direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C23.D11, C24.D11, C23⋊2Dic11, C23.32D22, (C22×C22)⋊4C4, C22.62(C2×D4), (C2×C22).44D4, C22⋊2(C22⋊C4), (C23×C22).2C2, (C2×C22).60C23, C22.28(C22×C4), C22⋊2(C2×Dic11), (C22×Dic11)⋊7C2, (C2×Dic11)⋊7C22, C2.9(C22×Dic11), C22.25(C11⋊D4), (C22×C22).41C22, C22.27(C22×D11), (C2×C22)⋊8(C2×C4), C11⋊3(C2×C22⋊C4), C2.4(C2×C11⋊D4), SmallGroup(352,147)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C23.D11
G = < a,b,c,d,e,f | a2=b2=c2=d2=e11=1, f2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, fbf-1=bd=db, be=eb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e-1 >
Subgroups: 458 in 132 conjugacy classes, 65 normal (11 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C23, C23, C23, C11, C22⋊C4, C22×C4, C24, C22, C22, C22, C2×C22⋊C4, Dic11, C2×C22, C2×C22, C2×C22, C2×Dic11, C2×Dic11, C22×C22, C22×C22, C22×C22, C23.D11, C22×Dic11, C23×C22, C2×C23.D11
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, C22⋊C4, C22×C4, C2×D4, D11, C2×C22⋊C4, Dic11, D22, C2×Dic11, C11⋊D4, C22×D11, C23.D11, C22×Dic11, C2×C11⋊D4, C2×C23.D11
►On 176 points
Generators in S176
(1 78)(2 79)(3 80)(4 81)(5 82)(6 83)(7 84)(8 85)(9 86)(10 87)(11 88)(12 67)(13 68)(14 69)(15 70)(16 71)(17 72)(18 73)(19 74)(20 75)(21 76)(22 77)(23 56)(24 57)(25 58)(26 59)(27 60)(28 61)(29 62)(30 63)(31 64)(32 65)(33 66)(34 45)(35 46)(36 47)(37 48)(38 49)(39 50)(40 51)(41 52)(42 53)(43 54)(44 55)(89 166)(90 167)(91 168)(92 169)(93 170)(94 171)(95 172)(96 173)(97 174)(98 175)(99 176)(100 155)(101 156)(102 157)(103 158)(104 159)(105 160)(106 161)(107 162)(108 163)(109 164)(110 165)(111 144)(112 145)(113 146)(114 147)(115 148)(116 149)(117 150)(118 151)(119 152)(120 153)(121 154)(122 133)(123 134)(124 135)(125 136)(126 137)(127 138)(128 139)(129 140)(130 141)(131 142)(132 143)
(89 100)(90 101)(91 102)(92 103)(93 104)(94 105)(95 106)(96 107)(97 108)(98 109)(99 110)(111 122)(112 123)(113 124)(114 125)(115 126)(116 127)(117 128)(118 129)(119 130)(120 131)(121 132)(133 144)(134 145)(135 146)(136 147)(137 148)(138 149)(139 150)(140 151)(141 152)(142 153)(143 154)(155 166)(156 167)(157 168)(158 169)(159 170)(160 171)(161 172)(162 173)(163 174)(164 175)(165 176)
(1 23)(2 24)(3 25)(4 26)(5 27)(6 28)(7 29)(8 30)(9 31)(10 32)(11 33)(12 34)(13 35)(14 36)(15 37)(16 38)(17 39)(18 40)(19 41)(20 42)(21 43)(22 44)(45 67)(46 68)(47 69)(48 70)(49 71)(50 72)(51 73)(52 74)(53 75)(54 76)(55 77)(56 78)(57 79)(58 80)(59 81)(60 82)(61 83)(62 84)(63 85)(64 86)(65 87)(66 88)(89 111)(90 112)(91 113)(92 114)(93 115)(94 116)(95 117)(96 118)(97 119)(98 120)(99 121)(100 122)(101 123)(102 124)(103 125)(104 126)(105 127)(106 128)(107 129)(108 130)(109 131)(110 132)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 161)(140 162)(141 163)(142 164)(143 165)(144 166)(145 167)(146 168)(147 169)(148 170)(149 171)(150 172)(151 173)(152 174)(153 175)(154 176)
(1 12)(2 13)(3 14)(4 15)(5 16)(6 17)(7 18)(8 19)(9 20)(10 21)(11 22)(23 34)(24 35)(25 36)(26 37)(27 38)(28 39)(29 40)(30 41)(31 42)(32 43)(33 44)(45 56)(46 57)(47 58)(48 59)(49 60)(50 61)(51 62)(52 63)(53 64)(54 65)(55 66)(67 78)(68 79)(69 80)(70 81)(71 82)(72 83)(73 84)(74 85)(75 86)(76 87)(77 88)(89 100)(90 101)(91 102)(92 103)(93 104)(94 105)(95 106)(96 107)(97 108)(98 109)(99 110)(111 122)(112 123)(113 124)(114 125)(115 126)(116 127)(117 128)(118 129)(119 130)(120 131)(121 132)(133 144)(134 145)(135 146)(136 147)(137 148)(138 149)(139 150)(140 151)(141 152)(142 153)(143 154)(155 166)(156 167)(157 168)(158 169)(159 170)(160 171)(161 172)(162 173)(163 174)(164 175)(165 176)
(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)
(1 119 23 97)(2 118 24 96)(3 117 25 95)(4 116 26 94)(5 115 27 93)(6 114 28 92)(7 113 29 91)(8 112 30 90)(9 111 31 89)(10 121 32 99)(11 120 33 98)(12 130 34 108)(13 129 35 107)(14 128 36 106)(15 127 37 105)(16 126 38 104)(17 125 39 103)(18 124 40 102)(19 123 41 101)(20 122 42 100)(21 132 43 110)(22 131 44 109)(45 163 67 141)(46 162 68 140)(47 161 69 139)(48 160 70 138)(49 159 71 137)(50 158 72 136)(51 157 73 135)(52 156 74 134)(53 155 75 133)(54 165 76 143)(55 164 77 142)(56 174 78 152)(57 173 79 151)(58 172 80 150)(59 171 81 149)(60 170 82 148)(61 169 83 147)(62 168 84 146)(63 167 85 145)(64 166 86 144)(65 176 87 154)(66 175 88 153)
G:=sub<Sym(176)| (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,85)(9,86)(10,87)(11,88)(12,67)(13,68)(14,69)(15,70)(16,71)(17,72)(18,73)(19,74)(20,75)(21,76)(22,77)(23,56)(24,57)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,45)(35,46)(36,47)(37,48)(38,49)(39,50)(40,51)(41,52)(42,53)(43,54)(44,55)(89,166)(90,167)(91,168)(92,169)(93,170)(94,171)(95,172)(96,173)(97,174)(98,175)(99,176)(100,155)(101,156)(102,157)(103,158)(104,159)(105,160)(106,161)(107,162)(108,163)(109,164)(110,165)(111,144)(112,145)(113,146)(114,147)(115,148)(116,149)(117,150)(118,151)(119,152)(120,153)(121,154)(122,133)(123,134)(124,135)(125,136)(126,137)(127,138)(128,139)(129,140)(130,141)(131,142)(132,143), (89,100)(90,101)(91,102)(92,103)(93,104)(94,105)(95,106)(96,107)(97,108)(98,109)(99,110)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176), (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88)(89,111)(90,112)(91,113)(92,114)(93,115)(94,116)(95,117)(96,118)(97,119)(98,120)(99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)(145,167)(146,168)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)(153,175)(154,176), (1,12)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(67,78)(68,79)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(89,100)(90,101)(91,102)(92,103)(93,104)(94,105)(95,106)(96,107)(97,108)(98,109)(99,110)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176), (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), (1,119,23,97)(2,118,24,96)(3,117,25,95)(4,116,26,94)(5,115,27,93)(6,114,28,92)(7,113,29,91)(8,112,30,90)(9,111,31,89)(10,121,32,99)(11,120,33,98)(12,130,34,108)(13,129,35,107)(14,128,36,106)(15,127,37,105)(16,126,38,104)(17,125,39,103)(18,124,40,102)(19,123,41,101)(20,122,42,100)(21,132,43,110)(22,131,44,109)(45,163,67,141)(46,162,68,140)(47,161,69,139)(48,160,70,138)(49,159,71,137)(50,158,72,136)(51,157,73,135)(52,156,74,134)(53,155,75,133)(54,165,76,143)(55,164,77,142)(56,174,78,152)(57,173,79,151)(58,172,80,150)(59,171,81,149)(60,170,82,148)(61,169,83,147)(62,168,84,146)(63,167,85,145)(64,166,86,144)(65,176,87,154)(66,175,88,153)>;
G:=Group( (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,85)(9,86)(10,87)(11,88)(12,67)(13,68)(14,69)(15,70)(16,71)(17,72)(18,73)(19,74)(20,75)(21,76)(22,77)(23,56)(24,57)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,45)(35,46)(36,47)(37,48)(38,49)(39,50)(40,51)(41,52)(42,53)(43,54)(44,55)(89,166)(90,167)(91,168)(92,169)(93,170)(94,171)(95,172)(96,173)(97,174)(98,175)(99,176)(100,155)(101,156)(102,157)(103,158)(104,159)(105,160)(106,161)(107,162)(108,163)(109,164)(110,165)(111,144)(112,145)(113,146)(114,147)(115,148)(116,149)(117,150)(118,151)(119,152)(120,153)(121,154)(122,133)(123,134)(124,135)(125,136)(126,137)(127,138)(128,139)(129,140)(130,141)(131,142)(132,143), (89,100)(90,101)(91,102)(92,103)(93,104)(94,105)(95,106)(96,107)(97,108)(98,109)(99,110)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176), (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88)(89,111)(90,112)(91,113)(92,114)(93,115)(94,116)(95,117)(96,118)(97,119)(98,120)(99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)(145,167)(146,168)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)(153,175)(154,176), (1,12)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(67,78)(68,79)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(89,100)(90,101)(91,102)(92,103)(93,104)(94,105)(95,106)(96,107)(97,108)(98,109)(99,110)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176), (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), (1,119,23,97)(2,118,24,96)(3,117,25,95)(4,116,26,94)(5,115,27,93)(6,114,28,92)(7,113,29,91)(8,112,30,90)(9,111,31,89)(10,121,32,99)(11,120,33,98)(12,130,34,108)(13,129,35,107)(14,128,36,106)(15,127,37,105)(16,126,38,104)(17,125,39,103)(18,124,40,102)(19,123,41,101)(20,122,42,100)(21,132,43,110)(22,131,44,109)(45,163,67,141)(46,162,68,140)(47,161,69,139)(48,160,70,138)(49,159,71,137)(50,158,72,136)(51,157,73,135)(52,156,74,134)(53,155,75,133)(54,165,76,143)(55,164,77,142)(56,174,78,152)(57,173,79,151)(58,172,80,150)(59,171,81,149)(60,170,82,148)(61,169,83,147)(62,168,84,146)(63,167,85,145)(64,166,86,144)(65,176,87,154)(66,175,88,153) );
G=PermutationGroup([[(1,78),(2,79),(3,80),(4,81),(5,82),(6,83),(7,84),(8,85),(9,86),(10,87),(11,88),(12,67),(13,68),(14,69),(15,70),(16,71),(17,72),(18,73),(19,74),(20,75),(21,76),(22,77),(23,56),(24,57),(25,58),(26,59),(27,60),(28,61),(29,62),(30,63),(31,64),(32,65),(33,66),(34,45),(35,46),(36,47),(37,48),(38,49),(39,50),(40,51),(41,52),(42,53),(43,54),(44,55),(89,166),(90,167),(91,168),(92,169),(93,170),(94,171),(95,172),(96,173),(97,174),(98,175),(99,176),(100,155),(101,156),(102,157),(103,158),(104,159),(105,160),(106,161),(107,162),(108,163),(109,164),(110,165),(111,144),(112,145),(113,146),(114,147),(115,148),(116,149),(117,150),(118,151),(119,152),(120,153),(121,154),(122,133),(123,134),(124,135),(125,136),(126,137),(127,138),(128,139),(129,140),(130,141),(131,142),(132,143)], [(89,100),(90,101),(91,102),(92,103),(93,104),(94,105),(95,106),(96,107),(97,108),(98,109),(99,110),(111,122),(112,123),(113,124),(114,125),(115,126),(116,127),(117,128),(118,129),(119,130),(120,131),(121,132),(133,144),(134,145),(135,146),(136,147),(137,148),(138,149),(139,150),(140,151),(141,152),(142,153),(143,154),(155,166),(156,167),(157,168),(158,169),(159,170),(160,171),(161,172),(162,173),(163,174),(164,175),(165,176)], [(1,23),(2,24),(3,25),(4,26),(5,27),(6,28),(7,29),(8,30),(9,31),(10,32),(11,33),(12,34),(13,35),(14,36),(15,37),(16,38),(17,39),(18,40),(19,41),(20,42),(21,43),(22,44),(45,67),(46,68),(47,69),(48,70),(49,71),(50,72),(51,73),(52,74),(53,75),(54,76),(55,77),(56,78),(57,79),(58,80),(59,81),(60,82),(61,83),(62,84),(63,85),(64,86),(65,87),(66,88),(89,111),(90,112),(91,113),(92,114),(93,115),(94,116),(95,117),(96,118),(97,119),(98,120),(99,121),(100,122),(101,123),(102,124),(103,125),(104,126),(105,127),(106,128),(107,129),(108,130),(109,131),(110,132),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,161),(140,162),(141,163),(142,164),(143,165),(144,166),(145,167),(146,168),(147,169),(148,170),(149,171),(150,172),(151,173),(152,174),(153,175),(154,176)], [(1,12),(2,13),(3,14),(4,15),(5,16),(6,17),(7,18),(8,19),(9,20),(10,21),(11,22),(23,34),(24,35),(25,36),(26,37),(27,38),(28,39),(29,40),(30,41),(31,42),(32,43),(33,44),(45,56),(46,57),(47,58),(48,59),(49,60),(50,61),(51,62),(52,63),(53,64),(54,65),(55,66),(67,78),(68,79),(69,80),(70,81),(71,82),(72,83),(73,84),(74,85),(75,86),(76,87),(77,88),(89,100),(90,101),(91,102),(92,103),(93,104),(94,105),(95,106),(96,107),(97,108),(98,109),(99,110),(111,122),(112,123),(113,124),(114,125),(115,126),(116,127),(117,128),(118,129),(119,130),(120,131),(121,132),(133,144),(134,145),(135,146),(136,147),(137,148),(138,149),(139,150),(140,151),(141,152),(142,153),(143,154),(155,166),(156,167),(157,168),(158,169),(159,170),(160,171),(161,172),(162,173),(163,174),(164,175),(165,176)], [(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)], [(1,119,23,97),(2,118,24,96),(3,117,25,95),(4,116,26,94),(5,115,27,93),(6,114,28,92),(7,113,29,91),(8,112,30,90),(9,111,31,89),(10,121,32,99),(11,120,33,98),(12,130,34,108),(13,129,35,107),(14,128,36,106),(15,127,37,105),(16,126,38,104),(17,125,39,103),(18,124,40,102),(19,123,41,101),(20,122,42,100),(21,132,43,110),(22,131,44,109),(45,163,67,141),(46,162,68,140),(47,161,69,139),(48,160,70,138),(49,159,71,137),(50,158,72,136),(51,157,73,135),(52,156,74,134),(53,155,75,133),(54,165,76,143),(55,164,77,142),(56,174,78,152),(57,173,79,151),(58,172,80,150),(59,171,81,149),(60,170,82,148),(61,169,83,147),(62,168,84,146),(63,167,85,145),(64,166,86,144),(65,176,87,154),(66,175,88,153)]])
100 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 11A | ··· | 11E | 22A | ··· | 22BW |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 11 | ··· | 11 | 22 | ··· | 22 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 22 | ··· | 22 | 2 | ··· | 2 | 2 | ··· | 2 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C4 | D4 | D11 | Dic11 | D22 | C11⋊D4 |
| kernel | C2×C23.D11 | C23.D11 | C22×Dic11 | C23×C22 | C22×C22 | C2×C22 | C24 | C23 | C23 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 4 | 5 | 20 | 15 | 40 |
Matrix representation of C2×C23.D11 ►in GL4(𝔽89) generated by
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 88 |
| 88 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 45 | 0 |
| 0 | 0 | 0 | 2 |
| 34 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 2 |
| 0 | 0 | 44 | 0 |
G:=sub<GL(4,GF(89))| [88,0,0,0,0,88,0,0,0,0,1,0,0,0,0,1],[88,0,0,0,0,88,0,0,0,0,1,0,0,0,0,88],[88,0,0,0,0,1,0,0,0,0,88,0,0,0,0,88],[1,0,0,0,0,1,0,0,0,0,88,0,0,0,0,88],[1,0,0,0,0,1,0,0,0,0,45,0,0,0,0,2],[34,0,0,0,0,1,0,0,0,0,0,44,0,0,2,0] >;
C2×C23.D11 in GAP, Magma, Sage, TeX
C_2\times C_2^3.D_{11} % in TeX
G:=Group("C2xC2^3.D11"); // GroupNames label
G:=SmallGroup(352,147);
// by ID
G=gap.SmallGroup(352,147);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,48,362,11525]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^11=1,f^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,f*b*f^-1=b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=e^-1>;
// generators/relations