direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4.8D10, C20.34C24, D20.30C23, Dic10.29C23, C4○D4⋊15D10, C10⋊5(C4○D8), D4⋊D5⋊23C22, (C2×C20).502D4, C20.263(C2×D4), Q8⋊D5⋊21C22, C4.34(C23×D5), (C2×D4).232D10, C4○D20⋊20C22, C5⋊2C8.30C23, D4.D5⋊20C22, (C2×Q8).190D10, C5⋊Q16⋊20C22, (C5×D4).22C23, D4.22(C22×D5), (C5×Q8).22C23, Q8.22(C22×D5), (C2×C20).556C23, (C22×C10).123D4, C10.159(C22×D4), (C22×C4).387D10, C23.45(C5⋊D4), (D4×C10).272C22, (C2×D20).288C22, (Q8×C10).237C22, (C22×C20).291C22, (C2×Dic10).317C22, C5⋊6(C2×C4○D8), (C2×C4○D4)⋊3D5, (C2×D4⋊D5)⋊33C2, (C10×C4○D4)⋊3C2, (C2×Q8⋊D5)⋊33C2, C4.30(C2×C5⋊D4), (C2×C4○D20)⋊30C2, (C2×D4.D5)⋊33C2, (C2×C5⋊Q16)⋊33C2, (C2×C10).76(C2×D4), (C2×C5⋊2C8)⋊42C22, (C22×C5⋊2C8)⋊15C2, (C5×C4○D4)⋊17C22, C2.32(C22×C5⋊D4), (C2×C4).158(C5⋊D4), (C2×C4).636(C22×D5), C22.119(C2×C5⋊D4), SmallGroup(320,1493)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4.8D10
G = < a,b,c,d,e | a2=b4=c2=1, d10=e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=ebe-1=b-1, bd=db, cd=dc, ece-1=bc, ede-1=d9 >
Subgroups: 830 in 266 conjugacy classes, 111 normal (35 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×10], C5, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×10], D4 [×2], D4 [×12], Q8 [×2], Q8 [×4], C23, C23 [×2], D5 [×2], C10, C10 [×2], C10 [×4], C2×C8 [×6], D8 [×4], SD16 [×8], Q16 [×4], C22×C4, C22×C4 [×2], C2×D4, C2×D4 [×3], C2×Q8, C2×Q8, C4○D4 [×4], C4○D4 [×8], Dic5 [×2], C20 [×2], C20 [×2], C20 [×2], D10 [×4], C2×C10, C2×C10 [×2], C2×C10 [×6], C22×C8, C2×D8, C2×SD16 [×2], C2×Q16, C4○D8 [×8], C2×C4○D4, C2×C4○D4, C5⋊2C8 [×4], Dic10 [×2], Dic10, C4×D5 [×4], D20 [×2], D20, C2×Dic5, C5⋊D4 [×4], C2×C20 [×2], C2×C20 [×4], C2×C20 [×5], C5×D4 [×2], C5×D4 [×5], C5×Q8 [×2], C5×Q8, C22×D5, C22×C10, C22×C10, C2×C4○D8, C2×C5⋊2C8 [×2], C2×C5⋊2C8 [×4], D4⋊D5 [×4], D4.D5 [×4], Q8⋊D5 [×4], C5⋊Q16 [×4], C2×Dic10, C2×C4×D5, C2×D20, C4○D20 [×4], C4○D20 [×2], C2×C5⋊D4, C22×C20, C22×C20, D4×C10, D4×C10, Q8×C10, C5×C4○D4 [×4], C5×C4○D4 [×2], C22×C5⋊2C8, C2×D4⋊D5, C2×D4.D5, C2×Q8⋊D5, C2×C5⋊Q16, D4.8D10 [×8], C2×C4○D20, C10×C4○D4, C2×D4.8D10
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C4○D8 [×2], C22×D4, C5⋊D4 [×4], C22×D5 [×7], C2×C4○D8, C2×C5⋊D4 [×6], C23×D5, D4.8D10 [×2], C22×C5⋊D4, C2×D4.8D10
►On 160 points
Generators in S160
(1 90)(2 91)(3 92)(4 93)(5 94)(6 95)(7 96)(8 97)(9 98)(10 99)(11 100)(12 81)(13 82)(14 83)(15 84)(16 85)(17 86)(18 87)(19 88)(20 89)(21 66)(22 67)(23 68)(24 69)(25 70)(26 71)(27 72)(28 73)(29 74)(30 75)(31 76)(32 77)(33 78)(34 79)(35 80)(36 61)(37 62)(38 63)(39 64)(40 65)(41 152)(42 153)(43 154)(44 155)(45 156)(46 157)(47 158)(48 159)(49 160)(50 141)(51 142)(52 143)(53 144)(54 145)(55 146)(56 147)(57 148)(58 149)(59 150)(60 151)(101 136)(102 137)(103 138)(104 139)(105 140)(106 121)(107 122)(108 123)(109 124)(110 125)(111 126)(112 127)(113 128)(114 129)(115 130)(116 131)(117 132)(118 133)(119 134)(120 135)
(1 113 11 103)(2 114 12 104)(3 115 13 105)(4 116 14 106)(5 117 15 107)(6 118 16 108)(7 119 17 109)(8 120 18 110)(9 101 19 111)(10 102 20 112)(21 154 31 144)(22 155 32 145)(23 156 33 146)(24 157 34 147)(25 158 35 148)(26 159 36 149)(27 160 37 150)(28 141 38 151)(29 142 39 152)(30 143 40 153)(41 74 51 64)(42 75 52 65)(43 76 53 66)(44 77 54 67)(45 78 55 68)(46 79 56 69)(47 80 57 70)(48 61 58 71)(49 62 59 72)(50 63 60 73)(81 139 91 129)(82 140 92 130)(83 121 93 131)(84 122 94 132)(85 123 95 133)(86 124 96 134)(87 125 97 135)(88 126 98 136)(89 127 99 137)(90 128 100 138)
(1 148)(2 149)(3 150)(4 151)(5 152)(6 153)(7 154)(8 155)(9 156)(10 157)(11 158)(12 159)(13 160)(14 141)(15 142)(16 143)(17 144)(18 145)(19 146)(20 147)(21 119)(22 120)(23 101)(24 102)(25 103)(26 104)(27 105)(28 106)(29 107)(30 108)(31 109)(32 110)(33 111)(34 112)(35 113)(36 114)(37 115)(38 116)(39 117)(40 118)(41 94)(42 95)(43 96)(44 97)(45 98)(46 99)(47 100)(48 81)(49 82)(50 83)(51 84)(52 85)(53 86)(54 87)(55 88)(56 89)(57 90)(58 91)(59 92)(60 93)(61 129)(62 130)(63 131)(64 132)(65 133)(66 134)(67 135)(68 136)(69 137)(70 138)(71 139)(72 140)(73 121)(74 122)(75 123)(76 124)(77 125)(78 126)(79 127)(80 128)
(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 10 11 20)(2 19 12 9)(3 8 13 18)(4 17 14 7)(5 6 15 16)(21 151 31 141)(22 160 32 150)(23 149 33 159)(24 158 34 148)(25 147 35 157)(26 156 36 146)(27 145 37 155)(28 154 38 144)(29 143 39 153)(30 152 40 142)(41 65 51 75)(42 74 52 64)(43 63 53 73)(44 72 54 62)(45 61 55 71)(46 70 56 80)(47 79 57 69)(48 68 58 78)(49 77 59 67)(50 66 60 76)(81 98 91 88)(82 87 92 97)(83 96 93 86)(84 85 94 95)(89 90 99 100)(101 104 111 114)(102 113 112 103)(105 120 115 110)(106 109 116 119)(107 118 117 108)(121 124 131 134)(122 133 132 123)(125 140 135 130)(126 129 136 139)(127 138 137 128)
G:=sub<Sym(160)| (1,90)(2,91)(3,92)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,81)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,88)(20,89)(21,66)(22,67)(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,75)(31,76)(32,77)(33,78)(34,79)(35,80)(36,61)(37,62)(38,63)(39,64)(40,65)(41,152)(42,153)(43,154)(44,155)(45,156)(46,157)(47,158)(48,159)(49,160)(50,141)(51,142)(52,143)(53,144)(54,145)(55,146)(56,147)(57,148)(58,149)(59,150)(60,151)(101,136)(102,137)(103,138)(104,139)(105,140)(106,121)(107,122)(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)(115,130)(116,131)(117,132)(118,133)(119,134)(120,135), (1,113,11,103)(2,114,12,104)(3,115,13,105)(4,116,14,106)(5,117,15,107)(6,118,16,108)(7,119,17,109)(8,120,18,110)(9,101,19,111)(10,102,20,112)(21,154,31,144)(22,155,32,145)(23,156,33,146)(24,157,34,147)(25,158,35,148)(26,159,36,149)(27,160,37,150)(28,141,38,151)(29,142,39,152)(30,143,40,153)(41,74,51,64)(42,75,52,65)(43,76,53,66)(44,77,54,67)(45,78,55,68)(46,79,56,69)(47,80,57,70)(48,61,58,71)(49,62,59,72)(50,63,60,73)(81,139,91,129)(82,140,92,130)(83,121,93,131)(84,122,94,132)(85,123,95,133)(86,124,96,134)(87,125,97,135)(88,126,98,136)(89,127,99,137)(90,128,100,138), (1,148)(2,149)(3,150)(4,151)(5,152)(6,153)(7,154)(8,155)(9,156)(10,157)(11,158)(12,159)(13,160)(14,141)(15,142)(16,143)(17,144)(18,145)(19,146)(20,147)(21,119)(22,120)(23,101)(24,102)(25,103)(26,104)(27,105)(28,106)(29,107)(30,108)(31,109)(32,110)(33,111)(34,112)(35,113)(36,114)(37,115)(38,116)(39,117)(40,118)(41,94)(42,95)(43,96)(44,97)(45,98)(46,99)(47,100)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)(55,88)(56,89)(57,90)(58,91)(59,92)(60,93)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,121)(74,122)(75,123)(76,124)(77,125)(78,126)(79,127)(80,128), (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), (1,10,11,20)(2,19,12,9)(3,8,13,18)(4,17,14,7)(5,6,15,16)(21,151,31,141)(22,160,32,150)(23,149,33,159)(24,158,34,148)(25,147,35,157)(26,156,36,146)(27,145,37,155)(28,154,38,144)(29,143,39,153)(30,152,40,142)(41,65,51,75)(42,74,52,64)(43,63,53,73)(44,72,54,62)(45,61,55,71)(46,70,56,80)(47,79,57,69)(48,68,58,78)(49,77,59,67)(50,66,60,76)(81,98,91,88)(82,87,92,97)(83,96,93,86)(84,85,94,95)(89,90,99,100)(101,104,111,114)(102,113,112,103)(105,120,115,110)(106,109,116,119)(107,118,117,108)(121,124,131,134)(122,133,132,123)(125,140,135,130)(126,129,136,139)(127,138,137,128)>;
G:=Group( (1,90)(2,91)(3,92)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,81)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,88)(20,89)(21,66)(22,67)(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,75)(31,76)(32,77)(33,78)(34,79)(35,80)(36,61)(37,62)(38,63)(39,64)(40,65)(41,152)(42,153)(43,154)(44,155)(45,156)(46,157)(47,158)(48,159)(49,160)(50,141)(51,142)(52,143)(53,144)(54,145)(55,146)(56,147)(57,148)(58,149)(59,150)(60,151)(101,136)(102,137)(103,138)(104,139)(105,140)(106,121)(107,122)(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)(115,130)(116,131)(117,132)(118,133)(119,134)(120,135), (1,113,11,103)(2,114,12,104)(3,115,13,105)(4,116,14,106)(5,117,15,107)(6,118,16,108)(7,119,17,109)(8,120,18,110)(9,101,19,111)(10,102,20,112)(21,154,31,144)(22,155,32,145)(23,156,33,146)(24,157,34,147)(25,158,35,148)(26,159,36,149)(27,160,37,150)(28,141,38,151)(29,142,39,152)(30,143,40,153)(41,74,51,64)(42,75,52,65)(43,76,53,66)(44,77,54,67)(45,78,55,68)(46,79,56,69)(47,80,57,70)(48,61,58,71)(49,62,59,72)(50,63,60,73)(81,139,91,129)(82,140,92,130)(83,121,93,131)(84,122,94,132)(85,123,95,133)(86,124,96,134)(87,125,97,135)(88,126,98,136)(89,127,99,137)(90,128,100,138), (1,148)(2,149)(3,150)(4,151)(5,152)(6,153)(7,154)(8,155)(9,156)(10,157)(11,158)(12,159)(13,160)(14,141)(15,142)(16,143)(17,144)(18,145)(19,146)(20,147)(21,119)(22,120)(23,101)(24,102)(25,103)(26,104)(27,105)(28,106)(29,107)(30,108)(31,109)(32,110)(33,111)(34,112)(35,113)(36,114)(37,115)(38,116)(39,117)(40,118)(41,94)(42,95)(43,96)(44,97)(45,98)(46,99)(47,100)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)(55,88)(56,89)(57,90)(58,91)(59,92)(60,93)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,121)(74,122)(75,123)(76,124)(77,125)(78,126)(79,127)(80,128), (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), (1,10,11,20)(2,19,12,9)(3,8,13,18)(4,17,14,7)(5,6,15,16)(21,151,31,141)(22,160,32,150)(23,149,33,159)(24,158,34,148)(25,147,35,157)(26,156,36,146)(27,145,37,155)(28,154,38,144)(29,143,39,153)(30,152,40,142)(41,65,51,75)(42,74,52,64)(43,63,53,73)(44,72,54,62)(45,61,55,71)(46,70,56,80)(47,79,57,69)(48,68,58,78)(49,77,59,67)(50,66,60,76)(81,98,91,88)(82,87,92,97)(83,96,93,86)(84,85,94,95)(89,90,99,100)(101,104,111,114)(102,113,112,103)(105,120,115,110)(106,109,116,119)(107,118,117,108)(121,124,131,134)(122,133,132,123)(125,140,135,130)(126,129,136,139)(127,138,137,128) );
G=PermutationGroup([(1,90),(2,91),(3,92),(4,93),(5,94),(6,95),(7,96),(8,97),(9,98),(10,99),(11,100),(12,81),(13,82),(14,83),(15,84),(16,85),(17,86),(18,87),(19,88),(20,89),(21,66),(22,67),(23,68),(24,69),(25,70),(26,71),(27,72),(28,73),(29,74),(30,75),(31,76),(32,77),(33,78),(34,79),(35,80),(36,61),(37,62),(38,63),(39,64),(40,65),(41,152),(42,153),(43,154),(44,155),(45,156),(46,157),(47,158),(48,159),(49,160),(50,141),(51,142),(52,143),(53,144),(54,145),(55,146),(56,147),(57,148),(58,149),(59,150),(60,151),(101,136),(102,137),(103,138),(104,139),(105,140),(106,121),(107,122),(108,123),(109,124),(110,125),(111,126),(112,127),(113,128),(114,129),(115,130),(116,131),(117,132),(118,133),(119,134),(120,135)], [(1,113,11,103),(2,114,12,104),(3,115,13,105),(4,116,14,106),(5,117,15,107),(6,118,16,108),(7,119,17,109),(8,120,18,110),(9,101,19,111),(10,102,20,112),(21,154,31,144),(22,155,32,145),(23,156,33,146),(24,157,34,147),(25,158,35,148),(26,159,36,149),(27,160,37,150),(28,141,38,151),(29,142,39,152),(30,143,40,153),(41,74,51,64),(42,75,52,65),(43,76,53,66),(44,77,54,67),(45,78,55,68),(46,79,56,69),(47,80,57,70),(48,61,58,71),(49,62,59,72),(50,63,60,73),(81,139,91,129),(82,140,92,130),(83,121,93,131),(84,122,94,132),(85,123,95,133),(86,124,96,134),(87,125,97,135),(88,126,98,136),(89,127,99,137),(90,128,100,138)], [(1,148),(2,149),(3,150),(4,151),(5,152),(6,153),(7,154),(8,155),(9,156),(10,157),(11,158),(12,159),(13,160),(14,141),(15,142),(16,143),(17,144),(18,145),(19,146),(20,147),(21,119),(22,120),(23,101),(24,102),(25,103),(26,104),(27,105),(28,106),(29,107),(30,108),(31,109),(32,110),(33,111),(34,112),(35,113),(36,114),(37,115),(38,116),(39,117),(40,118),(41,94),(42,95),(43,96),(44,97),(45,98),(46,99),(47,100),(48,81),(49,82),(50,83),(51,84),(52,85),(53,86),(54,87),(55,88),(56,89),(57,90),(58,91),(59,92),(60,93),(61,129),(62,130),(63,131),(64,132),(65,133),(66,134),(67,135),(68,136),(69,137),(70,138),(71,139),(72,140),(73,121),(74,122),(75,123),(76,124),(77,125),(78,126),(79,127),(80,128)], [(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)], [(1,10,11,20),(2,19,12,9),(3,8,13,18),(4,17,14,7),(5,6,15,16),(21,151,31,141),(22,160,32,150),(23,149,33,159),(24,158,34,148),(25,147,35,157),(26,156,36,146),(27,145,37,155),(28,154,38,144),(29,143,39,153),(30,152,40,142),(41,65,51,75),(42,74,52,64),(43,63,53,73),(44,72,54,62),(45,61,55,71),(46,70,56,80),(47,79,57,69),(48,68,58,78),(49,77,59,67),(50,66,60,76),(81,98,91,88),(82,87,92,97),(83,96,93,86),(84,85,94,95),(89,90,99,100),(101,104,111,114),(102,113,112,103),(105,120,115,110),(106,109,116,119),(107,118,117,108),(121,124,131,134),(122,133,132,123),(125,140,135,130),(126,129,136,139),(127,138,137,128)])
68 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10F | 10G | ··· | 10R | 20A | ··· | 20H | 20I | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 20 | 20 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | D10 | D10 | D10 | D10 | C4○D8 | C5⋊D4 | C5⋊D4 | D4.8D10 |
| kernel | C2×D4.8D10 | C22×C5⋊2C8 | C2×D4⋊D5 | C2×D4.D5 | C2×Q8⋊D5 | C2×C5⋊Q16 | D4.8D10 | C2×C4○D20 | C10×C4○D4 | C2×C20 | C22×C10 | C2×C4○D4 | C22×C4 | C2×D4 | C2×Q8 | C4○D4 | C10 | C2×C4 | C23 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 1 | 3 | 1 | 2 | 2 | 2 | 2 | 8 | 8 | 12 | 4 | 8 |
Matrix representation of C2×D4.8D10 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 39 |
| 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 4 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 17 |
| 0 | 0 | 0 | 0 | 12 | 24 |
| 1 | 35 | 0 | 0 | 0 | 0 |
| 6 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 0 | 9 |
| 1 | 35 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 21 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 32 | 32 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,1,0,0,0,0,39,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,4,1,0,0,0,0,0,0,17,12,0,0,0,0,17,24],[1,6,0,0,0,0,35,6,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,0,0,0,0,0,0,9],[1,0,0,0,0,0,35,40,0,0,0,0,0,0,1,21,0,0,0,0,0,40,0,0,0,0,0,0,9,32,0,0,0,0,0,32] >;
C2×D4.8D10 in GAP, Magma, Sage, TeX
C_2\times D_4._8D_{10} % in TeX
G:=Group("C2xD4.8D10"); // GroupNames label
G:=SmallGroup(320,1493);
// by ID
G=gap.SmallGroup(320,1493);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,675,1684,235,102,12550]);
// 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=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b*c,e*d*e^-1=d^9>;
// generators/relations