Copied to
clipboard

G = C24×D11  order 352 = 25·11

Direct product of C24 and D11

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C24×D11, C11⋊C25, C22⋊C24, (C23×C22)⋊5C2, (C2×C22)⋊4C23, (C22×C22)⋊8C22, SmallGroup(352,194)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C11 — C24×D11
Chief series
C1 — C11 — D11 — D22 — C22×D11 — C23×D11 — C24×D11
Lower central
C11 — C24×D11
Upper central
C1 — C24

Generators and relations for C24×D11
 G = < a,b,c,d,e,f | a2=b2=c2=d2=e11=f2=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef=e-1 >

Subgroups: 3818 in 748 conjugacy classes, 441 normal (5 characteristic)
C1, C2, C2, C22, C22, C23, C23, C11, C24, C24, D11, C22, C25, D22, C2×C22, C22×D11, C22×C22, C23×D11, C23×C22, C24×D11
Quotients: C1, C2, C22, C23, C24, D11, C25, D22, C22×D11, C23×D11, C24×D11

Smallest permutation representation of C24×D11
►On 176 points
Generators in S176
(1 175)(2 176)(3 166)(4 167)(5 168)(6 169)(7 170)(8 171)(9 172)(10 173)(11 174)(12 155)(13 156)(14 157)(15 158)(16 159)(17 160)(18 161)(19 162)(20 163)(21 164)(22 165)(23 144)(24 145)(25 146)(26 147)(27 148)(28 149)(29 150)(30 151)(31 152)(32 153)(33 154)(34 133)(35 134)(36 135)(37 136)(38 137)(39 138)(40 139)(41 140)(42 141)(43 142)(44 143)(45 122)(46 123)(47 124)(48 125)(49 126)(50 127)(51 128)(52 129)(53 130)(54 131)(55 132)(56 111)(57 112)(58 113)(59 114)(60 115)(61 116)(62 117)(63 118)(64 119)(65 120)(66 121)(67 100)(68 101)(69 102)(70 103)(71 104)(72 105)(73 106)(74 107)(75 108)(76 109)(77 110)(78 89)(79 90)(80 91)(81 92)(82 93)(83 94)(84 95)(85 96)(86 97)(87 98)(88 99)

(1 87)(2 88)(3 78)(4 79)(5 80)(6 81)(7 82)(8 83)(9 84)(10 85)(11 86)(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)

(1 32)(2 33)(3 23)(4 24)(5 25)(6 26)(7 27)(8 28)(9 29)(10 30)(11 31)(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 21)(2 22)(3 12)(4 13)(5 14)(6 15)(7 16)(8 17)(9 18)(10 19)(11 20)(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)

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

112 conjugacy classes

class 1 2A···2O2P···2AE11A···11E22A···22BW
order12···22···211···1122···22
size11···111···112···22···2

112 irreducible representations

dim11122
type+++++
imageC1C2C2D11D22
kernelC24×D11C23×D11C23×C22C24C23
# reps1301575

Matrix representation of C24×D11 ►in GL5(𝔽23)

220000
01000
002200
00010
00001
,
220000
01000
002200
000220
000022
,
220000
01000
00100
00010
00001
,
10000
022000
00100
00010
00001
,
10000
01000
00100
00081
000152
,
10000
01000
002200
0001913
000134

G:=sub<GL(5,GF(23))| [22,0,0,0,0,0,1,0,0,0,0,0,22,0,0,0,0,0,1,0,0,0,0,0,1],[22,0,0,0,0,0,1,0,0,0,0,0,22,0,0,0,0,0,22,0,0,0,0,0,22],[22,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,22,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,8,15,0,0,0,1,2],[1,0,0,0,0,0,1,0,0,0,0,0,22,0,0,0,0,0,19,13,0,0,0,13,4] >;
 

C24×D11 in GAP, Magma, Sage, TeX 

C_2^4\times D_{11}
 
% in TeX
 
G:=Group("C2^4xD11");
 
// GroupNames label
 
G:=SmallGroup(352,194);
 
// by ID
 
G=gap.SmallGroup(352,194);
 
# by ID
 
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,11525]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^11=f^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f=e^-1>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁