direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q8⋊D11, Q8⋊3D22, C22⋊3SD16, C44.18D4, C44.14C23, D44.9C22, C11⋊C8⋊9C22, (C2×Q8)⋊1D11, (Q8×C22)⋊1C2, C11⋊4(C2×SD16), (C2×D44).8C2, (C2×C4).53D22, (C2×C22).41D4, C22.53(C2×D4), C4.8(C11⋊D4), (Q8×C11)⋊3C22, (C2×C44).36C22, C4.14(C22×D11), C22.23(C11⋊D4), (C2×C11⋊C8)⋊6C2, C2.17(C2×C11⋊D4), SmallGroup(352,136)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Q8⋊D11
G = < a,b,c,d,e | a2=b4=d11=e2=1, c2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe=b-1, bd=db, cd=dc, ece=b-1c, ede=d-1 >
Subgroups: 458 in 68 conjugacy classes, 33 normal (17 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, C11, C2×C8, SD16, C2×D4, C2×Q8, D11, C22, C22, C2×SD16, C44, C44, D22, C2×C22, C11⋊C8, D44, D44, C2×C44, C2×C44, Q8×C11, Q8×C11, C22×D11, C2×C11⋊C8, Q8⋊D11, C2×D44, Q8×C22, C2×Q8⋊D11
Quotients: C1, C2, C22, D4, C23, SD16, C2×D4, D11, C2×SD16, D22, C11⋊D4, C22×D11, Q8⋊D11, C2×C11⋊D4, C2×Q8⋊D11
►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 34 12 23)(2 35 13 24)(3 36 14 25)(4 37 15 26)(5 38 16 27)(6 39 17 28)(7 40 18 29)(8 41 19 30)(9 42 20 31)(10 43 21 32)(11 44 22 33)(45 67 56 78)(46 68 57 79)(47 69 58 80)(48 70 59 81)(49 71 60 82)(50 72 61 83)(51 73 62 84)(52 74 63 85)(53 75 64 86)(54 76 65 87)(55 77 66 88)(89 122 100 111)(90 123 101 112)(91 124 102 113)(92 125 103 114)(93 126 104 115)(94 127 105 116)(95 128 106 117)(96 129 107 118)(97 130 108 119)(98 131 109 120)(99 132 110 121)(133 155 144 166)(134 156 145 167)(135 157 146 168)(136 158 147 169)(137 159 148 170)(138 160 149 171)(139 161 150 172)(140 162 151 173)(141 163 152 174)(142 164 153 175)(143 165 154 176)
(1 144 12 133)(2 145 13 134)(3 146 14 135)(4 147 15 136)(5 148 16 137)(6 149 17 138)(7 150 18 139)(8 151 19 140)(9 152 20 141)(10 153 21 142)(11 154 22 143)(23 166 34 155)(24 167 35 156)(25 168 36 157)(26 169 37 158)(27 170 38 159)(28 171 39 160)(29 172 40 161)(30 173 41 162)(31 174 42 163)(32 175 43 164)(33 176 44 165)(45 89 56 100)(46 90 57 101)(47 91 58 102)(48 92 59 103)(49 93 60 104)(50 94 61 105)(51 95 62 106)(52 96 63 107)(53 97 64 108)(54 98 65 109)(55 99 66 110)(67 111 78 122)(68 112 79 123)(69 113 80 124)(70 114 81 125)(71 115 82 126)(72 116 83 127)(73 117 84 128)(74 118 85 129)(75 119 86 130)(76 120 87 131)(77 121 88 132)
(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 77)(46 76)(47 75)(48 74)(49 73)(50 72)(51 71)(52 70)(53 69)(54 68)(55 67)(56 88)(57 87)(58 86)(59 85)(60 84)(61 83)(62 82)(63 81)(64 80)(65 79)(66 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)(133 165)(134 164)(135 163)(136 162)(137 161)(138 160)(139 159)(140 158)(141 157)(142 156)(143 155)(144 176)(145 175)(146 174)(147 173)(148 172)(149 171)(150 170)(151 169)(152 168)(153 167)(154 166)
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), (1,34,12,23)(2,35,13,24)(3,36,14,25)(4,37,15,26)(5,38,16,27)(6,39,17,28)(7,40,18,29)(8,41,19,30)(9,42,20,31)(10,43,21,32)(11,44,22,33)(45,67,56,78)(46,68,57,79)(47,69,58,80)(48,70,59,81)(49,71,60,82)(50,72,61,83)(51,73,62,84)(52,74,63,85)(53,75,64,86)(54,76,65,87)(55,77,66,88)(89,122,100,111)(90,123,101,112)(91,124,102,113)(92,125,103,114)(93,126,104,115)(94,127,105,116)(95,128,106,117)(96,129,107,118)(97,130,108,119)(98,131,109,120)(99,132,110,121)(133,155,144,166)(134,156,145,167)(135,157,146,168)(136,158,147,169)(137,159,148,170)(138,160,149,171)(139,161,150,172)(140,162,151,173)(141,163,152,174)(142,164,153,175)(143,165,154,176), (1,144,12,133)(2,145,13,134)(3,146,14,135)(4,147,15,136)(5,148,16,137)(6,149,17,138)(7,150,18,139)(8,151,19,140)(9,152,20,141)(10,153,21,142)(11,154,22,143)(23,166,34,155)(24,167,35,156)(25,168,36,157)(26,169,37,158)(27,170,38,159)(28,171,39,160)(29,172,40,161)(30,173,41,162)(31,174,42,163)(32,175,43,164)(33,176,44,165)(45,89,56,100)(46,90,57,101)(47,91,58,102)(48,92,59,103)(49,93,60,104)(50,94,61,105)(51,95,62,106)(52,96,63,107)(53,97,64,108)(54,98,65,109)(55,99,66,110)(67,111,78,122)(68,112,79,123)(69,113,80,124)(70,114,81,125)(71,115,82,126)(72,116,83,127)(73,117,84,128)(74,118,85,129)(75,119,86,130)(76,120,87,131)(77,121,88,132), (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)(45,77)(46,76)(47,75)(48,74)(49,73)(50,72)(51,71)(52,70)(53,69)(54,68)(55,67)(56,88)(57,87)(58,86)(59,85)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(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)(133,165)(134,164)(135,163)(136,162)(137,161)(138,160)(139,159)(140,158)(141,157)(142,156)(143,155)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)(150,170)(151,169)(152,168)(153,167)(154,166)>;
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), (1,34,12,23)(2,35,13,24)(3,36,14,25)(4,37,15,26)(5,38,16,27)(6,39,17,28)(7,40,18,29)(8,41,19,30)(9,42,20,31)(10,43,21,32)(11,44,22,33)(45,67,56,78)(46,68,57,79)(47,69,58,80)(48,70,59,81)(49,71,60,82)(50,72,61,83)(51,73,62,84)(52,74,63,85)(53,75,64,86)(54,76,65,87)(55,77,66,88)(89,122,100,111)(90,123,101,112)(91,124,102,113)(92,125,103,114)(93,126,104,115)(94,127,105,116)(95,128,106,117)(96,129,107,118)(97,130,108,119)(98,131,109,120)(99,132,110,121)(133,155,144,166)(134,156,145,167)(135,157,146,168)(136,158,147,169)(137,159,148,170)(138,160,149,171)(139,161,150,172)(140,162,151,173)(141,163,152,174)(142,164,153,175)(143,165,154,176), (1,144,12,133)(2,145,13,134)(3,146,14,135)(4,147,15,136)(5,148,16,137)(6,149,17,138)(7,150,18,139)(8,151,19,140)(9,152,20,141)(10,153,21,142)(11,154,22,143)(23,166,34,155)(24,167,35,156)(25,168,36,157)(26,169,37,158)(27,170,38,159)(28,171,39,160)(29,172,40,161)(30,173,41,162)(31,174,42,163)(32,175,43,164)(33,176,44,165)(45,89,56,100)(46,90,57,101)(47,91,58,102)(48,92,59,103)(49,93,60,104)(50,94,61,105)(51,95,62,106)(52,96,63,107)(53,97,64,108)(54,98,65,109)(55,99,66,110)(67,111,78,122)(68,112,79,123)(69,113,80,124)(70,114,81,125)(71,115,82,126)(72,116,83,127)(73,117,84,128)(74,118,85,129)(75,119,86,130)(76,120,87,131)(77,121,88,132), (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)(45,77)(46,76)(47,75)(48,74)(49,73)(50,72)(51,71)(52,70)(53,69)(54,68)(55,67)(56,88)(57,87)(58,86)(59,85)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(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)(133,165)(134,164)(135,163)(136,162)(137,161)(138,160)(139,159)(140,158)(141,157)(142,156)(143,155)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)(150,170)(151,169)(152,168)(153,167)(154,166) );
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)], [(1,34,12,23),(2,35,13,24),(3,36,14,25),(4,37,15,26),(5,38,16,27),(6,39,17,28),(7,40,18,29),(8,41,19,30),(9,42,20,31),(10,43,21,32),(11,44,22,33),(45,67,56,78),(46,68,57,79),(47,69,58,80),(48,70,59,81),(49,71,60,82),(50,72,61,83),(51,73,62,84),(52,74,63,85),(53,75,64,86),(54,76,65,87),(55,77,66,88),(89,122,100,111),(90,123,101,112),(91,124,102,113),(92,125,103,114),(93,126,104,115),(94,127,105,116),(95,128,106,117),(96,129,107,118),(97,130,108,119),(98,131,109,120),(99,132,110,121),(133,155,144,166),(134,156,145,167),(135,157,146,168),(136,158,147,169),(137,159,148,170),(138,160,149,171),(139,161,150,172),(140,162,151,173),(141,163,152,174),(142,164,153,175),(143,165,154,176)], [(1,144,12,133),(2,145,13,134),(3,146,14,135),(4,147,15,136),(5,148,16,137),(6,149,17,138),(7,150,18,139),(8,151,19,140),(9,152,20,141),(10,153,21,142),(11,154,22,143),(23,166,34,155),(24,167,35,156),(25,168,36,157),(26,169,37,158),(27,170,38,159),(28,171,39,160),(29,172,40,161),(30,173,41,162),(31,174,42,163),(32,175,43,164),(33,176,44,165),(45,89,56,100),(46,90,57,101),(47,91,58,102),(48,92,59,103),(49,93,60,104),(50,94,61,105),(51,95,62,106),(52,96,63,107),(53,97,64,108),(54,98,65,109),(55,99,66,110),(67,111,78,122),(68,112,79,123),(69,113,80,124),(70,114,81,125),(71,115,82,126),(72,116,83,127),(73,117,84,128),(74,118,85,129),(75,119,86,130),(76,120,87,131),(77,121,88,132)], [(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),(45,77),(46,76),(47,75),(48,74),(49,73),(50,72),(51,71),(52,70),(53,69),(54,68),(55,67),(56,88),(57,87),(58,86),(59,85),(60,84),(61,83),(62,82),(63,81),(64,80),(65,79),(66,78),(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),(133,165),(134,164),(135,163),(136,162),(137,161),(138,160),(139,159),(140,158),(141,157),(142,156),(143,155),(144,176),(145,175),(146,174),(147,173),(148,172),(149,171),(150,170),(151,169),(152,168),(153,167),(154,166)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 8A | 8B | 8C | 8D | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 44 | 44 | 2 | 2 | 4 | 4 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | SD16 | D11 | D22 | D22 | C11⋊D4 | C11⋊D4 | Q8⋊D11 |
| kernel | C2×Q8⋊D11 | C2×C11⋊C8 | Q8⋊D11 | C2×D44 | Q8×C22 | C44 | C2×C22 | C22 | C2×Q8 | C2×C4 | Q8 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 5 | 5 | 10 | 10 | 10 | 10 |
Matrix representation of C2×Q8⋊D11 ►in GL4(𝔽89) generated by
| 88 | 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 | 1 | 36 |
| 0 | 0 | 84 | 88 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 49 | 81 |
| 0 | 0 | 11 | 40 |
| 55 | 88 | 0 | 0 |
| 60 | 41 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 20 | 62 | 0 | 0 |
| 84 | 69 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 84 | 88 |
G:=sub<GL(4,GF(89))| [88,0,0,0,0,88,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,1,84,0,0,36,88],[1,0,0,0,0,1,0,0,0,0,49,11,0,0,81,40],[55,60,0,0,88,41,0,0,0,0,1,0,0,0,0,1],[20,84,0,0,62,69,0,0,0,0,1,84,0,0,0,88] >;
C2×Q8⋊D11 in GAP, Magma, Sage, TeX
C_2\times Q_8\rtimes D_{11} % in TeX
G:=Group("C2xQ8:D11"); // GroupNames label
G:=SmallGroup(352,136);
// by ID
G=gap.SmallGroup(352,136);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,218,86,579,159,69,11525]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=d^11=e^2=1,c^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e=b^-1,b*d=d*b,c*d=d*c,e*c*e=b^-1*c,e*d*e=d^-1>;
// generators/relations