direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7×D4⋊2S3, C28.40D6, Dic6⋊3C14, C84.47C22, C42.53C23, (C7×D4)⋊5S3, D4⋊2(S3×C7), (S3×C28)⋊7C2, (C4×S3)⋊2C14, (D4×C21)⋊9C2, (C3×D4)⋊3C14, C3⋊D4⋊2C14, C4.5(S3×C14), (C2×C14).4D6, C21⋊16(C4○D4), C12.5(C2×C14), (C7×Dic6)⋊9C2, D6.2(C2×C14), (Dic3×C14)⋊9C2, (C2×Dic3)⋊3C14, C22.1(S3×C14), C6.6(C22×C14), (C2×C42).20C22, C14.43(C22×S3), Dic3.3(C2×C14), (S3×C14).13C22, (C7×Dic3).16C22, C3⋊2(C7×C4○D4), (C2×C6).(C2×C14), C2.7(S3×C2×C14), (C7×C3⋊D4)⋊6C2, SmallGroup(336,189)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×D4⋊2S3
G = < a,b,c,d,e | a7=b4=c2=d3=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: 144 in 80 conjugacy classes, 46 normal (26 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C7, C2×C4, D4, D4, Q8, Dic3, Dic3, C12, D6, C2×C6, C14, C14, C4○D4, C21, Dic6, C4×S3, C2×Dic3, C3⋊D4, C3×D4, C28, C28, C2×C14, C2×C14, S3×C7, C42, C42, D4⋊2S3, C2×C28, C7×D4, C7×D4, C7×Q8, C7×Dic3, C7×Dic3, C84, S3×C14, C2×C42, C7×C4○D4, C7×Dic6, S3×C28, Dic3×C14, C7×C3⋊D4, D4×C21, C7×D4⋊2S3
Quotients: C1, C2, C22, S3, C7, C23, D6, C14, C4○D4, C22×S3, C2×C14, S3×C7, D4⋊2S3, C22×C14, S3×C14, C7×C4○D4, S3×C2×C14, C7×D4⋊2S3
►On 168 points
Generators in S168
(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)
(1 141 57 120)(2 142 58 121)(3 143 59 122)(4 144 60 123)(5 145 61 124)(6 146 62 125)(7 147 63 126)(8 85 29 106)(9 86 30 107)(10 87 31 108)(11 88 32 109)(12 89 33 110)(13 90 34 111)(14 91 35 112)(15 92 36 113)(16 93 37 114)(17 94 38 115)(18 95 39 116)(19 96 40 117)(20 97 41 118)(21 98 42 119)(22 99 162 78)(23 100 163 79)(24 101 164 80)(25 102 165 81)(26 103 166 82)(27 104 167 83)(28 105 168 84)(43 148 64 127)(44 149 65 128)(45 150 66 129)(46 151 67 130)(47 152 68 131)(48 153 69 132)(49 154 70 133)(50 155 71 134)(51 156 72 135)(52 157 73 136)(53 158 74 137)(54 159 75 138)(55 160 76 139)(56 161 77 140)
(1 162)(2 163)(3 164)(4 165)(5 166)(6 167)(7 168)(8 43)(9 44)(10 45)(11 46)(12 47)(13 48)(14 49)(15 50)(16 51)(17 52)(18 53)(19 54)(20 55)(21 56)(22 57)(23 58)(24 59)(25 60)(26 61)(27 62)(28 63)(29 64)(30 65)(31 66)(32 67)(33 68)(34 69)(35 70)(36 71)(37 72)(38 73)(39 74)(40 75)(41 76)(42 77)(78 120)(79 121)(80 122)(81 123)(82 124)(83 125)(84 126)(85 127)(86 128)(87 129)(88 130)(89 131)(90 132)(91 133)(92 134)(93 135)(94 136)(95 137)(96 138)(97 139)(98 140)(99 141)(100 142)(101 143)(102 144)(103 145)(104 146)(105 147)(106 148)(107 149)(108 150)(109 151)(110 152)(111 153)(112 154)(113 155)(114 156)(115 157)(116 158)(117 159)(118 160)(119 161)
(1 50 43)(2 51 44)(3 52 45)(4 53 46)(5 54 47)(6 55 48)(7 56 49)(8 162 15)(9 163 16)(10 164 17)(11 165 18)(12 166 19)(13 167 20)(14 168 21)(22 36 29)(23 37 30)(24 38 31)(25 39 32)(26 40 33)(27 41 34)(28 42 35)(57 71 64)(58 72 65)(59 73 66)(60 74 67)(61 75 68)(62 76 69)(63 77 70)(78 92 85)(79 93 86)(80 94 87)(81 95 88)(82 96 89)(83 97 90)(84 98 91)(99 113 106)(100 114 107)(101 115 108)(102 116 109)(103 117 110)(104 118 111)(105 119 112)(120 134 127)(121 135 128)(122 136 129)(123 137 130)(124 138 131)(125 139 132)(126 140 133)(141 155 148)(142 156 149)(143 157 150)(144 158 151)(145 159 152)(146 160 153)(147 161 154)
(8 36)(9 37)(10 38)(11 39)(12 40)(13 41)(14 42)(15 29)(16 30)(17 31)(18 32)(19 33)(20 34)(21 35)(22 162)(23 163)(24 164)(25 165)(26 166)(27 167)(28 168)(43 50)(44 51)(45 52)(46 53)(47 54)(48 55)(49 56)(64 71)(65 72)(66 73)(67 74)(68 75)(69 76)(70 77)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)(85 113)(86 114)(87 115)(88 116)(89 117)(90 118)(91 119)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(127 134)(128 135)(129 136)(130 137)(131 138)(132 139)(133 140)(148 155)(149 156)(150 157)(151 158)(152 159)(153 160)(154 161)
G:=sub<Sym(168)| (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), (1,141,57,120)(2,142,58,121)(3,143,59,122)(4,144,60,123)(5,145,61,124)(6,146,62,125)(7,147,63,126)(8,85,29,106)(9,86,30,107)(10,87,31,108)(11,88,32,109)(12,89,33,110)(13,90,34,111)(14,91,35,112)(15,92,36,113)(16,93,37,114)(17,94,38,115)(18,95,39,116)(19,96,40,117)(20,97,41,118)(21,98,42,119)(22,99,162,78)(23,100,163,79)(24,101,164,80)(25,102,165,81)(26,103,166,82)(27,104,167,83)(28,105,168,84)(43,148,64,127)(44,149,65,128)(45,150,66,129)(46,151,67,130)(47,152,68,131)(48,153,69,132)(49,154,70,133)(50,155,71,134)(51,156,72,135)(52,157,73,136)(53,158,74,137)(54,159,75,138)(55,160,76,139)(56,161,77,140), (1,162)(2,163)(3,164)(4,165)(5,166)(6,167)(7,168)(8,43)(9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,63)(29,64)(30,65)(31,66)(32,67)(33,68)(34,69)(35,70)(36,71)(37,72)(38,73)(39,74)(40,75)(41,76)(42,77)(78,120)(79,121)(80,122)(81,123)(82,124)(83,125)(84,126)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,161), (1,50,43)(2,51,44)(3,52,45)(4,53,46)(5,54,47)(6,55,48)(7,56,49)(8,162,15)(9,163,16)(10,164,17)(11,165,18)(12,166,19)(13,167,20)(14,168,21)(22,36,29)(23,37,30)(24,38,31)(25,39,32)(26,40,33)(27,41,34)(28,42,35)(57,71,64)(58,72,65)(59,73,66)(60,74,67)(61,75,68)(62,76,69)(63,77,70)(78,92,85)(79,93,86)(80,94,87)(81,95,88)(82,96,89)(83,97,90)(84,98,91)(99,113,106)(100,114,107)(101,115,108)(102,116,109)(103,117,110)(104,118,111)(105,119,112)(120,134,127)(121,135,128)(122,136,129)(123,137,130)(124,138,131)(125,139,132)(126,140,133)(141,155,148)(142,156,149)(143,157,150)(144,158,151)(145,159,152)(146,160,153)(147,161,154), (8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)(22,162)(23,163)(24,164)(25,165)(26,166)(27,167)(28,168)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(64,71)(65,72)(66,73)(67,74)(68,75)(69,76)(70,77)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(85,113)(86,114)(87,115)(88,116)(89,117)(90,118)(91,119)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)>;
G:=Group( (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), (1,141,57,120)(2,142,58,121)(3,143,59,122)(4,144,60,123)(5,145,61,124)(6,146,62,125)(7,147,63,126)(8,85,29,106)(9,86,30,107)(10,87,31,108)(11,88,32,109)(12,89,33,110)(13,90,34,111)(14,91,35,112)(15,92,36,113)(16,93,37,114)(17,94,38,115)(18,95,39,116)(19,96,40,117)(20,97,41,118)(21,98,42,119)(22,99,162,78)(23,100,163,79)(24,101,164,80)(25,102,165,81)(26,103,166,82)(27,104,167,83)(28,105,168,84)(43,148,64,127)(44,149,65,128)(45,150,66,129)(46,151,67,130)(47,152,68,131)(48,153,69,132)(49,154,70,133)(50,155,71,134)(51,156,72,135)(52,157,73,136)(53,158,74,137)(54,159,75,138)(55,160,76,139)(56,161,77,140), (1,162)(2,163)(3,164)(4,165)(5,166)(6,167)(7,168)(8,43)(9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,63)(29,64)(30,65)(31,66)(32,67)(33,68)(34,69)(35,70)(36,71)(37,72)(38,73)(39,74)(40,75)(41,76)(42,77)(78,120)(79,121)(80,122)(81,123)(82,124)(83,125)(84,126)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,161), (1,50,43)(2,51,44)(3,52,45)(4,53,46)(5,54,47)(6,55,48)(7,56,49)(8,162,15)(9,163,16)(10,164,17)(11,165,18)(12,166,19)(13,167,20)(14,168,21)(22,36,29)(23,37,30)(24,38,31)(25,39,32)(26,40,33)(27,41,34)(28,42,35)(57,71,64)(58,72,65)(59,73,66)(60,74,67)(61,75,68)(62,76,69)(63,77,70)(78,92,85)(79,93,86)(80,94,87)(81,95,88)(82,96,89)(83,97,90)(84,98,91)(99,113,106)(100,114,107)(101,115,108)(102,116,109)(103,117,110)(104,118,111)(105,119,112)(120,134,127)(121,135,128)(122,136,129)(123,137,130)(124,138,131)(125,139,132)(126,140,133)(141,155,148)(142,156,149)(143,157,150)(144,158,151)(145,159,152)(146,160,153)(147,161,154), (8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)(22,162)(23,163)(24,164)(25,165)(26,166)(27,167)(28,168)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(64,71)(65,72)(66,73)(67,74)(68,75)(69,76)(70,77)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(85,113)(86,114)(87,115)(88,116)(89,117)(90,118)(91,119)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161) );
G=PermutationGroup([[(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)], [(1,141,57,120),(2,142,58,121),(3,143,59,122),(4,144,60,123),(5,145,61,124),(6,146,62,125),(7,147,63,126),(8,85,29,106),(9,86,30,107),(10,87,31,108),(11,88,32,109),(12,89,33,110),(13,90,34,111),(14,91,35,112),(15,92,36,113),(16,93,37,114),(17,94,38,115),(18,95,39,116),(19,96,40,117),(20,97,41,118),(21,98,42,119),(22,99,162,78),(23,100,163,79),(24,101,164,80),(25,102,165,81),(26,103,166,82),(27,104,167,83),(28,105,168,84),(43,148,64,127),(44,149,65,128),(45,150,66,129),(46,151,67,130),(47,152,68,131),(48,153,69,132),(49,154,70,133),(50,155,71,134),(51,156,72,135),(52,157,73,136),(53,158,74,137),(54,159,75,138),(55,160,76,139),(56,161,77,140)], [(1,162),(2,163),(3,164),(4,165),(5,166),(6,167),(7,168),(8,43),(9,44),(10,45),(11,46),(12,47),(13,48),(14,49),(15,50),(16,51),(17,52),(18,53),(19,54),(20,55),(21,56),(22,57),(23,58),(24,59),(25,60),(26,61),(27,62),(28,63),(29,64),(30,65),(31,66),(32,67),(33,68),(34,69),(35,70),(36,71),(37,72),(38,73),(39,74),(40,75),(41,76),(42,77),(78,120),(79,121),(80,122),(81,123),(82,124),(83,125),(84,126),(85,127),(86,128),(87,129),(88,130),(89,131),(90,132),(91,133),(92,134),(93,135),(94,136),(95,137),(96,138),(97,139),(98,140),(99,141),(100,142),(101,143),(102,144),(103,145),(104,146),(105,147),(106,148),(107,149),(108,150),(109,151),(110,152),(111,153),(112,154),(113,155),(114,156),(115,157),(116,158),(117,159),(118,160),(119,161)], [(1,50,43),(2,51,44),(3,52,45),(4,53,46),(5,54,47),(6,55,48),(7,56,49),(8,162,15),(9,163,16),(10,164,17),(11,165,18),(12,166,19),(13,167,20),(14,168,21),(22,36,29),(23,37,30),(24,38,31),(25,39,32),(26,40,33),(27,41,34),(28,42,35),(57,71,64),(58,72,65),(59,73,66),(60,74,67),(61,75,68),(62,76,69),(63,77,70),(78,92,85),(79,93,86),(80,94,87),(81,95,88),(82,96,89),(83,97,90),(84,98,91),(99,113,106),(100,114,107),(101,115,108),(102,116,109),(103,117,110),(104,118,111),(105,119,112),(120,134,127),(121,135,128),(122,136,129),(123,137,130),(124,138,131),(125,139,132),(126,140,133),(141,155,148),(142,156,149),(143,157,150),(144,158,151),(145,159,152),(146,160,153),(147,161,154)], [(8,36),(9,37),(10,38),(11,39),(12,40),(13,41),(14,42),(15,29),(16,30),(17,31),(18,32),(19,33),(20,34),(21,35),(22,162),(23,163),(24,164),(25,165),(26,166),(27,167),(28,168),(43,50),(44,51),(45,52),(46,53),(47,54),(48,55),(49,56),(64,71),(65,72),(66,73),(67,74),(68,75),(69,76),(70,77),(78,99),(79,100),(80,101),(81,102),(82,103),(83,104),(84,105),(85,113),(86,114),(87,115),(88,116),(89,117),(90,118),(91,119),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(127,134),(128,135),(129,136),(130,137),(131,138),(132,139),(133,140),(148,155),(149,156),(150,157),(151,158),(152,159),(153,160),(154,161)]])
105 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3 | 4A | 4B | 4C | 4D | 4E | 6A | 6B | 6C | 7A | ··· | 7F | 12 | 14A | ··· | 14F | 14G | ··· | 14R | 14S | ··· | 14X | 21A | ··· | 21F | 28A | ··· | 28F | 28G | ··· | 28R | 28S | ··· | 28AD | 42A | ··· | 42F | 42G | ··· | 42R | 84A | ··· | 84F |
| order | 1 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 7 | ··· | 7 | 12 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 28 | ··· | 28 | 28 | ··· | 28 | 42 | ··· | 42 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 2 | 2 | 6 | 2 | 2 | 3 | 3 | 6 | 6 | 2 | 4 | 4 | 1 | ··· | 1 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 | 3 | ··· | 3 | 6 | ··· | 6 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
105 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | S3 | D6 | D6 | C4○D4 | S3×C7 | S3×C14 | S3×C14 | C7×C4○D4 | D4⋊2S3 | C7×D4⋊2S3 |
| kernel | C7×D4⋊2S3 | C7×Dic6 | S3×C28 | Dic3×C14 | C7×C3⋊D4 | D4×C21 | D4⋊2S3 | Dic6 | C4×S3 | C2×Dic3 | C3⋊D4 | C3×D4 | C7×D4 | C28 | C2×C14 | C21 | D4 | C4 | C22 | C3 | C7 | C1 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 6 | 6 | 6 | 12 | 12 | 6 | 1 | 1 | 2 | 2 | 6 | 6 | 12 | 12 | 1 | 6 |
Matrix representation of C7×D4⋊2S3 ►in GL4(𝔽337) generated by
| 8 | 0 | 0 | 0 |
| 0 | 8 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 52 |
| 148 | 0 | 0 | 0 |
| 189 | 189 | 0 | 0 |
| 0 | 0 | 336 | 0 |
| 0 | 0 | 0 | 336 |
| 148 | 296 | 0 | 0 |
| 189 | 189 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 336 | 1 |
| 0 | 0 | 336 | 0 |
| 1 | 0 | 0 | 0 |
| 336 | 336 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
G:=sub<GL(4,GF(337))| [8,0,0,0,0,8,0,0,0,0,52,0,0,0,0,52],[148,189,0,0,0,189,0,0,0,0,336,0,0,0,0,336],[148,189,0,0,296,189,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,336,336,0,0,1,0],[1,336,0,0,0,336,0,0,0,0,0,1,0,0,1,0] >;
C7×D4⋊2S3 in GAP, Magma, Sage, TeX
C_7\times D_4\rtimes_2S_3
% in TeX
G:=Group("C7xD4:2S3"); // GroupNames label
G:=SmallGroup(336,189);
// by ID
G=gap.SmallGroup(336,189);
# by ID
G:=PCGroup([6,-2,-2,-2,-7,-2,-3,343,1082,548,8069]);
// Polycyclic
G:=Group<a,b,c,d,e|a^7=b^4=c^2=d^3=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