direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4⋊2D11, D4⋊5D22, C22.6C24, C44.20C23, D22.2C23, C23.19D22, Dic22⋊7C22, Dic11.3C23, (D4×C22)⋊6C2, (C2×D4)⋊8D11, C22⋊2(C4○D4), (C2×C4).60D22, (D4×C11)⋊6C22, (C4×D11)⋊4C22, C11⋊D4⋊2C22, (C2×C22).1C23, C2.7(C23×D11), (C2×Dic22)⋊12C2, (C2×C44).45C22, C4.20(C22×D11), (C2×Dic11)⋊9C22, (C22×Dic11)⋊8C2, C22.1(C22×D11), (C22×C22).23C22, (C22×D11).29C22, (C2×C4×D11)⋊4C2, C11⋊2(C2×C4○D4), (C2×C11⋊D4)⋊10C2, SmallGroup(352,178)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4⋊2D11
G = < a,b,c,d,e | a2=b4=c2=d11=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ece=b2c, ede=d-1 >
Subgroups: 778 in 164 conjugacy classes, 89 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C2×C4, C2×C4, D4, D4, Q8, C23, C23, C11, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, D11, C22, C22, C22, C2×C4○D4, Dic11, C44, D22, D22, C2×C22, C2×C22, C2×C22, Dic22, C4×D11, C2×Dic11, C2×Dic11, C11⋊D4, C2×C44, D4×C11, C22×D11, C22×C22, C2×Dic22, C2×C4×D11, D4⋊2D11, C22×Dic11, C2×C11⋊D4, D4×C22, C2×D4⋊2D11
Quotients: C1, C2, C22, C23, C4○D4, C24, D11, C2×C4○D4, D22, C22×D11, D4⋊2D11, C23×D11, C2×D4⋊2D11
►On 176 points
Generators in S176
(1 89)(2 90)(3 91)(4 92)(5 93)(6 94)(7 95)(8 96)(9 97)(10 98)(11 99)(12 100)(13 101)(14 102)(15 103)(16 104)(17 105)(18 106)(19 107)(20 108)(21 109)(22 110)(23 111)(24 112)(25 113)(26 114)(27 115)(28 116)(29 117)(30 118)(31 119)(32 120)(33 121)(34 122)(35 123)(36 124)(37 125)(38 126)(39 127)(40 128)(41 129)(42 130)(43 131)(44 132)(45 133)(46 134)(47 135)(48 136)(49 137)(50 138)(51 139)(52 140)(53 141)(54 142)(55 143)(56 144)(57 145)(58 146)(59 147)(60 148)(61 149)(62 150)(63 151)(64 152)(65 153)(66 154)(67 155)(68 156)(69 157)(70 158)(71 159)(72 160)(73 161)(74 162)(75 163)(76 164)(77 165)(78 166)(79 167)(80 168)(81 169)(82 170)(83 171)(84 172)(85 173)(86 174)(87 175)(88 176)
(1 56 12 45)(2 57 13 46)(3 58 14 47)(4 59 15 48)(5 60 16 49)(6 61 17 50)(7 62 18 51)(8 63 19 52)(9 64 20 53)(10 65 21 54)(11 66 22 55)(23 78 34 67)(24 79 35 68)(25 80 36 69)(26 81 37 70)(27 82 38 71)(28 83 39 72)(29 84 40 73)(30 85 41 74)(31 86 42 75)(32 87 43 76)(33 88 44 77)(89 144 100 133)(90 145 101 134)(91 146 102 135)(92 147 103 136)(93 148 104 137)(94 149 105 138)(95 150 106 139)(96 151 107 140)(97 152 108 141)(98 153 109 142)(99 154 110 143)(111 166 122 155)(112 167 123 156)(113 168 124 157)(114 169 125 158)(115 170 126 159)(116 171 127 160)(117 172 128 161)(118 173 129 162)(119 174 130 163)(120 175 131 164)(121 176 132 165)
(1 67)(2 68)(3 69)(4 70)(5 71)(6 72)(7 73)(8 74)(9 75)(10 76)(11 77)(12 78)(13 79)(14 80)(15 81)(16 82)(17 83)(18 84)(19 85)(20 86)(21 87)(22 88)(23 45)(24 46)(25 47)(26 48)(27 49)(28 50)(29 51)(30 52)(31 53)(32 54)(33 55)(34 56)(35 57)(36 58)(37 59)(38 60)(39 61)(40 62)(41 63)(42 64)(43 65)(44 66)(89 155)(90 156)(91 157)(92 158)(93 159)(94 160)(95 161)(96 162)(97 163)(98 164)(99 165)(100 166)(101 167)(102 168)(103 169)(104 170)(105 171)(106 172)(107 173)(108 174)(109 175)(110 176)(111 133)(112 134)(113 135)(114 136)(115 137)(116 138)(117 139)(118 140)(119 141)(120 142)(121 143)(122 144)(123 145)(124 146)(125 147)(126 148)(127 149)(128 150)(129 151)(130 152)(131 153)(132 154)
(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 11)(2 10)(3 9)(4 8)(5 7)(12 22)(13 21)(14 20)(15 19)(16 18)(23 44)(24 43)(25 42)(26 41)(27 40)(28 39)(29 38)(30 37)(31 36)(32 35)(33 34)(45 55)(46 54)(47 53)(48 52)(49 51)(56 66)(57 65)(58 64)(59 63)(60 62)(67 88)(68 87)(69 86)(70 85)(71 84)(72 83)(73 82)(74 81)(75 80)(76 79)(77 78)(89 99)(90 98)(91 97)(92 96)(93 95)(100 110)(101 109)(102 108)(103 107)(104 106)(111 132)(112 131)(113 130)(114 129)(115 128)(116 127)(117 126)(118 125)(119 124)(120 123)(121 122)(133 143)(134 142)(135 141)(136 140)(137 139)(144 154)(145 153)(146 152)(147 151)(148 150)(155 176)(156 175)(157 174)(158 173)(159 172)(160 171)(161 170)(162 169)(163 168)(164 167)(165 166)
G:=sub<Sym(176)| (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,97)(10,98)(11,99)(12,100)(13,101)(14,102)(15,103)(16,104)(17,105)(18,106)(19,107)(20,108)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,129)(42,130)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,148)(61,149)(62,150)(63,151)(64,152)(65,153)(66,154)(67,155)(68,156)(69,157)(70,158)(71,159)(72,160)(73,161)(74,162)(75,163)(76,164)(77,165)(78,166)(79,167)(80,168)(81,169)(82,170)(83,171)(84,172)(85,173)(86,174)(87,175)(88,176), (1,56,12,45)(2,57,13,46)(3,58,14,47)(4,59,15,48)(5,60,16,49)(6,61,17,50)(7,62,18,51)(8,63,19,52)(9,64,20,53)(10,65,21,54)(11,66,22,55)(23,78,34,67)(24,79,35,68)(25,80,36,69)(26,81,37,70)(27,82,38,71)(28,83,39,72)(29,84,40,73)(30,85,41,74)(31,86,42,75)(32,87,43,76)(33,88,44,77)(89,144,100,133)(90,145,101,134)(91,146,102,135)(92,147,103,136)(93,148,104,137)(94,149,105,138)(95,150,106,139)(96,151,107,140)(97,152,108,141)(98,153,109,142)(99,154,110,143)(111,166,122,155)(112,167,123,156)(113,168,124,157)(114,169,125,158)(115,170,126,159)(116,171,127,160)(117,172,128,161)(118,173,129,162)(119,174,130,163)(120,175,131,164)(121,176,132,165), (1,67)(2,68)(3,69)(4,70)(5,71)(6,72)(7,73)(8,74)(9,75)(10,76)(11,77)(12,78)(13,79)(14,80)(15,81)(16,82)(17,83)(18,84)(19,85)(20,86)(21,87)(22,88)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,51)(30,52)(31,53)(32,54)(33,55)(34,56)(35,57)(36,58)(37,59)(38,60)(39,61)(40,62)(41,63)(42,64)(43,65)(44,66)(89,155)(90,156)(91,157)(92,158)(93,159)(94,160)(95,161)(96,162)(97,163)(98,164)(99,165)(100,166)(101,167)(102,168)(103,169)(104,170)(105,171)(106,172)(107,173)(108,174)(109,175)(110,176)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,141)(120,142)(121,143)(122,144)(123,145)(124,146)(125,147)(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154), (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), (1,11)(2,10)(3,9)(4,8)(5,7)(12,22)(13,21)(14,20)(15,19)(16,18)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(45,55)(46,54)(47,53)(48,52)(49,51)(56,66)(57,65)(58,64)(59,63)(60,62)(67,88)(68,87)(69,86)(70,85)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(89,99)(90,98)(91,97)(92,96)(93,95)(100,110)(101,109)(102,108)(103,107)(104,106)(111,132)(112,131)(113,130)(114,129)(115,128)(116,127)(117,126)(118,125)(119,124)(120,123)(121,122)(133,143)(134,142)(135,141)(136,140)(137,139)(144,154)(145,153)(146,152)(147,151)(148,150)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)>;
G:=Group( (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,97)(10,98)(11,99)(12,100)(13,101)(14,102)(15,103)(16,104)(17,105)(18,106)(19,107)(20,108)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,129)(42,130)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,148)(61,149)(62,150)(63,151)(64,152)(65,153)(66,154)(67,155)(68,156)(69,157)(70,158)(71,159)(72,160)(73,161)(74,162)(75,163)(76,164)(77,165)(78,166)(79,167)(80,168)(81,169)(82,170)(83,171)(84,172)(85,173)(86,174)(87,175)(88,176), (1,56,12,45)(2,57,13,46)(3,58,14,47)(4,59,15,48)(5,60,16,49)(6,61,17,50)(7,62,18,51)(8,63,19,52)(9,64,20,53)(10,65,21,54)(11,66,22,55)(23,78,34,67)(24,79,35,68)(25,80,36,69)(26,81,37,70)(27,82,38,71)(28,83,39,72)(29,84,40,73)(30,85,41,74)(31,86,42,75)(32,87,43,76)(33,88,44,77)(89,144,100,133)(90,145,101,134)(91,146,102,135)(92,147,103,136)(93,148,104,137)(94,149,105,138)(95,150,106,139)(96,151,107,140)(97,152,108,141)(98,153,109,142)(99,154,110,143)(111,166,122,155)(112,167,123,156)(113,168,124,157)(114,169,125,158)(115,170,126,159)(116,171,127,160)(117,172,128,161)(118,173,129,162)(119,174,130,163)(120,175,131,164)(121,176,132,165), (1,67)(2,68)(3,69)(4,70)(5,71)(6,72)(7,73)(8,74)(9,75)(10,76)(11,77)(12,78)(13,79)(14,80)(15,81)(16,82)(17,83)(18,84)(19,85)(20,86)(21,87)(22,88)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,51)(30,52)(31,53)(32,54)(33,55)(34,56)(35,57)(36,58)(37,59)(38,60)(39,61)(40,62)(41,63)(42,64)(43,65)(44,66)(89,155)(90,156)(91,157)(92,158)(93,159)(94,160)(95,161)(96,162)(97,163)(98,164)(99,165)(100,166)(101,167)(102,168)(103,169)(104,170)(105,171)(106,172)(107,173)(108,174)(109,175)(110,176)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,141)(120,142)(121,143)(122,144)(123,145)(124,146)(125,147)(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154), (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), (1,11)(2,10)(3,9)(4,8)(5,7)(12,22)(13,21)(14,20)(15,19)(16,18)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(45,55)(46,54)(47,53)(48,52)(49,51)(56,66)(57,65)(58,64)(59,63)(60,62)(67,88)(68,87)(69,86)(70,85)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(89,99)(90,98)(91,97)(92,96)(93,95)(100,110)(101,109)(102,108)(103,107)(104,106)(111,132)(112,131)(113,130)(114,129)(115,128)(116,127)(117,126)(118,125)(119,124)(120,123)(121,122)(133,143)(134,142)(135,141)(136,140)(137,139)(144,154)(145,153)(146,152)(147,151)(148,150)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166) );
G=PermutationGroup([[(1,89),(2,90),(3,91),(4,92),(5,93),(6,94),(7,95),(8,96),(9,97),(10,98),(11,99),(12,100),(13,101),(14,102),(15,103),(16,104),(17,105),(18,106),(19,107),(20,108),(21,109),(22,110),(23,111),(24,112),(25,113),(26,114),(27,115),(28,116),(29,117),(30,118),(31,119),(32,120),(33,121),(34,122),(35,123),(36,124),(37,125),(38,126),(39,127),(40,128),(41,129),(42,130),(43,131),(44,132),(45,133),(46,134),(47,135),(48,136),(49,137),(50,138),(51,139),(52,140),(53,141),(54,142),(55,143),(56,144),(57,145),(58,146),(59,147),(60,148),(61,149),(62,150),(63,151),(64,152),(65,153),(66,154),(67,155),(68,156),(69,157),(70,158),(71,159),(72,160),(73,161),(74,162),(75,163),(76,164),(77,165),(78,166),(79,167),(80,168),(81,169),(82,170),(83,171),(84,172),(85,173),(86,174),(87,175),(88,176)], [(1,56,12,45),(2,57,13,46),(3,58,14,47),(4,59,15,48),(5,60,16,49),(6,61,17,50),(7,62,18,51),(8,63,19,52),(9,64,20,53),(10,65,21,54),(11,66,22,55),(23,78,34,67),(24,79,35,68),(25,80,36,69),(26,81,37,70),(27,82,38,71),(28,83,39,72),(29,84,40,73),(30,85,41,74),(31,86,42,75),(32,87,43,76),(33,88,44,77),(89,144,100,133),(90,145,101,134),(91,146,102,135),(92,147,103,136),(93,148,104,137),(94,149,105,138),(95,150,106,139),(96,151,107,140),(97,152,108,141),(98,153,109,142),(99,154,110,143),(111,166,122,155),(112,167,123,156),(113,168,124,157),(114,169,125,158),(115,170,126,159),(116,171,127,160),(117,172,128,161),(118,173,129,162),(119,174,130,163),(120,175,131,164),(121,176,132,165)], [(1,67),(2,68),(3,69),(4,70),(5,71),(6,72),(7,73),(8,74),(9,75),(10,76),(11,77),(12,78),(13,79),(14,80),(15,81),(16,82),(17,83),(18,84),(19,85),(20,86),(21,87),(22,88),(23,45),(24,46),(25,47),(26,48),(27,49),(28,50),(29,51),(30,52),(31,53),(32,54),(33,55),(34,56),(35,57),(36,58),(37,59),(38,60),(39,61),(40,62),(41,63),(42,64),(43,65),(44,66),(89,155),(90,156),(91,157),(92,158),(93,159),(94,160),(95,161),(96,162),(97,163),(98,164),(99,165),(100,166),(101,167),(102,168),(103,169),(104,170),(105,171),(106,172),(107,173),(108,174),(109,175),(110,176),(111,133),(112,134),(113,135),(114,136),(115,137),(116,138),(117,139),(118,140),(119,141),(120,142),(121,143),(122,144),(123,145),(124,146),(125,147),(126,148),(127,149),(128,150),(129,151),(130,152),(131,153),(132,154)], [(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)], [(1,11),(2,10),(3,9),(4,8),(5,7),(12,22),(13,21),(14,20),(15,19),(16,18),(23,44),(24,43),(25,42),(26,41),(27,40),(28,39),(29,38),(30,37),(31,36),(32,35),(33,34),(45,55),(46,54),(47,53),(48,52),(49,51),(56,66),(57,65),(58,64),(59,63),(60,62),(67,88),(68,87),(69,86),(70,85),(71,84),(72,83),(73,82),(74,81),(75,80),(76,79),(77,78),(89,99),(90,98),(91,97),(92,96),(93,95),(100,110),(101,109),(102,108),(103,107),(104,106),(111,132),(112,131),(113,130),(114,129),(115,128),(116,127),(117,126),(118,125),(119,124),(120,123),(121,122),(133,143),(134,142),(135,141),(136,140),(137,139),(144,154),(145,153),(146,152),(147,151),(148,150),(155,176),(156,175),(157,174),(158,173),(159,172),(160,171),(161,170),(162,169),(163,168),(164,167),(165,166)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 11A | ··· | 11E | 22A | ··· | 22O | 22P | ··· | 22AI | 44A | ··· | 44J |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 22 | 22 | 2 | 2 | 11 | 11 | 11 | 11 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4○D4 | D11 | D22 | D22 | D22 | D4⋊2D11 |
| kernel | C2×D4⋊2D11 | C2×Dic22 | C2×C4×D11 | D4⋊2D11 | C22×Dic11 | C2×C11⋊D4 | D4×C22 | C22 | C2×D4 | C2×C4 | D4 | C23 | C2 |
| # reps | 1 | 1 | 1 | 8 | 2 | 2 | 1 | 4 | 5 | 5 | 20 | 10 | 10 |
Matrix representation of C2×D4⋊2D11 ►in GL4(𝔽89) generated by
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 34 | 0 |
| 0 | 0 | 0 | 55 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 0 | 34 |
| 0 | 0 | 55 | 0 |
| 0 | 88 | 0 | 0 |
| 1 | 86 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 3 | 88 | 0 | 0 |
| 8 | 86 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 88 |
G:=sub<GL(4,GF(89))| [88,0,0,0,0,88,0,0,0,0,88,0,0,0,0,88],[88,0,0,0,0,88,0,0,0,0,34,0,0,0,0,55],[88,0,0,0,0,88,0,0,0,0,0,55,0,0,34,0],[0,1,0,0,88,86,0,0,0,0,1,0,0,0,0,1],[3,8,0,0,88,86,0,0,0,0,1,0,0,0,0,88] >;
C2×D4⋊2D11 in GAP, Magma, Sage, TeX
C_2\times D_4\rtimes_2D_{11} % in TeX
G:=Group("C2xD4:2D11"); // GroupNames label
G:=SmallGroup(352,178);
// by ID
G=gap.SmallGroup(352,178);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,86,579,159,11525]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^11=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^2*c,e*d*e=d^-1>;
// generators/relations