direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×D4⋊2D7, Dic14⋊9C6, C12.40D14, C42.43C23, C84.40C22, (C4×D7)⋊7C6, (C7×D4)⋊9C6, (C3×D4)⋊5D7, D4⋊2(C3×D7), C7⋊D4⋊6C6, C4.5(C6×D7), (C12×D7)⋊7C2, (D4×C21)⋊6C2, (C2×C6).4D14, C21⋊15(C4○D4), C28.26(C2×C6), (C2×Dic7)⋊9C6, (C6×Dic7)⋊9C2, D14.7(C2×C6), C22.1(C6×D7), (C3×Dic14)⋊9C2, Dic7.8(C2×C6), C6.43(C22×D7), (C2×C42).19C22, C14.20(C22×C6), (C6×D7).13C22, (C3×Dic7).15C22, C7⋊6(C3×C4○D4), C2.7(C2×C6×D7), (C3×C7⋊D4)⋊6C2, (C2×C14).13(C2×C6), SmallGroup(336,179)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×D4⋊2D7
G = < a,b,c,d,e | a3=b4=c2=d7=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: 248 in 80 conjugacy classes, 46 normal (26 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C7, C2×C4, D4, D4, Q8, C12, C12, C2×C6, C2×C6, D7, C14, C14, C4○D4, C21, C2×C12, C3×D4, C3×D4, C3×Q8, Dic7, Dic7, C28, D14, C2×C14, C3×D7, C42, C42, C3×C4○D4, Dic14, C4×D7, C2×Dic7, C7⋊D4, C7×D4, C3×Dic7, C3×Dic7, C84, C6×D7, C2×C42, D4⋊2D7, C3×Dic14, C12×D7, C6×Dic7, C3×C7⋊D4, D4×C21, C3×D4⋊2D7
Quotients: C1, C2, C3, C22, C6, C23, C2×C6, D7, C4○D4, C22×C6, D14, C3×D7, C3×C4○D4, C22×D7, C6×D7, D4⋊2D7, C2×C6×D7, C3×D4⋊2D7
►On 168 points
Generators in S168
(1 29 15)(2 30 16)(3 31 17)(4 32 18)(5 33 19)(6 34 20)(7 35 21)(8 36 22)(9 37 23)(10 38 24)(11 39 25)(12 40 26)(13 41 27)(14 42 28)(43 71 57)(44 72 58)(45 73 59)(46 74 60)(47 75 61)(48 76 62)(49 77 63)(50 78 64)(51 79 65)(52 80 66)(53 81 67)(54 82 68)(55 83 69)(56 84 70)(85 113 99)(86 114 100)(87 115 101)(88 116 102)(89 117 103)(90 118 104)(91 119 105)(92 120 106)(93 121 107)(94 122 108)(95 123 109)(96 124 110)(97 125 111)(98 126 112)(127 155 141)(128 156 142)(129 157 143)(130 158 144)(131 159 145)(132 160 146)(133 161 147)(134 162 148)(135 163 149)(136 164 150)(137 165 151)(138 166 152)(139 167 153)(140 168 154)
(1 92 8 85)(2 93 9 86)(3 94 10 87)(4 95 11 88)(5 96 12 89)(6 97 13 90)(7 98 14 91)(15 106 22 99)(16 107 23 100)(17 108 24 101)(18 109 25 102)(19 110 26 103)(20 111 27 104)(21 112 28 105)(29 120 36 113)(30 121 37 114)(31 122 38 115)(32 123 39 116)(33 124 40 117)(34 125 41 118)(35 126 42 119)(43 134 50 127)(44 135 51 128)(45 136 52 129)(46 137 53 130)(47 138 54 131)(48 139 55 132)(49 140 56 133)(57 148 64 141)(58 149 65 142)(59 150 66 143)(60 151 67 144)(61 152 68 145)(62 153 69 146)(63 154 70 147)(71 162 78 155)(72 163 79 156)(73 164 80 157)(74 165 81 158)(75 166 82 159)(76 167 83 160)(77 168 84 161)
(1 127)(2 128)(3 129)(4 130)(5 131)(6 132)(7 133)(8 134)(9 135)(10 136)(11 137)(12 138)(13 139)(14 140)(15 141)(16 142)(17 143)(18 144)(19 145)(20 146)(21 147)(22 148)(23 149)(24 150)(25 151)(26 152)(27 153)(28 154)(29 155)(30 156)(31 157)(32 158)(33 159)(34 160)(35 161)(36 162)(37 163)(38 164)(39 165)(40 166)(41 167)(42 168)(43 85)(44 86)(45 87)(46 88)(47 89)(48 90)(49 91)(50 92)(51 93)(52 94)(53 95)(54 96)(55 97)(56 98)(57 99)(58 100)(59 101)(60 102)(61 103)(62 104)(63 105)(64 106)(65 107)(66 108)(67 109)(68 110)(69 111)(70 112)(71 113)(72 114)(73 115)(74 116)(75 117)(76 118)(77 119)(78 120)(79 121)(80 122)(81 123)(82 124)(83 125)(84 126)
(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 7)(2 6)(3 5)(8 14)(9 13)(10 12)(15 21)(16 20)(17 19)(22 28)(23 27)(24 26)(29 35)(30 34)(31 33)(36 42)(37 41)(38 40)(43 56)(44 55)(45 54)(46 53)(47 52)(48 51)(49 50)(57 70)(58 69)(59 68)(60 67)(61 66)(62 65)(63 64)(71 84)(72 83)(73 82)(74 81)(75 80)(76 79)(77 78)(85 91)(86 90)(87 89)(92 98)(93 97)(94 96)(99 105)(100 104)(101 103)(106 112)(107 111)(108 110)(113 119)(114 118)(115 117)(120 126)(121 125)(122 124)(127 140)(128 139)(129 138)(130 137)(131 136)(132 135)(133 134)(141 154)(142 153)(143 152)(144 151)(145 150)(146 149)(147 148)(155 168)(156 167)(157 166)(158 165)(159 164)(160 163)(161 162)
G:=sub<Sym(168)| (1,29,15)(2,30,16)(3,31,17)(4,32,18)(5,33,19)(6,34,20)(7,35,21)(8,36,22)(9,37,23)(10,38,24)(11,39,25)(12,40,26)(13,41,27)(14,42,28)(43,71,57)(44,72,58)(45,73,59)(46,74,60)(47,75,61)(48,76,62)(49,77,63)(50,78,64)(51,79,65)(52,80,66)(53,81,67)(54,82,68)(55,83,69)(56,84,70)(85,113,99)(86,114,100)(87,115,101)(88,116,102)(89,117,103)(90,118,104)(91,119,105)(92,120,106)(93,121,107)(94,122,108)(95,123,109)(96,124,110)(97,125,111)(98,126,112)(127,155,141)(128,156,142)(129,157,143)(130,158,144)(131,159,145)(132,160,146)(133,161,147)(134,162,148)(135,163,149)(136,164,150)(137,165,151)(138,166,152)(139,167,153)(140,168,154), (1,92,8,85)(2,93,9,86)(3,94,10,87)(4,95,11,88)(5,96,12,89)(6,97,13,90)(7,98,14,91)(15,106,22,99)(16,107,23,100)(17,108,24,101)(18,109,25,102)(19,110,26,103)(20,111,27,104)(21,112,28,105)(29,120,36,113)(30,121,37,114)(31,122,38,115)(32,123,39,116)(33,124,40,117)(34,125,41,118)(35,126,42,119)(43,134,50,127)(44,135,51,128)(45,136,52,129)(46,137,53,130)(47,138,54,131)(48,139,55,132)(49,140,56,133)(57,148,64,141)(58,149,65,142)(59,150,66,143)(60,151,67,144)(61,152,68,145)(62,153,69,146)(63,154,70,147)(71,162,78,155)(72,163,79,156)(73,164,80,157)(74,165,81,158)(75,166,82,159)(76,167,83,160)(77,168,84,161), (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,141)(16,142)(17,143)(18,144)(19,145)(20,146)(21,147)(22,148)(23,149)(24,150)(25,151)(26,152)(27,153)(28,154)(29,155)(30,156)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,163)(38,164)(39,165)(40,166)(41,167)(42,168)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,97)(56,98)(57,99)(58,100)(59,101)(60,102)(61,103)(62,104)(63,105)(64,106)(65,107)(66,108)(67,109)(68,110)(69,111)(70,112)(71,113)(72,114)(73,115)(74,116)(75,117)(76,118)(77,119)(78,120)(79,121)(80,122)(81,123)(82,124)(83,125)(84,126), (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), (1,7)(2,6)(3,5)(8,14)(9,13)(10,12)(15,21)(16,20)(17,19)(22,28)(23,27)(24,26)(29,35)(30,34)(31,33)(36,42)(37,41)(38,40)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,91)(86,90)(87,89)(92,98)(93,97)(94,96)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,119)(114,118)(115,117)(120,126)(121,125)(122,124)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)>;
G:=Group( (1,29,15)(2,30,16)(3,31,17)(4,32,18)(5,33,19)(6,34,20)(7,35,21)(8,36,22)(9,37,23)(10,38,24)(11,39,25)(12,40,26)(13,41,27)(14,42,28)(43,71,57)(44,72,58)(45,73,59)(46,74,60)(47,75,61)(48,76,62)(49,77,63)(50,78,64)(51,79,65)(52,80,66)(53,81,67)(54,82,68)(55,83,69)(56,84,70)(85,113,99)(86,114,100)(87,115,101)(88,116,102)(89,117,103)(90,118,104)(91,119,105)(92,120,106)(93,121,107)(94,122,108)(95,123,109)(96,124,110)(97,125,111)(98,126,112)(127,155,141)(128,156,142)(129,157,143)(130,158,144)(131,159,145)(132,160,146)(133,161,147)(134,162,148)(135,163,149)(136,164,150)(137,165,151)(138,166,152)(139,167,153)(140,168,154), (1,92,8,85)(2,93,9,86)(3,94,10,87)(4,95,11,88)(5,96,12,89)(6,97,13,90)(7,98,14,91)(15,106,22,99)(16,107,23,100)(17,108,24,101)(18,109,25,102)(19,110,26,103)(20,111,27,104)(21,112,28,105)(29,120,36,113)(30,121,37,114)(31,122,38,115)(32,123,39,116)(33,124,40,117)(34,125,41,118)(35,126,42,119)(43,134,50,127)(44,135,51,128)(45,136,52,129)(46,137,53,130)(47,138,54,131)(48,139,55,132)(49,140,56,133)(57,148,64,141)(58,149,65,142)(59,150,66,143)(60,151,67,144)(61,152,68,145)(62,153,69,146)(63,154,70,147)(71,162,78,155)(72,163,79,156)(73,164,80,157)(74,165,81,158)(75,166,82,159)(76,167,83,160)(77,168,84,161), (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,141)(16,142)(17,143)(18,144)(19,145)(20,146)(21,147)(22,148)(23,149)(24,150)(25,151)(26,152)(27,153)(28,154)(29,155)(30,156)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,163)(38,164)(39,165)(40,166)(41,167)(42,168)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,97)(56,98)(57,99)(58,100)(59,101)(60,102)(61,103)(62,104)(63,105)(64,106)(65,107)(66,108)(67,109)(68,110)(69,111)(70,112)(71,113)(72,114)(73,115)(74,116)(75,117)(76,118)(77,119)(78,120)(79,121)(80,122)(81,123)(82,124)(83,125)(84,126), (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), (1,7)(2,6)(3,5)(8,14)(9,13)(10,12)(15,21)(16,20)(17,19)(22,28)(23,27)(24,26)(29,35)(30,34)(31,33)(36,42)(37,41)(38,40)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,91)(86,90)(87,89)(92,98)(93,97)(94,96)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,119)(114,118)(115,117)(120,126)(121,125)(122,124)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162) );
G=PermutationGroup([[(1,29,15),(2,30,16),(3,31,17),(4,32,18),(5,33,19),(6,34,20),(7,35,21),(8,36,22),(9,37,23),(10,38,24),(11,39,25),(12,40,26),(13,41,27),(14,42,28),(43,71,57),(44,72,58),(45,73,59),(46,74,60),(47,75,61),(48,76,62),(49,77,63),(50,78,64),(51,79,65),(52,80,66),(53,81,67),(54,82,68),(55,83,69),(56,84,70),(85,113,99),(86,114,100),(87,115,101),(88,116,102),(89,117,103),(90,118,104),(91,119,105),(92,120,106),(93,121,107),(94,122,108),(95,123,109),(96,124,110),(97,125,111),(98,126,112),(127,155,141),(128,156,142),(129,157,143),(130,158,144),(131,159,145),(132,160,146),(133,161,147),(134,162,148),(135,163,149),(136,164,150),(137,165,151),(138,166,152),(139,167,153),(140,168,154)], [(1,92,8,85),(2,93,9,86),(3,94,10,87),(4,95,11,88),(5,96,12,89),(6,97,13,90),(7,98,14,91),(15,106,22,99),(16,107,23,100),(17,108,24,101),(18,109,25,102),(19,110,26,103),(20,111,27,104),(21,112,28,105),(29,120,36,113),(30,121,37,114),(31,122,38,115),(32,123,39,116),(33,124,40,117),(34,125,41,118),(35,126,42,119),(43,134,50,127),(44,135,51,128),(45,136,52,129),(46,137,53,130),(47,138,54,131),(48,139,55,132),(49,140,56,133),(57,148,64,141),(58,149,65,142),(59,150,66,143),(60,151,67,144),(61,152,68,145),(62,153,69,146),(63,154,70,147),(71,162,78,155),(72,163,79,156),(73,164,80,157),(74,165,81,158),(75,166,82,159),(76,167,83,160),(77,168,84,161)], [(1,127),(2,128),(3,129),(4,130),(5,131),(6,132),(7,133),(8,134),(9,135),(10,136),(11,137),(12,138),(13,139),(14,140),(15,141),(16,142),(17,143),(18,144),(19,145),(20,146),(21,147),(22,148),(23,149),(24,150),(25,151),(26,152),(27,153),(28,154),(29,155),(30,156),(31,157),(32,158),(33,159),(34,160),(35,161),(36,162),(37,163),(38,164),(39,165),(40,166),(41,167),(42,168),(43,85),(44,86),(45,87),(46,88),(47,89),(48,90),(49,91),(50,92),(51,93),(52,94),(53,95),(54,96),(55,97),(56,98),(57,99),(58,100),(59,101),(60,102),(61,103),(62,104),(63,105),(64,106),(65,107),(66,108),(67,109),(68,110),(69,111),(70,112),(71,113),(72,114),(73,115),(74,116),(75,117),(76,118),(77,119),(78,120),(79,121),(80,122),(81,123),(82,124),(83,125),(84,126)], [(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)], [(1,7),(2,6),(3,5),(8,14),(9,13),(10,12),(15,21),(16,20),(17,19),(22,28),(23,27),(24,26),(29,35),(30,34),(31,33),(36,42),(37,41),(38,40),(43,56),(44,55),(45,54),(46,53),(47,52),(48,51),(49,50),(57,70),(58,69),(59,68),(60,67),(61,66),(62,65),(63,64),(71,84),(72,83),(73,82),(74,81),(75,80),(76,79),(77,78),(85,91),(86,90),(87,89),(92,98),(93,97),(94,96),(99,105),(100,104),(101,103),(106,112),(107,111),(108,110),(113,119),(114,118),(115,117),(120,126),(121,125),(122,124),(127,140),(128,139),(129,138),(130,137),(131,136),(132,135),(133,134),(141,154),(142,153),(143,152),(144,151),(145,150),(146,149),(147,148),(155,168),(156,167),(157,166),(158,165),(159,164),(160,163),(161,162)]])
75 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 6H | 7A | 7B | 7C | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 12I | 12J | 14A | 14B | 14C | 14D | ··· | 14I | 21A | ··· | 21F | 28A | 28B | 28C | 42A | ··· | 42F | 42G | ··· | 42R | 84A | ··· | 84F |
| order | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 7 | 7 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 14 | 14 | 14 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | 28 | 28 | 42 | ··· | 42 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 2 | 2 | 14 | 1 | 1 | 2 | 7 | 7 | 14 | 14 | 1 | 1 | 2 | 2 | 2 | 2 | 14 | 14 | 2 | 2 | 2 | 2 | 2 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
75 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 | C3 | C6 | C6 | C6 | C6 | C6 | D7 | C4○D4 | D14 | D14 | C3×D7 | C3×C4○D4 | C6×D7 | C6×D7 | D4⋊2D7 | C3×D4⋊2D7 |
| kernel | C3×D4⋊2D7 | C3×Dic14 | C12×D7 | C6×Dic7 | C3×C7⋊D4 | D4×C21 | D4⋊2D7 | Dic14 | C4×D7 | C2×Dic7 | C7⋊D4 | C7×D4 | C3×D4 | C21 | C12 | C2×C6 | D4 | C7 | C4 | C22 | C3 | C1 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 2 | 3 | 2 | 3 | 6 | 6 | 4 | 6 | 12 | 3 | 6 |
Matrix representation of C3×D4⋊2D7 ►in GL4(𝔽337) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 128 | 0 |
| 0 | 0 | 0 | 128 |
| 336 | 0 | 0 | 0 |
| 0 | 336 | 0 | 0 |
| 0 | 0 | 189 | 0 |
| 0 | 0 | 148 | 148 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 189 | 41 |
| 0 | 0 | 148 | 148 |
| 304 | 336 | 0 | 0 |
| 305 | 336 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 227 | 303 | 0 | 0 |
| 227 | 110 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 336 | 336 |
G:=sub<GL(4,GF(337))| [1,0,0,0,0,1,0,0,0,0,128,0,0,0,0,128],[336,0,0,0,0,336,0,0,0,0,189,148,0,0,0,148],[1,0,0,0,0,1,0,0,0,0,189,148,0,0,41,148],[304,305,0,0,336,336,0,0,0,0,1,0,0,0,0,1],[227,227,0,0,303,110,0,0,0,0,1,336,0,0,0,336] >;
C3×D4⋊2D7 in GAP, Magma, Sage, TeX
C_3\times D_4\rtimes_2D_7
% in TeX
G:=Group("C3xD4:2D7"); // GroupNames label
G:=SmallGroup(336,179);
// by ID
G=gap.SmallGroup(336,179);
# by ID
G:=PCGroup([6,-2,-2,-2,-3,-2,-7,151,506,260,10373]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^4=c^2=d^7=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