)(66,152)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,186)(74,187)(75,188)(76,189)(77,190)(78,191)(79,192)(80,185)(97,160)(98,153)(99,154)(100,155)(101,156)(102,157)(103,158)(104,159)(113,132)(114,133)(115,134)(116,135)(117,136)(118,129)(119,130)(120,131)(137,184)(138,177)(139,178)(140,179)(141,180)(142,181)(143,182)(144,183), (1,51,27)(2,28,52)(3,53,29)(4,30,54)(5,55,31)(6,32,56)(7,49,25)(8,26,50)(9,114,23)(10,24,115)(11,116,17)(12,18,117)(13,118,19)(14,20,119)(15,120,21)(16,22,113)(33,47,160)(34,153,48)(35,41,154)(36,155,42)(37,43,156)(38,157,44)(39,45,158)(40,159,46)(57,85,176)(58,169,86)(59,87,170)(60,171,88)(61,81,172)(62,173,82)(63,83,174)(64,175,84)(65,143,187)(66,188,144)(67,137,189)(68,190,138)(69,139,191)(70,192,140)(71,141,185)(72,186,142)(73,181,150)(74,151,182)(75,183,152)(76,145,184)(77,177,146)(78,147,178)(79,179,148)(80,149,180)(89,103,163)(90,164,104)(91,97,165)(92,166,98)(93,99,167)(94,168,100)(95,101,161)(96,162,102)(105,135,127)(106,128,136)(107,129,121)(108,122,130)(109,131,123)(110,124,132)(111,133,125)(112,126,134), (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( (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,127)(8,128)(9,86)(10,87)(11,88)(12,81)(13,82)(14,83)(15,84)(16,85)(17,171)(18,172)(19,173)(20,174)(21,175)(22,176)(23,169)(24,170)(25,135)(26,136)(27,129)(28,130)(29,131)(30,132)(31,133)(32,134)(33,189)(34,190)(35,191)(36,192)(37,185)(38,186)(39,187)(40,188)(41,69)(42,70)(43,71)(44,72)(45,65)(46,66)(47,67)(48,68)(49,105)(50,106)(51,107)(52,108)(53,109)(54,110)(55,111)(56,112)(57,113)(58,114)(59,115)(60,116)(61,117)(62,118)(63,119)(64,120)(73,162)(74,163)(75,164)(76,165)(77,166)(78,167)(79,168)(80,161)(89,151)(90,152)(91,145)(92,146)(93,147)(94,148)(95,149)(96,150)(97,184)(98,177)(99,178)(100,179)(101,180)(102,181)(103,182)(104,183)(137,160)(138,153)(139,154)(140,155)(141,156)(142,157)(143,158)(144,159), (1,45)(2,46)(3,47)(4,48)(5,41)(6,42)(7,43)(8,44)(9,178)(10,179)(11,180)(12,181)(13,182)(14,183)(15,184)(16,177)(17,149)(18,150)(19,151)(20,152)(21,145)(22,146)(23,147)(24,148)(25,37)(26,38)(27,39)(28,40)(29,33)(30,34)(31,35)(32,36)(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)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,117)(74,118)(75,119)(76,120)(77,113)(78,114)(79,115)(80,116)(81,102)(82,103)(83,104)(84,97)(85,98)(86,99)(87,100)(88,101)(89,173)(90,174)(91,175)(92,176)(93,169)(94,170)(95,171)(96,172)(105,141)(106,142)(107,143)(108,144)(109,137)(110,138)(111,139)(112,140)(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)(9,111)(10,112)(11,105)(12,106)(13,107)(14,108)(15,109)(16,110)(17,127)(18,128)(19,121)(20,122)(21,123)(22,124)(23,125)(24,126)(25,60)(26,61)(27,62)(28,63)(29,64)(30,57)(31,58)(32,59)(33,165)(34,166)(35,167)(36,168)(37,161)(38,162)(39,163)(40,164)(41,93)(42,94)(43,95)(44,96)(45,89)(46,90)(47,91)(48,92)(49,88)(50,81)(51,82)(52,83)(53,84)(54,85)(55,86)(56,87)(65,151)(66,152)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,186)(74,187)(75,188)(76,189)(77,190)(78,191)(79,192)(80,185)(97,160)(98,153)(99,154)(100,155)(101,156)(102,157)(103,158)(104,159)(113,132)(114,133)(115,134)(116,135)(117,136)(118,129)(119,130)(120,131)(137,184)(138,177)(139,178)(140,179)(141,180)(142,181)(143,182)(144,183), (1,51,27)(2,28,52)(3,53,29)(4,30,54)(5,55,31)(6,32,56)(7,49,25)(8,26,50)(9,114,23)(10,24,115)(11,116,17)(12,18,117)(13,118,19)(14,20,119)(15,120,21)(16,22,113)(33,47,160)(34,153,48)(35,41,154)(36,155,42)(37,43,156)(38,157,44)(39,45,158)(40,159,46)(57,85,176)(58,169,86)(59,87,170)(60,171,88)(61,81,172)(62,173,82)(63,83,174)(64,175,84)(65,143,187)(66,188,144)(67,137,189)(68,190,138)(69,139,191)(70,192,140)(71,141,185)(72,186,142)(73,181,150)(74,151,182)(75,183,152)(76,145,184)(77,177,146)(78,147,178)(79,179,148)(80,149,180)(89,103,163)(90,164,104)(91,97,165)(92,166,98)(93,99,167)(94,168,100)(95,101,161)(96,162,102)(105,135,127)(106,128,136)(107,129,121)(108,122,130)(109,131,123)(110,124,132)(111,133,125)(112,126,134), (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([(1,121),(2,122),(3,123),(4,124),(5,125),(6,126),(7,127),(8,128),(9,86),(10,87),(11,88),(12,81),(13,82),(14,83),(15,84),(16,85),(17,171),(18,172),(19,173),(20,174),(21,175),(22,176),(23,169),(24,170),(25,135),(26,136),(27,129),(28,130),(29,131),(30,132),(31,133),(32,134),(33,189),(34,190),(35,191),(36,192),(37,185),(38,186),(39,187),(40,188),(41,69),(42,70),(43,71),(44,72),(45,65),(46,66),(47,67),(48,68),(49,105),(50,106),(51,107),(52,108),(53,109),(54,110),(55,111),(56,112),(57,113),(58,114),(59,115),(60,116),(61,117),(62,118),(63,119),(64,120),(73,162),(74,163),(75,164),(76,165),(77,166),(78,167),(79,168),(80,161),(89,151),(90,152),(91,145),(92,146),(93,147),(94,148),(95,149),(96,150),(97,184),(98,177),(99,178),(100,179),(101,180),(102,181),(103,182),(104,183),(137,160),(138,153),(139,154),(140,155),(141,156),(142,157),(143,158),(144,159)], [(1,45),(2,46),(3,47),(4,48),(5,41),(6,42),(7,43),(8,44),(9,178),(10,179),(11,180),(12,181),(13,182),(14,183),(15,184),(16,177),(17,149),(18,150),(19,151),(20,152),(21,145),(22,146),(23,147),(24,148),(25,37),(26,38),(27,39),(28,40),(29,33),(30,34),(31,35),(32,36),(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),(65,121),(66,122),(67,123),(68,124),(69,125),(70,126),(71,127),(72,128),(73,117),(74,118),(75,119),(76,120),(77,113),(78,114),(79,115),(80,116),(81,102),(82,103),(83,104),(84,97),(85,98),(86,99),(87,100),(88,101),(89,173),(90,174),(91,175),(92,176),(93,169),(94,170),(95,171),(96,172),(105,141),(106,142),(107,143),(108,144),(109,137),(110,138),(111,139),(112,140),(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),(9,111),(10,112),(11,105),(12,106),(13,107),(14,108),(15,109),(16,110),(17,127),(18,128),(19,121),(20,122),(21,123),(22,124),(23,125),(24,126),(25,60),(26,61),(27,62),(28,63),(29,64),(30,57),(31,58),(32,59),(33,165),(34,166),(35,167),(36,168),(37,161),(38,162),(39,163),(40,164),(41,93),(42,94),(43,95),(44,96),(45,89),(46,90),(47,91),(48,92),(49,88),(50,81),(51,82),(52,83),(53,84),(54,85),(55,86),(56,87),(65,151),(66,152),(67,145),(68,146),(69,147),(70,148),(71,149),(72,150),(73,186),(74,187),(75,188),(76,189),(77,190),(78,191),(79,192),(80,185),(97,160),(98,153),(99,154),(100,155),(101,156),(102,157),(103,158),(104,159),(113,132),(114,133),(115,134),(116,135),(117,136),(118,129),(119,130),(120,131),(137,184),(138,177),(139,178),(140,179),(141,180),(142,181),(143,182),(144,183)], [(1,51,27),(2,28,52),(3,53,29),(4,30,54),(5,55,31),(6,32,56),(7,49,25),(8,26,50),(9,114,23),(10,24,115),(11,116,17),(12,18,117),(13,118,19),(14,20,119),(15,120,21),(16,22,113),(33,47,160),(34,153,48),(35,41,154),(36,155,42),(37,43,156),(38,157,44),(39,45,158),(40,159,46),(57,85,176),(58,169,86),(59,87,170),(60,171,88),(61,81,172),(62,173,82),(63,83,174),(64,175,84),(65,143,187),(66,188,144),(67,137,189),(68,190,138),(69,139,191),(70,192,140),(71,141,185),(72,186,142),(73,181,150),(74,151,182),(75,183,152),(76,145,184),(77,177,146),(78,147,178),(79,179,148),(80,149,180),(89,103,163),(90,164,104),(91,97,165),(92,166,98),(93,99,167),(94,168,100),(95,101,161),(96,162,102),(105,135,127),(106,128,136),(107,129,121),(108,122,130),(109,131,123),(110,124,132),(111,133,125),(112,126,134)], [(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(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] >;
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 |
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
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