direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C11⋊D4, C23⋊4D22, C24⋊2D11, D22⋊3C23, C22.15C24, Dic11⋊2C23, (C2×C22)⋊9D4, C22⋊3(C2×D4), C11⋊3(C22×D4), (C23×C22)⋊4C2, (C2×C22)⋊3C23, (C23×D11)⋊5C2, (C22×C22)⋊7C22, C2.15(C23×D11), C22⋊2(C22×D11), (C22×Dic11)⋊9C2, (C22×D11)⋊7C22, (C2×Dic11)⋊11C22, SmallGroup(352,187)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22×C11⋊D4
G = < a,b,c,d,e | a2=b2=c11=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=ece=c-1, ede=d-1 >
Subgroups: 1226 in 236 conjugacy classes, 105 normal (11 characteristic)
C1, C2, C2, C2, C4, C22, C22, C2×C4, D4, C23, C23, C23, C11, C22×C4, C2×D4, C24, C24, D11, C22, C22, C22, C22×D4, Dic11, D22, D22, C2×C22, C2×C22, C2×Dic11, C11⋊D4, C22×D11, C22×D11, C22×C22, C22×C22, C22×C22, C22×Dic11, C2×C11⋊D4, C23×D11, C23×C22, C22×C11⋊D4
Quotients: C1, C2, C22, D4, C23, C2×D4, C24, D11, C22×D4, D22, C11⋊D4, C22×D11, C2×C11⋊D4, C23×D11, C22×C11⋊D4
►On 176 points
Generators in S176
(1 100)(2 101)(3 102)(4 103)(5 104)(6 105)(7 106)(8 107)(9 108)(10 109)(11 110)(12 89)(13 90)(14 91)(15 92)(16 93)(17 94)(18 95)(19 96)(20 97)(21 98)(22 99)(23 122)(24 123)(25 124)(26 125)(27 126)(28 127)(29 128)(30 129)(31 130)(32 131)(33 132)(34 111)(35 112)(36 113)(37 114)(38 115)(39 116)(40 117)(41 118)(42 119)(43 120)(44 121)(45 144)(46 145)(47 146)(48 147)(49 148)(50 149)(51 150)(52 151)(53 152)(54 153)(55 154)(56 133)(57 134)(58 135)(59 136)(60 137)(61 138)(62 139)(63 140)(64 141)(65 142)(66 143)(67 166)(68 167)(69 168)(70 169)(71 170)(72 171)(73 172)(74 173)(75 174)(76 175)(77 176)(78 155)(79 156)(80 157)(81 158)(82 159)(83 160)(84 161)(85 162)(86 163)(87 164)(88 165)
(1 56)(2 57)(3 58)(4 59)(5 60)(6 61)(7 62)(8 63)(9 64)(10 65)(11 66)(12 45)(13 46)(14 47)(15 48)(16 49)(17 50)(18 51)(19 52)(20 53)(21 54)(22 55)(23 78)(24 79)(25 80)(26 81)(27 82)(28 83)(29 84)(30 85)(31 86)(32 87)(33 88)(34 67)(35 68)(36 69)(37 70)(38 71)(39 72)(40 73)(41 74)(42 75)(43 76)(44 77)(89 144)(90 145)(91 146)(92 147)(93 148)(94 149)(95 150)(96 151)(97 152)(98 153)(99 154)(100 133)(101 134)(102 135)(103 136)(104 137)(105 138)(106 139)(107 140)(108 141)(109 142)(110 143)(111 166)(112 167)(113 168)(114 169)(115 170)(116 171)(117 172)(118 173)(119 174)(120 175)(121 176)(122 155)(123 156)(124 157)(125 158)(126 159)(127 160)(128 161)(129 162)(130 163)(131 164)(132 165)
(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)
(1 111 12 122)(2 121 13 132)(3 120 14 131)(4 119 15 130)(5 118 16 129)(6 117 17 128)(7 116 18 127)(8 115 19 126)(9 114 20 125)(10 113 21 124)(11 112 22 123)(23 100 34 89)(24 110 35 99)(25 109 36 98)(26 108 37 97)(27 107 38 96)(28 106 39 95)(29 105 40 94)(30 104 41 93)(31 103 42 92)(32 102 43 91)(33 101 44 90)(45 155 56 166)(46 165 57 176)(47 164 58 175)(48 163 59 174)(49 162 60 173)(50 161 61 172)(51 160 62 171)(52 159 63 170)(53 158 64 169)(54 157 65 168)(55 156 66 167)(67 144 78 133)(68 154 79 143)(69 153 80 142)(70 152 81 141)(71 151 82 140)(72 150 83 139)(73 149 84 138)(74 148 85 137)(75 147 86 136)(76 146 87 135)(77 145 88 134)
(1 133)(2 143)(3 142)(4 141)(5 140)(6 139)(7 138)(8 137)(9 136)(10 135)(11 134)(12 144)(13 154)(14 153)(15 152)(16 151)(17 150)(18 149)(19 148)(20 147)(21 146)(22 145)(23 166)(24 176)(25 175)(26 174)(27 173)(28 172)(29 171)(30 170)(31 169)(32 168)(33 167)(34 155)(35 165)(36 164)(37 163)(38 162)(39 161)(40 160)(41 159)(42 158)(43 157)(44 156)(45 89)(46 99)(47 98)(48 97)(49 96)(50 95)(51 94)(52 93)(53 92)(54 91)(55 90)(56 100)(57 110)(58 109)(59 108)(60 107)(61 106)(62 105)(63 104)(64 103)(65 102)(66 101)(67 122)(68 132)(69 131)(70 130)(71 129)(72 128)(73 127)(74 126)(75 125)(76 124)(77 123)(78 111)(79 121)(80 120)(81 119)(82 118)(83 117)(84 116)(85 115)(86 114)(87 113)(88 112)
G:=sub<Sym(176)| (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,109)(11,110)(12,89)(13,90)(14,91)(15,92)(16,93)(17,94)(18,95)(19,96)(20,97)(21,98)(22,99)(23,122)(24,123)(25,124)(26,125)(27,126)(28,127)(29,128)(30,129)(31,130)(32,131)(33,132)(34,111)(35,112)(36,113)(37,114)(38,115)(39,116)(40,117)(41,118)(42,119)(43,120)(44,121)(45,144)(46,145)(47,146)(48,147)(49,148)(50,149)(51,150)(52,151)(53,152)(54,153)(55,154)(56,133)(57,134)(58,135)(59,136)(60,137)(61,138)(62,139)(63,140)(64,141)(65,142)(66,143)(67,166)(68,167)(69,168)(70,169)(71,170)(72,171)(73,172)(74,173)(75,174)(76,175)(77,176)(78,155)(79,156)(80,157)(81,158)(82,159)(83,160)(84,161)(85,162)(86,163)(87,164)(88,165), (1,56)(2,57)(3,58)(4,59)(5,60)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,45)(13,46)(14,47)(15,48)(16,49)(17,50)(18,51)(19,52)(20,53)(21,54)(22,55)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,152)(98,153)(99,154)(100,133)(101,134)(102,135)(103,136)(104,137)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)(111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,155)(123,156)(124,157)(125,158)(126,159)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165), (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), (1,111,12,122)(2,121,13,132)(3,120,14,131)(4,119,15,130)(5,118,16,129)(6,117,17,128)(7,116,18,127)(8,115,19,126)(9,114,20,125)(10,113,21,124)(11,112,22,123)(23,100,34,89)(24,110,35,99)(25,109,36,98)(26,108,37,97)(27,107,38,96)(28,106,39,95)(29,105,40,94)(30,104,41,93)(31,103,42,92)(32,102,43,91)(33,101,44,90)(45,155,56,166)(46,165,57,176)(47,164,58,175)(48,163,59,174)(49,162,60,173)(50,161,61,172)(51,160,62,171)(52,159,63,170)(53,158,64,169)(54,157,65,168)(55,156,66,167)(67,144,78,133)(68,154,79,143)(69,153,80,142)(70,152,81,141)(71,151,82,140)(72,150,83,139)(73,149,84,138)(74,148,85,137)(75,147,86,136)(76,146,87,135)(77,145,88,134), (1,133)(2,143)(3,142)(4,141)(5,140)(6,139)(7,138)(8,137)(9,136)(10,135)(11,134)(12,144)(13,154)(14,153)(15,152)(16,151)(17,150)(18,149)(19,148)(20,147)(21,146)(22,145)(23,166)(24,176)(25,175)(26,174)(27,173)(28,172)(29,171)(30,170)(31,169)(32,168)(33,167)(34,155)(35,165)(36,164)(37,163)(38,162)(39,161)(40,160)(41,159)(42,158)(43,157)(44,156)(45,89)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,100)(57,110)(58,109)(59,108)(60,107)(61,106)(62,105)(63,104)(64,103)(65,102)(66,101)(67,122)(68,132)(69,131)(70,130)(71,129)(72,128)(73,127)(74,126)(75,125)(76,124)(77,123)(78,111)(79,121)(80,120)(81,119)(82,118)(83,117)(84,116)(85,115)(86,114)(87,113)(88,112)>;
G:=Group( (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,109)(11,110)(12,89)(13,90)(14,91)(15,92)(16,93)(17,94)(18,95)(19,96)(20,97)(21,98)(22,99)(23,122)(24,123)(25,124)(26,125)(27,126)(28,127)(29,128)(30,129)(31,130)(32,131)(33,132)(34,111)(35,112)(36,113)(37,114)(38,115)(39,116)(40,117)(41,118)(42,119)(43,120)(44,121)(45,144)(46,145)(47,146)(48,147)(49,148)(50,149)(51,150)(52,151)(53,152)(54,153)(55,154)(56,133)(57,134)(58,135)(59,136)(60,137)(61,138)(62,139)(63,140)(64,141)(65,142)(66,143)(67,166)(68,167)(69,168)(70,169)(71,170)(72,171)(73,172)(74,173)(75,174)(76,175)(77,176)(78,155)(79,156)(80,157)(81,158)(82,159)(83,160)(84,161)(85,162)(86,163)(87,164)(88,165), (1,56)(2,57)(3,58)(4,59)(5,60)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,45)(13,46)(14,47)(15,48)(16,49)(17,50)(18,51)(19,52)(20,53)(21,54)(22,55)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,152)(98,153)(99,154)(100,133)(101,134)(102,135)(103,136)(104,137)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)(111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,155)(123,156)(124,157)(125,158)(126,159)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165), (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), (1,111,12,122)(2,121,13,132)(3,120,14,131)(4,119,15,130)(5,118,16,129)(6,117,17,128)(7,116,18,127)(8,115,19,126)(9,114,20,125)(10,113,21,124)(11,112,22,123)(23,100,34,89)(24,110,35,99)(25,109,36,98)(26,108,37,97)(27,107,38,96)(28,106,39,95)(29,105,40,94)(30,104,41,93)(31,103,42,92)(32,102,43,91)(33,101,44,90)(45,155,56,166)(46,165,57,176)(47,164,58,175)(48,163,59,174)(49,162,60,173)(50,161,61,172)(51,160,62,171)(52,159,63,170)(53,158,64,169)(54,157,65,168)(55,156,66,167)(67,144,78,133)(68,154,79,143)(69,153,80,142)(70,152,81,141)(71,151,82,140)(72,150,83,139)(73,149,84,138)(74,148,85,137)(75,147,86,136)(76,146,87,135)(77,145,88,134), (1,133)(2,143)(3,142)(4,141)(5,140)(6,139)(7,138)(8,137)(9,136)(10,135)(11,134)(12,144)(13,154)(14,153)(15,152)(16,151)(17,150)(18,149)(19,148)(20,147)(21,146)(22,145)(23,166)(24,176)(25,175)(26,174)(27,173)(28,172)(29,171)(30,170)(31,169)(32,168)(33,167)(34,155)(35,165)(36,164)(37,163)(38,162)(39,161)(40,160)(41,159)(42,158)(43,157)(44,156)(45,89)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,100)(57,110)(58,109)(59,108)(60,107)(61,106)(62,105)(63,104)(64,103)(65,102)(66,101)(67,122)(68,132)(69,131)(70,130)(71,129)(72,128)(73,127)(74,126)(75,125)(76,124)(77,123)(78,111)(79,121)(80,120)(81,119)(82,118)(83,117)(84,116)(85,115)(86,114)(87,113)(88,112) );
G=PermutationGroup([[(1,100),(2,101),(3,102),(4,103),(5,104),(6,105),(7,106),(8,107),(9,108),(10,109),(11,110),(12,89),(13,90),(14,91),(15,92),(16,93),(17,94),(18,95),(19,96),(20,97),(21,98),(22,99),(23,122),(24,123),(25,124),(26,125),(27,126),(28,127),(29,128),(30,129),(31,130),(32,131),(33,132),(34,111),(35,112),(36,113),(37,114),(38,115),(39,116),(40,117),(41,118),(42,119),(43,120),(44,121),(45,144),(46,145),(47,146),(48,147),(49,148),(50,149),(51,150),(52,151),(53,152),(54,153),(55,154),(56,133),(57,134),(58,135),(59,136),(60,137),(61,138),(62,139),(63,140),(64,141),(65,142),(66,143),(67,166),(68,167),(69,168),(70,169),(71,170),(72,171),(73,172),(74,173),(75,174),(76,175),(77,176),(78,155),(79,156),(80,157),(81,158),(82,159),(83,160),(84,161),(85,162),(86,163),(87,164),(88,165)], [(1,56),(2,57),(3,58),(4,59),(5,60),(6,61),(7,62),(8,63),(9,64),(10,65),(11,66),(12,45),(13,46),(14,47),(15,48),(16,49),(17,50),(18,51),(19,52),(20,53),(21,54),(22,55),(23,78),(24,79),(25,80),(26,81),(27,82),(28,83),(29,84),(30,85),(31,86),(32,87),(33,88),(34,67),(35,68),(36,69),(37,70),(38,71),(39,72),(40,73),(41,74),(42,75),(43,76),(44,77),(89,144),(90,145),(91,146),(92,147),(93,148),(94,149),(95,150),(96,151),(97,152),(98,153),(99,154),(100,133),(101,134),(102,135),(103,136),(104,137),(105,138),(106,139),(107,140),(108,141),(109,142),(110,143),(111,166),(112,167),(113,168),(114,169),(115,170),(116,171),(117,172),(118,173),(119,174),(120,175),(121,176),(122,155),(123,156),(124,157),(125,158),(126,159),(127,160),(128,161),(129,162),(130,163),(131,164),(132,165)], [(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)], [(1,111,12,122),(2,121,13,132),(3,120,14,131),(4,119,15,130),(5,118,16,129),(6,117,17,128),(7,116,18,127),(8,115,19,126),(9,114,20,125),(10,113,21,124),(11,112,22,123),(23,100,34,89),(24,110,35,99),(25,109,36,98),(26,108,37,97),(27,107,38,96),(28,106,39,95),(29,105,40,94),(30,104,41,93),(31,103,42,92),(32,102,43,91),(33,101,44,90),(45,155,56,166),(46,165,57,176),(47,164,58,175),(48,163,59,174),(49,162,60,173),(50,161,61,172),(51,160,62,171),(52,159,63,170),(53,158,64,169),(54,157,65,168),(55,156,66,167),(67,144,78,133),(68,154,79,143),(69,153,80,142),(70,152,81,141),(71,151,82,140),(72,150,83,139),(73,149,84,138),(74,148,85,137),(75,147,86,136),(76,146,87,135),(77,145,88,134)], [(1,133),(2,143),(3,142),(4,141),(5,140),(6,139),(7,138),(8,137),(9,136),(10,135),(11,134),(12,144),(13,154),(14,153),(15,152),(16,151),(17,150),(18,149),(19,148),(20,147),(21,146),(22,145),(23,166),(24,176),(25,175),(26,174),(27,173),(28,172),(29,171),(30,170),(31,169),(32,168),(33,167),(34,155),(35,165),(36,164),(37,163),(38,162),(39,161),(40,160),(41,159),(42,158),(43,157),(44,156),(45,89),(46,99),(47,98),(48,97),(49,96),(50,95),(51,94),(52,93),(53,92),(54,91),(55,90),(56,100),(57,110),(58,109),(59,108),(60,107),(61,106),(62,105),(63,104),(64,103),(65,102),(66,101),(67,122),(68,132),(69,131),(70,130),(71,129),(72,128),(73,127),(74,126),(75,125),(76,124),(77,123),(78,111),(79,121),(80,120),(81,119),(82,118),(83,117),(84,116),(85,115),(86,114),(87,113),(88,112)]])
100 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | 4D | 11A | ··· | 11E | 22A | ··· | 22BW |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | D4 | D11 | D22 | C11⋊D4 |
| kernel | C22×C11⋊D4 | C22×Dic11 | C2×C11⋊D4 | C23×D11 | C23×C22 | C2×C22 | C24 | C23 | C22 |
| # reps | 1 | 1 | 12 | 1 | 1 | 4 | 5 | 35 | 40 |
Matrix representation of C22×C11⋊D4 ►in GL4(𝔽89) generated by
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 1 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 88 |
| 0 | 0 | 1 | 86 |
| 1 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 42 | 80 |
| 0 | 0 | 28 | 47 |
| 1 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 88 | 3 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(89))| [88,0,0,0,0,88,0,0,0,0,88,0,0,0,0,88],[1,0,0,0,0,88,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,88,86],[1,0,0,0,0,88,0,0,0,0,42,28,0,0,80,47],[1,0,0,0,0,88,0,0,0,0,88,0,0,0,3,1] >;
C22×C11⋊D4 in GAP, Magma, Sage, TeX
C_2^2\times C_{11}\rtimes D_4 % in TeX
G:=Group("C2^2xC11:D4"); // GroupNames label
G:=SmallGroup(352,187);
// by ID
G=gap.SmallGroup(352,187);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,579,11525]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^11=d^4=e^2=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,d*c*d^-1=e*c*e=c^-1,e*d*e=d^-1>;
// generators/relations