metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.56D10, C4⋊D4.4D5, (C2×D4).36D10, (C2×C20).261D4, C10.95(C4○D8), C10.D8⋊35C2, C20.55D4⋊9C2, D4⋊Dic5⋊14C2, C20.Q8⋊34C2, (C22×C10).81D4, C20.182(C4○D4), C4.92(D4⋊2D5), C10.89(C8⋊C22), (C2×C20).354C23, (D4×C10).52C22, (C22×C4).118D10, C23.22(C5⋊D4), C5⋊7(C23.19D4), C4⋊Dic5.336C22, C2.10(D4.D10), C2.14(D4.8D10), C23.21D10⋊15C2, (C22×C20).158C22, C10.79(C22.D4), C2.13(C23.18D10), (C5×C4⋊D4).3C2, (C2×C10).485(C2×D4), (C2×C4).170(C5⋊D4), (C5×C4⋊C4).103C22, (C2×C4).454(C22×D5), C22.160(C2×C5⋊D4), (C2×C5⋊2C8).107C22, SmallGroup(320,662)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×D4).D10
G = < a,b,c,d,e | a2=b4=c2=1, d10=b2, e2=a, ab=ba, ac=ca, ad=da, ae=ea, cbc=ebe-1=b-1, bd=db, dcd-1=ab2c, ece-1=b-1c, ede-1=d9 >
Subgroups: 334 in 106 conjugacy classes, 39 normal (all characteristic)
C1, C2 [×3], C2 [×2], C4 [×2], C4 [×4], C22, C22 [×6], C5, C8 [×2], C2×C4 [×2], C2×C4 [×5], D4 [×4], C23, C23, C10 [×3], C10 [×2], C42, C22⋊C4 [×2], C4⋊C4, C4⋊C4 [×2], C2×C8 [×2], C22×C4, C2×D4, C2×D4, Dic5 [×2], C20 [×2], C20 [×2], C2×C10, C2×C10 [×6], C22⋊C8, D4⋊C4 [×2], C4.Q8, C2.D8, C42⋊C2, C4⋊D4, C5⋊2C8 [×2], C2×Dic5 [×2], C2×C20 [×2], C2×C20 [×3], C5×D4 [×4], C22×C10, C22×C10, C23.19D4, C2×C5⋊2C8 [×2], C4×Dic5, C4⋊Dic5 [×2], C23.D5, C5×C22⋊C4, C5×C4⋊C4, C22×C20, D4×C10, D4×C10, C10.D8, C20.Q8, C20.55D4, D4⋊Dic5 [×2], C23.21D10, C5×C4⋊D4, (C2×D4).D10
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D5, C2×D4, C4○D4 [×2], D10 [×3], C22.D4, C4○D8, C8⋊C22, C5⋊D4 [×2], C22×D5, C23.19D4, D4⋊2D5 [×2], C2×C5⋊D4, D4.D10, C23.18D10, D4.8D10, (C2×D4).D10
►On 160 points
Generators in S160
(1 52)(2 53)(3 54)(4 55)(5 56)(6 57)(7 58)(8 59)(9 60)(10 41)(11 42)(12 43)(13 44)(14 45)(15 46)(16 47)(17 48)(18 49)(19 50)(20 51)(21 148)(22 149)(23 150)(24 151)(25 152)(26 153)(27 154)(28 155)(29 156)(30 157)(31 158)(32 159)(33 160)(34 141)(35 142)(36 143)(37 144)(38 145)(39 146)(40 147)(61 101)(62 102)(63 103)(64 104)(65 105)(66 106)(67 107)(68 108)(69 109)(70 110)(71 111)(72 112)(73 113)(74 114)(75 115)(76 116)(77 117)(78 118)(79 119)(80 120)(81 133)(82 134)(83 135)(84 136)(85 137)(86 138)(87 139)(88 140)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 131)(100 132)
(1 106 11 116)(2 107 12 117)(3 108 13 118)(4 109 14 119)(5 110 15 120)(6 111 16 101)(7 112 17 102)(8 113 18 103)(9 114 19 104)(10 115 20 105)(21 96 31 86)(22 97 32 87)(23 98 33 88)(24 99 34 89)(25 100 35 90)(26 81 36 91)(27 82 37 92)(28 83 38 93)(29 84 39 94)(30 85 40 95)(41 75 51 65)(42 76 52 66)(43 77 53 67)(44 78 54 68)(45 79 55 69)(46 80 56 70)(47 61 57 71)(48 62 58 72)(49 63 59 73)(50 64 60 74)(121 151 131 141)(122 152 132 142)(123 153 133 143)(124 154 134 144)(125 155 135 145)(126 156 136 146)(127 157 137 147)(128 158 138 148)(129 159 139 149)(130 160 140 150)
(2 43)(4 45)(6 47)(8 49)(10 51)(12 53)(14 55)(16 57)(18 59)(20 41)(21 96)(22 139)(23 98)(24 121)(25 100)(26 123)(27 82)(28 125)(29 84)(30 127)(31 86)(32 129)(33 88)(34 131)(35 90)(36 133)(37 92)(38 135)(39 94)(40 137)(61 101)(62 72)(63 103)(64 74)(65 105)(66 76)(67 107)(68 78)(69 109)(70 80)(71 111)(73 113)(75 115)(77 117)(79 119)(81 143)(83 145)(85 147)(87 149)(89 151)(91 153)(93 155)(95 157)(97 159)(99 141)(102 112)(104 114)(106 116)(108 118)(110 120)(122 142)(124 144)(126 146)(128 148)(130 150)(132 152)(134 154)(136 156)(138 158)(140 160)
(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)
(1 140 52 88)(2 129 53 97)(3 138 54 86)(4 127 55 95)(5 136 56 84)(6 125 57 93)(7 134 58 82)(8 123 59 91)(9 132 60 100)(10 121 41 89)(11 130 42 98)(12 139 43 87)(13 128 44 96)(14 137 45 85)(15 126 46 94)(16 135 47 83)(17 124 48 92)(18 133 49 81)(19 122 50 90)(20 131 51 99)(21 118 148 78)(22 107 149 67)(23 116 150 76)(24 105 151 65)(25 114 152 74)(26 103 153 63)(27 112 154 72)(28 101 155 61)(29 110 156 70)(30 119 157 79)(31 108 158 68)(32 117 159 77)(33 106 160 66)(34 115 141 75)(35 104 142 64)(36 113 143 73)(37 102 144 62)(38 111 145 71)(39 120 146 80)(40 109 147 69)
G:=sub<Sym(160)| (1,52)(2,53)(3,54)(4,55)(5,56)(6,57)(7,58)(8,59)(9,60)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,148)(22,149)(23,150)(24,151)(25,152)(26,153)(27,154)(28,155)(29,156)(30,157)(31,158)(32,159)(33,160)(34,141)(35,142)(36,143)(37,144)(38,145)(39,146)(40,147)(61,101)(62,102)(63,103)(64,104)(65,105)(66,106)(67,107)(68,108)(69,109)(70,110)(71,111)(72,112)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,133)(82,134)(83,135)(84,136)(85,137)(86,138)(87,139)(88,140)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132), (1,106,11,116)(2,107,12,117)(3,108,13,118)(4,109,14,119)(5,110,15,120)(6,111,16,101)(7,112,17,102)(8,113,18,103)(9,114,19,104)(10,115,20,105)(21,96,31,86)(22,97,32,87)(23,98,33,88)(24,99,34,89)(25,100,35,90)(26,81,36,91)(27,82,37,92)(28,83,38,93)(29,84,39,94)(30,85,40,95)(41,75,51,65)(42,76,52,66)(43,77,53,67)(44,78,54,68)(45,79,55,69)(46,80,56,70)(47,61,57,71)(48,62,58,72)(49,63,59,73)(50,64,60,74)(121,151,131,141)(122,152,132,142)(123,153,133,143)(124,154,134,144)(125,155,135,145)(126,156,136,146)(127,157,137,147)(128,158,138,148)(129,159,139,149)(130,160,140,150), (2,43)(4,45)(6,47)(8,49)(10,51)(12,53)(14,55)(16,57)(18,59)(20,41)(21,96)(22,139)(23,98)(24,121)(25,100)(26,123)(27,82)(28,125)(29,84)(30,127)(31,86)(32,129)(33,88)(34,131)(35,90)(36,133)(37,92)(38,135)(39,94)(40,137)(61,101)(62,72)(63,103)(64,74)(65,105)(66,76)(67,107)(68,78)(69,109)(70,80)(71,111)(73,113)(75,115)(77,117)(79,119)(81,143)(83,145)(85,147)(87,149)(89,151)(91,153)(93,155)(95,157)(97,159)(99,141)(102,112)(104,114)(106,116)(108,118)(110,120)(122,142)(124,144)(126,146)(128,148)(130,150)(132,152)(134,154)(136,156)(138,158)(140,160), (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), (1,140,52,88)(2,129,53,97)(3,138,54,86)(4,127,55,95)(5,136,56,84)(6,125,57,93)(7,134,58,82)(8,123,59,91)(9,132,60,100)(10,121,41,89)(11,130,42,98)(12,139,43,87)(13,128,44,96)(14,137,45,85)(15,126,46,94)(16,135,47,83)(17,124,48,92)(18,133,49,81)(19,122,50,90)(20,131,51,99)(21,118,148,78)(22,107,149,67)(23,116,150,76)(24,105,151,65)(25,114,152,74)(26,103,153,63)(27,112,154,72)(28,101,155,61)(29,110,156,70)(30,119,157,79)(31,108,158,68)(32,117,159,77)(33,106,160,66)(34,115,141,75)(35,104,142,64)(36,113,143,73)(37,102,144,62)(38,111,145,71)(39,120,146,80)(40,109,147,69)>;
G:=Group( (1,52)(2,53)(3,54)(4,55)(5,56)(6,57)(7,58)(8,59)(9,60)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,148)(22,149)(23,150)(24,151)(25,152)(26,153)(27,154)(28,155)(29,156)(30,157)(31,158)(32,159)(33,160)(34,141)(35,142)(36,143)(37,144)(38,145)(39,146)(40,147)(61,101)(62,102)(63,103)(64,104)(65,105)(66,106)(67,107)(68,108)(69,109)(70,110)(71,111)(72,112)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,133)(82,134)(83,135)(84,136)(85,137)(86,138)(87,139)(88,140)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132), (1,106,11,116)(2,107,12,117)(3,108,13,118)(4,109,14,119)(5,110,15,120)(6,111,16,101)(7,112,17,102)(8,113,18,103)(9,114,19,104)(10,115,20,105)(21,96,31,86)(22,97,32,87)(23,98,33,88)(24,99,34,89)(25,100,35,90)(26,81,36,91)(27,82,37,92)(28,83,38,93)(29,84,39,94)(30,85,40,95)(41,75,51,65)(42,76,52,66)(43,77,53,67)(44,78,54,68)(45,79,55,69)(46,80,56,70)(47,61,57,71)(48,62,58,72)(49,63,59,73)(50,64,60,74)(121,151,131,141)(122,152,132,142)(123,153,133,143)(124,154,134,144)(125,155,135,145)(126,156,136,146)(127,157,137,147)(128,158,138,148)(129,159,139,149)(130,160,140,150), (2,43)(4,45)(6,47)(8,49)(10,51)(12,53)(14,55)(16,57)(18,59)(20,41)(21,96)(22,139)(23,98)(24,121)(25,100)(26,123)(27,82)(28,125)(29,84)(30,127)(31,86)(32,129)(33,88)(34,131)(35,90)(36,133)(37,92)(38,135)(39,94)(40,137)(61,101)(62,72)(63,103)(64,74)(65,105)(66,76)(67,107)(68,78)(69,109)(70,80)(71,111)(73,113)(75,115)(77,117)(79,119)(81,143)(83,145)(85,147)(87,149)(89,151)(91,153)(93,155)(95,157)(97,159)(99,141)(102,112)(104,114)(106,116)(108,118)(110,120)(122,142)(124,144)(126,146)(128,148)(130,150)(132,152)(134,154)(136,156)(138,158)(140,160), (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), (1,140,52,88)(2,129,53,97)(3,138,54,86)(4,127,55,95)(5,136,56,84)(6,125,57,93)(7,134,58,82)(8,123,59,91)(9,132,60,100)(10,121,41,89)(11,130,42,98)(12,139,43,87)(13,128,44,96)(14,137,45,85)(15,126,46,94)(16,135,47,83)(17,124,48,92)(18,133,49,81)(19,122,50,90)(20,131,51,99)(21,118,148,78)(22,107,149,67)(23,116,150,76)(24,105,151,65)(25,114,152,74)(26,103,153,63)(27,112,154,72)(28,101,155,61)(29,110,156,70)(30,119,157,79)(31,108,158,68)(32,117,159,77)(33,106,160,66)(34,115,141,75)(35,104,142,64)(36,113,143,73)(37,102,144,62)(38,111,145,71)(39,120,146,80)(40,109,147,69) );
G=PermutationGroup([(1,52),(2,53),(3,54),(4,55),(5,56),(6,57),(7,58),(8,59),(9,60),(10,41),(11,42),(12,43),(13,44),(14,45),(15,46),(16,47),(17,48),(18,49),(19,50),(20,51),(21,148),(22,149),(23,150),(24,151),(25,152),(26,153),(27,154),(28,155),(29,156),(30,157),(31,158),(32,159),(33,160),(34,141),(35,142),(36,143),(37,144),(38,145),(39,146),(40,147),(61,101),(62,102),(63,103),(64,104),(65,105),(66,106),(67,107),(68,108),(69,109),(70,110),(71,111),(72,112),(73,113),(74,114),(75,115),(76,116),(77,117),(78,118),(79,119),(80,120),(81,133),(82,134),(83,135),(84,136),(85,137),(86,138),(87,139),(88,140),(89,121),(90,122),(91,123),(92,124),(93,125),(94,126),(95,127),(96,128),(97,129),(98,130),(99,131),(100,132)], [(1,106,11,116),(2,107,12,117),(3,108,13,118),(4,109,14,119),(5,110,15,120),(6,111,16,101),(7,112,17,102),(8,113,18,103),(9,114,19,104),(10,115,20,105),(21,96,31,86),(22,97,32,87),(23,98,33,88),(24,99,34,89),(25,100,35,90),(26,81,36,91),(27,82,37,92),(28,83,38,93),(29,84,39,94),(30,85,40,95),(41,75,51,65),(42,76,52,66),(43,77,53,67),(44,78,54,68),(45,79,55,69),(46,80,56,70),(47,61,57,71),(48,62,58,72),(49,63,59,73),(50,64,60,74),(121,151,131,141),(122,152,132,142),(123,153,133,143),(124,154,134,144),(125,155,135,145),(126,156,136,146),(127,157,137,147),(128,158,138,148),(129,159,139,149),(130,160,140,150)], [(2,43),(4,45),(6,47),(8,49),(10,51),(12,53),(14,55),(16,57),(18,59),(20,41),(21,96),(22,139),(23,98),(24,121),(25,100),(26,123),(27,82),(28,125),(29,84),(30,127),(31,86),(32,129),(33,88),(34,131),(35,90),(36,133),(37,92),(38,135),(39,94),(40,137),(61,101),(62,72),(63,103),(64,74),(65,105),(66,76),(67,107),(68,78),(69,109),(70,80),(71,111),(73,113),(75,115),(77,117),(79,119),(81,143),(83,145),(85,147),(87,149),(89,151),(91,153),(93,155),(95,157),(97,159),(99,141),(102,112),(104,114),(106,116),(108,118),(110,120),(122,142),(124,144),(126,146),(128,148),(130,150),(132,152),(134,154),(136,156),(138,158),(140,160)], [(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)], [(1,140,52,88),(2,129,53,97),(3,138,54,86),(4,127,55,95),(5,136,56,84),(6,125,57,93),(7,134,58,82),(8,123,59,91),(9,132,60,100),(10,121,41,89),(11,130,42,98),(12,139,43,87),(13,128,44,96),(14,137,45,85),(15,126,46,94),(16,135,47,83),(17,124,48,92),(18,133,49,81),(19,122,50,90),(20,131,51,99),(21,118,148,78),(22,107,149,67),(23,116,150,76),(24,105,151,65),(25,114,152,74),(26,103,153,63),(27,112,154,72),(28,101,155,61),(29,110,156,70),(30,119,157,79),(31,108,158,68),(32,117,159,77),(33,106,160,66),(34,115,141,75),(35,104,142,64),(36,113,143,73),(37,102,144,62),(38,111,145,71),(39,120,146,80),(40,109,147,69)])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 10M | 10N | 20A | ··· | 20H | 20I | 20J | 20K | 20L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 8 | 2 | 2 | 2 | 2 | 8 | 20 | 20 | 20 | 20 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | 8 | 8 | 8 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4○D8 | C5⋊D4 | C5⋊D4 | C8⋊C22 | D4⋊2D5 | D4.D10 | D4.8D10 |
| kernel | (C2×D4).D10 | C10.D8 | C20.Q8 | C20.55D4 | D4⋊Dic5 | C23.21D10 | C5×C4⋊D4 | C2×C20 | C22×C10 | C4⋊D4 | C20 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C2×C4 | C23 | C10 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 2 | 4 | 4 | 4 | 1 | 4 | 4 | 4 |
Matrix representation of (C2×D4).D10 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 22 | 0 | 0 | 0 | 0 |
| 26 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 26 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 26 | 40 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 35 | 0 | 0 |
| 0 | 0 | 15 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 22 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 2 | 0 | 0 | 0 | 0 |
| 20 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 38 | 0 | 0 |
| 0 | 0 | 8 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 7 |
| 0 | 0 | 0 | 0 | 0 | 9 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,26,0,0,0,0,22,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,26,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,26,0,0,0,0,0,40],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,20,15,0,0,0,0,35,14,0,0,0,0,0,0,1,0,0,0,0,0,22,40],[0,20,0,0,0,0,2,0,0,0,0,0,0,0,36,8,0,0,0,0,38,5,0,0,0,0,0,0,32,0,0,0,0,0,7,9] >;
(C2×D4).D10 in GAP, Magma, Sage, TeX
(C_2\times D_4).D_{10} % in TeX
G:=Group("(C2xD4).D10"); // GroupNames label
G:=SmallGroup(320,662);
// by ID
G=gap.SmallGroup(320,662);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,254,219,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=1,d^10=b^2,e^2=a,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=a*b^2*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^9>;
// generators/relations