direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4.10D10, C10.13C25, C20.48C24, D10.7C24, D20.40C23, C10⋊22- 1+4, Dic5.8C24, Dic10.37C23, C4○D4⋊18D10, (C2×C10).4C24, (Q8×D5)⋊14C22, C2.14(D5×C24), C4.63(C23×D5), C5⋊D4.1C23, (C2×D4).254D10, C5⋊2(C2×2- 1+4), C4○D20⋊26C22, (C2×Q8).212D10, D4.29(C22×D5), (C4×D5).19C23, (C5×D4).29C23, (C5×Q8).30C23, Q8.30(C22×D5), D4⋊2D5⋊13C22, (C2×C20).567C23, (C22×C4).292D10, C22.57(C23×D5), (C2×Dic10)⋊75C22, (C22×Dic10)⋊25C2, (D4×C10).279C22, (C2×D20).298C22, (Q8×C10).247C22, C23.215(C22×D5), (C22×C10).249C23, (C22×C20).303C22, (C2×Dic5).167C23, (C22×D5).260C23, (C22×Dic5).169C22, (C2×Q8×D5)⋊21C2, (C2×C4○D4)⋊14D5, (C10×C4○D4)⋊15C2, (C2×C4○D20)⋊38C2, (C2×D4⋊2D5)⋊30C2, (C5×C4○D4)⋊21C22, (C2×C4×D5).182C22, (C2×C4).253(C22×D5), (C2×C5⋊D4).152C22, SmallGroup(320,1620)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4.10D10
G = < a,b,c,d,e | a2=b4=c2=1, d10=e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=dbd-1=ebe-1=b-1, dcd-1=b2c, ce=ec, ede-1=d9 >
Subgroups: 2126 in 794 conjugacy classes, 447 normal (14 characteristic)
C1, C2, C2 [×2], C2 [×10], C4 [×8], C4 [×12], C22, C22 [×6], C22 [×14], C5, C2×C4, C2×C4 [×15], C2×C4 [×54], D4 [×12], D4 [×28], Q8 [×4], Q8 [×36], C23 [×3], C23 [×2], D5 [×4], C10, C10 [×2], C10 [×6], C22×C4 [×3], C22×C4 [×12], C2×D4 [×3], C2×D4 [×7], C2×Q8, C2×Q8 [×49], C4○D4 [×8], C4○D4 [×72], Dic5 [×12], C20 [×8], D10 [×4], D10 [×4], C2×C10, C2×C10 [×6], C2×C10 [×6], C22×Q8 [×5], C2×C4○D4, C2×C4○D4 [×9], 2- 1+4 [×16], Dic10 [×36], C4×D5 [×24], D20 [×4], C2×Dic5 [×30], C5⋊D4 [×24], C2×C20, C2×C20 [×15], C5×D4 [×12], C5×Q8 [×4], C22×D5 [×2], C22×C10 [×3], C2×2- 1+4, C2×Dic10 [×33], C2×C4×D5 [×6], C2×D20, C4○D20 [×24], D4⋊2D5 [×48], Q8×D5 [×16], C22×Dic5 [×6], C2×C5⋊D4 [×6], C22×C20 [×3], D4×C10 [×3], Q8×C10, C5×C4○D4 [×8], C22×Dic10 [×3], C2×C4○D20 [×3], C2×D4⋊2D5 [×6], C2×Q8×D5 [×2], D4.10D10 [×16], C10×C4○D4, C2×D4.10D10
Quotients: C1, C2 [×31], C22 [×155], C23 [×155], D5, C24 [×31], D10 [×15], 2- 1+4 [×2], C25, C22×D5 [×35], C2×2- 1+4, C23×D5 [×15], D4.10D10 [×2], D5×C24, C2×D4.10D10
►On 160 points
Generators in S160
(1 139)(2 140)(3 121)(4 122)(5 123)(6 124)(7 125)(8 126)(9 127)(10 128)(11 129)(12 130)(13 131)(14 132)(15 133)(16 134)(17 135)(18 136)(19 137)(20 138)(21 89)(22 90)(23 91)(24 92)(25 93)(26 94)(27 95)(28 96)(29 97)(30 98)(31 99)(32 100)(33 81)(34 82)(35 83)(36 84)(37 85)(38 86)(39 87)(40 88)(41 145)(42 146)(43 147)(44 148)(45 149)(46 150)(47 151)(48 152)(49 153)(50 154)(51 155)(52 156)(53 157)(54 158)(55 159)(56 160)(57 141)(58 142)(59 143)(60 144)(61 114)(62 115)(63 116)(64 117)(65 118)(66 119)(67 120)(68 101)(69 102)(70 103)(71 104)(72 105)(73 106)(74 107)(75 108)(76 109)(77 110)(78 111)(79 112)(80 113)
(1 155 11 145)(2 146 12 156)(3 157 13 147)(4 148 14 158)(5 159 15 149)(6 150 16 160)(7 141 17 151)(8 152 18 142)(9 143 19 153)(10 154 20 144)(21 109 31 119)(22 120 32 110)(23 111 33 101)(24 102 34 112)(25 113 35 103)(26 104 36 114)(27 115 37 105)(28 106 38 116)(29 117 39 107)(30 108 40 118)(41 139 51 129)(42 130 52 140)(43 121 53 131)(44 132 54 122)(45 123 55 133)(46 134 56 124)(47 125 57 135)(48 136 58 126)(49 127 59 137)(50 138 60 128)(61 94 71 84)(62 85 72 95)(63 96 73 86)(64 87 74 97)(65 98 75 88)(66 89 76 99)(67 100 77 90)(68 91 78 81)(69 82 79 92)(70 93 80 83)
(1 67)(2 78)(3 69)(4 80)(5 71)(6 62)(7 73)(8 64)(9 75)(10 66)(11 77)(12 68)(13 79)(14 70)(15 61)(16 72)(17 63)(18 74)(19 65)(20 76)(21 60)(22 51)(23 42)(24 53)(25 44)(26 55)(27 46)(28 57)(29 48)(30 59)(31 50)(32 41)(33 52)(34 43)(35 54)(36 45)(37 56)(38 47)(39 58)(40 49)(81 156)(82 147)(83 158)(84 149)(85 160)(86 151)(87 142)(88 153)(89 144)(90 155)(91 146)(92 157)(93 148)(94 159)(95 150)(96 141)(97 152)(98 143)(99 154)(100 145)(101 130)(102 121)(103 132)(104 123)(105 134)(106 125)(107 136)(108 127)(109 138)(110 129)(111 140)(112 131)(113 122)(114 133)(115 124)(116 135)(117 126)(118 137)(119 128)(120 139)
(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)
(1 128 11 138)(2 137 12 127)(3 126 13 136)(4 135 14 125)(5 124 15 134)(6 133 16 123)(7 122 17 132)(8 131 18 121)(9 140 19 130)(10 129 20 139)(21 100 31 90)(22 89 32 99)(23 98 33 88)(24 87 34 97)(25 96 35 86)(26 85 36 95)(27 94 37 84)(28 83 38 93)(29 92 39 82)(30 81 40 91)(41 154 51 144)(42 143 52 153)(43 152 53 142)(44 141 54 151)(45 150 55 160)(46 159 56 149)(47 148 57 158)(48 157 58 147)(49 146 59 156)(50 155 60 145)(61 105 71 115)(62 114 72 104)(63 103 73 113)(64 112 74 102)(65 101 75 111)(66 110 76 120)(67 119 77 109)(68 108 78 118)(69 117 79 107)(70 106 80 116)
G:=sub<Sym(160)| (1,139)(2,140)(3,121)(4,122)(5,123)(6,124)(7,125)(8,126)(9,127)(10,128)(11,129)(12,130)(13,131)(14,132)(15,133)(16,134)(17,135)(18,136)(19,137)(20,138)(21,89)(22,90)(23,91)(24,92)(25,93)(26,94)(27,95)(28,96)(29,97)(30,98)(31,99)(32,100)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(57,141)(58,142)(59,143)(60,144)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,101)(69,102)(70,103)(71,104)(72,105)(73,106)(74,107)(75,108)(76,109)(77,110)(78,111)(79,112)(80,113), (1,155,11,145)(2,146,12,156)(3,157,13,147)(4,148,14,158)(5,159,15,149)(6,150,16,160)(7,141,17,151)(8,152,18,142)(9,143,19,153)(10,154,20,144)(21,109,31,119)(22,120,32,110)(23,111,33,101)(24,102,34,112)(25,113,35,103)(26,104,36,114)(27,115,37,105)(28,106,38,116)(29,117,39,107)(30,108,40,118)(41,139,51,129)(42,130,52,140)(43,121,53,131)(44,132,54,122)(45,123,55,133)(46,134,56,124)(47,125,57,135)(48,136,58,126)(49,127,59,137)(50,138,60,128)(61,94,71,84)(62,85,72,95)(63,96,73,86)(64,87,74,97)(65,98,75,88)(66,89,76,99)(67,100,77,90)(68,91,78,81)(69,82,79,92)(70,93,80,83), (1,67)(2,78)(3,69)(4,80)(5,71)(6,62)(7,73)(8,64)(9,75)(10,66)(11,77)(12,68)(13,79)(14,70)(15,61)(16,72)(17,63)(18,74)(19,65)(20,76)(21,60)(22,51)(23,42)(24,53)(25,44)(26,55)(27,46)(28,57)(29,48)(30,59)(31,50)(32,41)(33,52)(34,43)(35,54)(36,45)(37,56)(38,47)(39,58)(40,49)(81,156)(82,147)(83,158)(84,149)(85,160)(86,151)(87,142)(88,153)(89,144)(90,155)(91,146)(92,157)(93,148)(94,159)(95,150)(96,141)(97,152)(98,143)(99,154)(100,145)(101,130)(102,121)(103,132)(104,123)(105,134)(106,125)(107,136)(108,127)(109,138)(110,129)(111,140)(112,131)(113,122)(114,133)(115,124)(116,135)(117,126)(118,137)(119,128)(120,139), (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), (1,128,11,138)(2,137,12,127)(3,126,13,136)(4,135,14,125)(5,124,15,134)(6,133,16,123)(7,122,17,132)(8,131,18,121)(9,140,19,130)(10,129,20,139)(21,100,31,90)(22,89,32,99)(23,98,33,88)(24,87,34,97)(25,96,35,86)(26,85,36,95)(27,94,37,84)(28,83,38,93)(29,92,39,82)(30,81,40,91)(41,154,51,144)(42,143,52,153)(43,152,53,142)(44,141,54,151)(45,150,55,160)(46,159,56,149)(47,148,57,158)(48,157,58,147)(49,146,59,156)(50,155,60,145)(61,105,71,115)(62,114,72,104)(63,103,73,113)(64,112,74,102)(65,101,75,111)(66,110,76,120)(67,119,77,109)(68,108,78,118)(69,117,79,107)(70,106,80,116)>;
G:=Group( (1,139)(2,140)(3,121)(4,122)(5,123)(6,124)(7,125)(8,126)(9,127)(10,128)(11,129)(12,130)(13,131)(14,132)(15,133)(16,134)(17,135)(18,136)(19,137)(20,138)(21,89)(22,90)(23,91)(24,92)(25,93)(26,94)(27,95)(28,96)(29,97)(30,98)(31,99)(32,100)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(57,141)(58,142)(59,143)(60,144)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,101)(69,102)(70,103)(71,104)(72,105)(73,106)(74,107)(75,108)(76,109)(77,110)(78,111)(79,112)(80,113), (1,155,11,145)(2,146,12,156)(3,157,13,147)(4,148,14,158)(5,159,15,149)(6,150,16,160)(7,141,17,151)(8,152,18,142)(9,143,19,153)(10,154,20,144)(21,109,31,119)(22,120,32,110)(23,111,33,101)(24,102,34,112)(25,113,35,103)(26,104,36,114)(27,115,37,105)(28,106,38,116)(29,117,39,107)(30,108,40,118)(41,139,51,129)(42,130,52,140)(43,121,53,131)(44,132,54,122)(45,123,55,133)(46,134,56,124)(47,125,57,135)(48,136,58,126)(49,127,59,137)(50,138,60,128)(61,94,71,84)(62,85,72,95)(63,96,73,86)(64,87,74,97)(65,98,75,88)(66,89,76,99)(67,100,77,90)(68,91,78,81)(69,82,79,92)(70,93,80,83), (1,67)(2,78)(3,69)(4,80)(5,71)(6,62)(7,73)(8,64)(9,75)(10,66)(11,77)(12,68)(13,79)(14,70)(15,61)(16,72)(17,63)(18,74)(19,65)(20,76)(21,60)(22,51)(23,42)(24,53)(25,44)(26,55)(27,46)(28,57)(29,48)(30,59)(31,50)(32,41)(33,52)(34,43)(35,54)(36,45)(37,56)(38,47)(39,58)(40,49)(81,156)(82,147)(83,158)(84,149)(85,160)(86,151)(87,142)(88,153)(89,144)(90,155)(91,146)(92,157)(93,148)(94,159)(95,150)(96,141)(97,152)(98,143)(99,154)(100,145)(101,130)(102,121)(103,132)(104,123)(105,134)(106,125)(107,136)(108,127)(109,138)(110,129)(111,140)(112,131)(113,122)(114,133)(115,124)(116,135)(117,126)(118,137)(119,128)(120,139), (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), (1,128,11,138)(2,137,12,127)(3,126,13,136)(4,135,14,125)(5,124,15,134)(6,133,16,123)(7,122,17,132)(8,131,18,121)(9,140,19,130)(10,129,20,139)(21,100,31,90)(22,89,32,99)(23,98,33,88)(24,87,34,97)(25,96,35,86)(26,85,36,95)(27,94,37,84)(28,83,38,93)(29,92,39,82)(30,81,40,91)(41,154,51,144)(42,143,52,153)(43,152,53,142)(44,141,54,151)(45,150,55,160)(46,159,56,149)(47,148,57,158)(48,157,58,147)(49,146,59,156)(50,155,60,145)(61,105,71,115)(62,114,72,104)(63,103,73,113)(64,112,74,102)(65,101,75,111)(66,110,76,120)(67,119,77,109)(68,108,78,118)(69,117,79,107)(70,106,80,116) );
G=PermutationGroup([(1,139),(2,140),(3,121),(4,122),(5,123),(6,124),(7,125),(8,126),(9,127),(10,128),(11,129),(12,130),(13,131),(14,132),(15,133),(16,134),(17,135),(18,136),(19,137),(20,138),(21,89),(22,90),(23,91),(24,92),(25,93),(26,94),(27,95),(28,96),(29,97),(30,98),(31,99),(32,100),(33,81),(34,82),(35,83),(36,84),(37,85),(38,86),(39,87),(40,88),(41,145),(42,146),(43,147),(44,148),(45,149),(46,150),(47,151),(48,152),(49,153),(50,154),(51,155),(52,156),(53,157),(54,158),(55,159),(56,160),(57,141),(58,142),(59,143),(60,144),(61,114),(62,115),(63,116),(64,117),(65,118),(66,119),(67,120),(68,101),(69,102),(70,103),(71,104),(72,105),(73,106),(74,107),(75,108),(76,109),(77,110),(78,111),(79,112),(80,113)], [(1,155,11,145),(2,146,12,156),(3,157,13,147),(4,148,14,158),(5,159,15,149),(6,150,16,160),(7,141,17,151),(8,152,18,142),(9,143,19,153),(10,154,20,144),(21,109,31,119),(22,120,32,110),(23,111,33,101),(24,102,34,112),(25,113,35,103),(26,104,36,114),(27,115,37,105),(28,106,38,116),(29,117,39,107),(30,108,40,118),(41,139,51,129),(42,130,52,140),(43,121,53,131),(44,132,54,122),(45,123,55,133),(46,134,56,124),(47,125,57,135),(48,136,58,126),(49,127,59,137),(50,138,60,128),(61,94,71,84),(62,85,72,95),(63,96,73,86),(64,87,74,97),(65,98,75,88),(66,89,76,99),(67,100,77,90),(68,91,78,81),(69,82,79,92),(70,93,80,83)], [(1,67),(2,78),(3,69),(4,80),(5,71),(6,62),(7,73),(8,64),(9,75),(10,66),(11,77),(12,68),(13,79),(14,70),(15,61),(16,72),(17,63),(18,74),(19,65),(20,76),(21,60),(22,51),(23,42),(24,53),(25,44),(26,55),(27,46),(28,57),(29,48),(30,59),(31,50),(32,41),(33,52),(34,43),(35,54),(36,45),(37,56),(38,47),(39,58),(40,49),(81,156),(82,147),(83,158),(84,149),(85,160),(86,151),(87,142),(88,153),(89,144),(90,155),(91,146),(92,157),(93,148),(94,159),(95,150),(96,141),(97,152),(98,143),(99,154),(100,145),(101,130),(102,121),(103,132),(104,123),(105,134),(106,125),(107,136),(108,127),(109,138),(110,129),(111,140),(112,131),(113,122),(114,133),(115,124),(116,135),(117,126),(118,137),(119,128),(120,139)], [(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)], [(1,128,11,138),(2,137,12,127),(3,126,13,136),(4,135,14,125),(5,124,15,134),(6,133,16,123),(7,122,17,132),(8,131,18,121),(9,140,19,130),(10,129,20,139),(21,100,31,90),(22,89,32,99),(23,98,33,88),(24,87,34,97),(25,96,35,86),(26,85,36,95),(27,94,37,84),(28,83,38,93),(29,92,39,82),(30,81,40,91),(41,154,51,144),(42,143,52,153),(43,152,53,142),(44,141,54,151),(45,150,55,160),(46,159,56,149),(47,148,57,158),(48,157,58,147),(49,146,59,156),(50,155,60,145),(61,105,71,115),(62,114,72,104),(63,103,73,113),(64,112,74,102),(65,101,75,111),(66,110,76,120),(67,119,77,109),(68,108,78,118),(69,117,79,107),(70,106,80,116)])
74 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 2J | 2K | 2L | 2M | 4A | ··· | 4H | 4I | ··· | 4T | 5A | 5B | 10A | ··· | 10F | 10G | ··· | 10R | 20A | ··· | 20H | 20I | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
74 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | D10 | D10 | D10 | D10 | 2- 1+4 | D4.10D10 |
| kernel | C2×D4.10D10 | C22×Dic10 | C2×C4○D20 | C2×D4⋊2D5 | C2×Q8×D5 | D4.10D10 | C10×C4○D4 | C2×C4○D4 | C22×C4 | C2×D4 | C2×Q8 | C4○D4 | C10 | C2 |
| # reps | 1 | 3 | 3 | 6 | 2 | 16 | 1 | 2 | 6 | 6 | 2 | 16 | 2 | 8 |
Matrix representation of C2×D4.10D10 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 37 | 22 | 26 |
| 0 | 0 | 32 | 16 | 38 | 19 |
| 0 | 0 | 22 | 26 | 16 | 4 |
| 0 | 0 | 38 | 19 | 9 | 25 |
| 34 | 7 | 0 | 0 | 0 | 0 |
| 34 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 29 | 0 | 36 |
| 0 | 0 | 14 | 14 | 40 | 40 |
| 0 | 0 | 0 | 36 | 0 | 12 |
| 0 | 0 | 40 | 40 | 27 | 27 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 35 | 0 |
| 0 | 0 | 25 | 39 | 7 | 6 |
| 0 | 0 | 35 | 0 | 39 | 0 |
| 0 | 0 | 7 | 6 | 16 | 2 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,40,0,0,0,0,0,0,40,0,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,25,32,22,38,0,0,37,16,26,19,0,0,22,38,16,9,0,0,26,19,4,25],[34,34,0,0,0,0,7,1,0,0,0,0,0,0,0,14,0,40,0,0,29,14,36,40,0,0,0,40,0,27,0,0,36,40,12,27],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,2,25,35,7,0,0,0,39,0,6,0,0,35,7,39,16,0,0,0,6,0,2] >;
C2×D4.10D10 in GAP, Magma, Sage, TeX
C_2\times D_4._{10}D_{10} % in TeX
G:=Group("C2xD4.10D10"); // GroupNames label
G:=SmallGroup(320,1620);
// by ID
G=gap.SmallGroup(320,1620);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,297,136,1684,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=1,d^10=e^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=d*b*d^-1=e*b*e^-1=b^-1,d*c*d^-1=b^2*c,c*e=e*c,e*d*e^-1=d^9>;
// generators/relations