metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.64D10, C23.27D20, C23.16Dic10, (C23×C4).8D5, (C22×C20)⋊25C4, (C2×C20).475D4, C4⋊2(C23.D5), (C22×C4)⋊8Dic5, C20⋊10(C22⋊C4), C2.4(C20⋊7D4), (C23×C20).11C2, C22⋊2(C4⋊Dic5), C22.60(C2×D20), (C22×C10).26Q8, C10.79(C4⋊D4), C5⋊5(C23.7Q8), (C22×C4).433D10, (C22×C10).143D4, C10.68(C22⋊Q8), C23.31(C2×Dic5), C2.5(C20.48D4), C22.63(C4○D20), (C23×C10).99C22, C22.32(C2×Dic10), C23.303(C22×D5), C10.10C42⋊24C2, C10.68(C42⋊C2), (C22×C20).484C22, (C22×C10).363C23, C22.50(C22×Dic5), (C22×Dic5).66C22, C2.12(C23.21D10), C10.79(C2×C4⋊C4), (C2×C10)⋊10(C4⋊C4), (C2×C4⋊Dic5)⋊16C2, C2.16(C2×C4⋊Dic5), (C2×C10).44(C2×Q8), (C2×C20).455(C2×C4), C2.6(C2×C23.D5), (C2×C10).549(C2×D4), (C2×C4).85(C2×Dic5), C22.87(C2×C5⋊D4), (C2×C10).91(C4○D4), (C2×C4).260(C5⋊D4), C10.111(C2×C22⋊C4), (C2×C23.D5).18C2, (C22×C10).204(C2×C4), (C2×C10).294(C22×C4), SmallGroup(320,839)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.64D10
G = < a,b,c,d,e | a2=b2=c2=d20=1, e2=b, ab=ba, eae-1=ac=ca, ad=da, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 638 in 234 conjugacy classes, 103 normal (25 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C23, C23, C23, C10, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic5, C20, C20, C2×C10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C23×C4, C2×Dic5, C2×C20, C2×C20, C22×C10, C22×C10, C22×C10, C23.7Q8, C4⋊Dic5, C23.D5, C22×Dic5, C22×C20, C22×C20, C22×C20, C23×C10, C10.10C42, C2×C4⋊Dic5, C2×C23.D5, C23×C20, C24.64D10
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, D10, C2×C22⋊C4, C2×C4⋊C4, C42⋊C2, C4⋊D4, C22⋊Q8, Dic10, D20, C2×Dic5, C5⋊D4, C22×D5, C23.7Q8, C4⋊Dic5, C23.D5, C2×Dic10, C2×D20, C4○D20, C22×Dic5, C2×C5⋊D4, C20.48D4, C2×C4⋊Dic5, C23.21D10, C20⋊7D4, C2×C23.D5, C24.64D10
►On 160 points
Generators in S160
(1 24)(2 25)(3 26)(4 27)(5 28)(6 29)(7 30)(8 31)(9 32)(10 33)(11 34)(12 35)(13 36)(14 37)(15 38)(16 39)(17 40)(18 21)(19 22)(20 23)(41 116)(42 117)(43 118)(44 119)(45 120)(46 101)(47 102)(48 103)(49 104)(50 105)(51 106)(52 107)(53 108)(54 109)(55 110)(56 111)(57 112)(58 113)(59 114)(60 115)(61 81)(62 82)(63 83)(64 84)(65 85)(66 86)(67 87)(68 88)(69 89)(70 90)(71 91)(72 92)(73 93)(74 94)(75 95)(76 96)(77 97)(78 98)(79 99)(80 100)(121 150)(122 151)(123 152)(124 153)(125 154)(126 155)(127 156)(128 157)(129 158)(130 159)(131 160)(132 141)(133 142)(134 143)(135 144)(136 145)(137 146)(138 147)(139 148)(140 149)
(1 24)(2 25)(3 26)(4 27)(5 28)(6 29)(7 30)(8 31)(9 32)(10 33)(11 34)(12 35)(13 36)(14 37)(15 38)(16 39)(17 40)(18 21)(19 22)(20 23)(41 141)(42 142)(43 143)(44 144)(45 145)(46 146)(47 147)(48 148)(49 149)(50 150)(51 151)(52 152)(53 153)(54 154)(55 155)(56 156)(57 157)(58 158)(59 159)(60 160)(61 81)(62 82)(63 83)(64 84)(65 85)(66 86)(67 87)(68 88)(69 89)(70 90)(71 91)(72 92)(73 93)(74 94)(75 95)(76 96)(77 97)(78 98)(79 99)(80 100)(101 137)(102 138)(103 139)(104 140)(105 121)(106 122)(107 123)(108 124)(109 125)(110 126)(111 127)(112 128)(113 129)(114 130)(115 131)(116 132)(117 133)(118 134)(119 135)(120 136)
(1 85)(2 86)(3 87)(4 88)(5 89)(6 90)(7 91)(8 92)(9 93)(10 94)(11 95)(12 96)(13 97)(14 98)(15 99)(16 100)(17 81)(18 82)(19 83)(20 84)(21 62)(22 63)(23 64)(24 65)(25 66)(26 67)(27 68)(28 69)(29 70)(30 71)(31 72)(32 73)(33 74)(34 75)(35 76)(36 77)(37 78)(38 79)(39 80)(40 61)(41 132)(42 133)(43 134)(44 135)(45 136)(46 137)(47 138)(48 139)(49 140)(50 121)(51 122)(52 123)(53 124)(54 125)(55 126)(56 127)(57 128)(58 129)(59 130)(60 131)(101 146)(102 147)(103 148)(104 149)(105 150)(106 151)(107 152)(108 153)(109 154)(110 155)(111 156)(112 157)(113 158)(114 159)(115 160)(116 141)(117 142)(118 143)(119 144)(120 145)
(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)
(1 105 24 121)(2 104 25 140)(3 103 26 139)(4 102 27 138)(5 101 28 137)(6 120 29 136)(7 119 30 135)(8 118 31 134)(9 117 32 133)(10 116 33 132)(11 115 34 131)(12 114 35 130)(13 113 36 129)(14 112 37 128)(15 111 38 127)(16 110 39 126)(17 109 40 125)(18 108 21 124)(19 107 22 123)(20 106 23 122)(41 94 141 74)(42 93 142 73)(43 92 143 72)(44 91 144 71)(45 90 145 70)(46 89 146 69)(47 88 147 68)(48 87 148 67)(49 86 149 66)(50 85 150 65)(51 84 151 64)(52 83 152 63)(53 82 153 62)(54 81 154 61)(55 100 155 80)(56 99 156 79)(57 98 157 78)(58 97 158 77)(59 96 159 76)(60 95 160 75)
G:=sub<Sym(160)| (1,24)(2,25)(3,26)(4,27)(5,28)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,38)(16,39)(17,40)(18,21)(19,22)(20,23)(41,116)(42,117)(43,118)(44,119)(45,120)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,112)(58,113)(59,114)(60,115)(61,81)(62,82)(63,83)(64,84)(65,85)(66,86)(67,87)(68,88)(69,89)(70,90)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,141)(133,142)(134,143)(135,144)(136,145)(137,146)(138,147)(139,148)(140,149), (1,24)(2,25)(3,26)(4,27)(5,28)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,38)(16,39)(17,40)(18,21)(19,22)(20,23)(41,141)(42,142)(43,143)(44,144)(45,145)(46,146)(47,147)(48,148)(49,149)(50,150)(51,151)(52,152)(53,153)(54,154)(55,155)(56,156)(57,157)(58,158)(59,159)(60,160)(61,81)(62,82)(63,83)(64,84)(65,85)(66,86)(67,87)(68,88)(69,89)(70,90)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(101,137)(102,138)(103,139)(104,140)(105,121)(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136), (1,85)(2,86)(3,87)(4,88)(5,89)(6,90)(7,91)(8,92)(9,93)(10,94)(11,95)(12,96)(13,97)(14,98)(15,99)(16,100)(17,81)(18,82)(19,83)(20,84)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,70)(30,71)(31,72)(32,73)(33,74)(34,75)(35,76)(36,77)(37,78)(38,79)(39,80)(40,61)(41,132)(42,133)(43,134)(44,135)(45,136)(46,137)(47,138)(48,139)(49,140)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(101,146)(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,153)(109,154)(110,155)(111,156)(112,157)(113,158)(114,159)(115,160)(116,141)(117,142)(118,143)(119,144)(120,145), (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), (1,105,24,121)(2,104,25,140)(3,103,26,139)(4,102,27,138)(5,101,28,137)(6,120,29,136)(7,119,30,135)(8,118,31,134)(9,117,32,133)(10,116,33,132)(11,115,34,131)(12,114,35,130)(13,113,36,129)(14,112,37,128)(15,111,38,127)(16,110,39,126)(17,109,40,125)(18,108,21,124)(19,107,22,123)(20,106,23,122)(41,94,141,74)(42,93,142,73)(43,92,143,72)(44,91,144,71)(45,90,145,70)(46,89,146,69)(47,88,147,68)(48,87,148,67)(49,86,149,66)(50,85,150,65)(51,84,151,64)(52,83,152,63)(53,82,153,62)(54,81,154,61)(55,100,155,80)(56,99,156,79)(57,98,157,78)(58,97,158,77)(59,96,159,76)(60,95,160,75)>;
G:=Group( (1,24)(2,25)(3,26)(4,27)(5,28)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,38)(16,39)(17,40)(18,21)(19,22)(20,23)(41,116)(42,117)(43,118)(44,119)(45,120)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,112)(58,113)(59,114)(60,115)(61,81)(62,82)(63,83)(64,84)(65,85)(66,86)(67,87)(68,88)(69,89)(70,90)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,141)(133,142)(134,143)(135,144)(136,145)(137,146)(138,147)(139,148)(140,149), (1,24)(2,25)(3,26)(4,27)(5,28)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,38)(16,39)(17,40)(18,21)(19,22)(20,23)(41,141)(42,142)(43,143)(44,144)(45,145)(46,146)(47,147)(48,148)(49,149)(50,150)(51,151)(52,152)(53,153)(54,154)(55,155)(56,156)(57,157)(58,158)(59,159)(60,160)(61,81)(62,82)(63,83)(64,84)(65,85)(66,86)(67,87)(68,88)(69,89)(70,90)(71,91)(72,92)(73,93)(74,94)(75,95)(76,96)(77,97)(78,98)(79,99)(80,100)(101,137)(102,138)(103,139)(104,140)(105,121)(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136), (1,85)(2,86)(3,87)(4,88)(5,89)(6,90)(7,91)(8,92)(9,93)(10,94)(11,95)(12,96)(13,97)(14,98)(15,99)(16,100)(17,81)(18,82)(19,83)(20,84)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,70)(30,71)(31,72)(32,73)(33,74)(34,75)(35,76)(36,77)(37,78)(38,79)(39,80)(40,61)(41,132)(42,133)(43,134)(44,135)(45,136)(46,137)(47,138)(48,139)(49,140)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(101,146)(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,153)(109,154)(110,155)(111,156)(112,157)(113,158)(114,159)(115,160)(116,141)(117,142)(118,143)(119,144)(120,145), (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), (1,105,24,121)(2,104,25,140)(3,103,26,139)(4,102,27,138)(5,101,28,137)(6,120,29,136)(7,119,30,135)(8,118,31,134)(9,117,32,133)(10,116,33,132)(11,115,34,131)(12,114,35,130)(13,113,36,129)(14,112,37,128)(15,111,38,127)(16,110,39,126)(17,109,40,125)(18,108,21,124)(19,107,22,123)(20,106,23,122)(41,94,141,74)(42,93,142,73)(43,92,143,72)(44,91,144,71)(45,90,145,70)(46,89,146,69)(47,88,147,68)(48,87,148,67)(49,86,149,66)(50,85,150,65)(51,84,151,64)(52,83,152,63)(53,82,153,62)(54,81,154,61)(55,100,155,80)(56,99,156,79)(57,98,157,78)(58,97,158,77)(59,96,159,76)(60,95,160,75) );
G=PermutationGroup([[(1,24),(2,25),(3,26),(4,27),(5,28),(6,29),(7,30),(8,31),(9,32),(10,33),(11,34),(12,35),(13,36),(14,37),(15,38),(16,39),(17,40),(18,21),(19,22),(20,23),(41,116),(42,117),(43,118),(44,119),(45,120),(46,101),(47,102),(48,103),(49,104),(50,105),(51,106),(52,107),(53,108),(54,109),(55,110),(56,111),(57,112),(58,113),(59,114),(60,115),(61,81),(62,82),(63,83),(64,84),(65,85),(66,86),(67,87),(68,88),(69,89),(70,90),(71,91),(72,92),(73,93),(74,94),(75,95),(76,96),(77,97),(78,98),(79,99),(80,100),(121,150),(122,151),(123,152),(124,153),(125,154),(126,155),(127,156),(128,157),(129,158),(130,159),(131,160),(132,141),(133,142),(134,143),(135,144),(136,145),(137,146),(138,147),(139,148),(140,149)], [(1,24),(2,25),(3,26),(4,27),(5,28),(6,29),(7,30),(8,31),(9,32),(10,33),(11,34),(12,35),(13,36),(14,37),(15,38),(16,39),(17,40),(18,21),(19,22),(20,23),(41,141),(42,142),(43,143),(44,144),(45,145),(46,146),(47,147),(48,148),(49,149),(50,150),(51,151),(52,152),(53,153),(54,154),(55,155),(56,156),(57,157),(58,158),(59,159),(60,160),(61,81),(62,82),(63,83),(64,84),(65,85),(66,86),(67,87),(68,88),(69,89),(70,90),(71,91),(72,92),(73,93),(74,94),(75,95),(76,96),(77,97),(78,98),(79,99),(80,100),(101,137),(102,138),(103,139),(104,140),(105,121),(106,122),(107,123),(108,124),(109,125),(110,126),(111,127),(112,128),(113,129),(114,130),(115,131),(116,132),(117,133),(118,134),(119,135),(120,136)], [(1,85),(2,86),(3,87),(4,88),(5,89),(6,90),(7,91),(8,92),(9,93),(10,94),(11,95),(12,96),(13,97),(14,98),(15,99),(16,100),(17,81),(18,82),(19,83),(20,84),(21,62),(22,63),(23,64),(24,65),(25,66),(26,67),(27,68),(28,69),(29,70),(30,71),(31,72),(32,73),(33,74),(34,75),(35,76),(36,77),(37,78),(38,79),(39,80),(40,61),(41,132),(42,133),(43,134),(44,135),(45,136),(46,137),(47,138),(48,139),(49,140),(50,121),(51,122),(52,123),(53,124),(54,125),(55,126),(56,127),(57,128),(58,129),(59,130),(60,131),(101,146),(102,147),(103,148),(104,149),(105,150),(106,151),(107,152),(108,153),(109,154),(110,155),(111,156),(112,157),(113,158),(114,159),(115,160),(116,141),(117,142),(118,143),(119,144),(120,145)], [(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)], [(1,105,24,121),(2,104,25,140),(3,103,26,139),(4,102,27,138),(5,101,28,137),(6,120,29,136),(7,119,30,135),(8,118,31,134),(9,117,32,133),(10,116,33,132),(11,115,34,131),(12,114,35,130),(13,113,36,129),(14,112,37,128),(15,111,38,127),(16,110,39,126),(17,109,40,125),(18,108,21,124),(19,107,22,123),(20,106,23,122),(41,94,141,74),(42,93,142,73),(43,92,143,72),(44,91,144,71),(45,90,145,70),(46,89,146,69),(47,88,147,68),(48,87,148,67),(49,86,149,66),(50,85,150,65),(51,84,151,64),(52,83,152,63),(53,82,153,62),(54,81,154,61),(55,100,155,80),(56,99,156,79),(57,98,157,78),(58,97,158,77),(59,96,159,76),(60,95,160,75)]])
92 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | ··· | 4P | 5A | 5B | 10A | ··· | 10AD | 20A | ··· | 20AF |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | - | + | - | + | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D5 | C4○D4 | Dic5 | D10 | D10 | C5⋊D4 | Dic10 | D20 | C4○D20 |
| kernel | C24.64D10 | C10.10C42 | C2×C4⋊Dic5 | C2×C23.D5 | C23×C20 | C22×C20 | C2×C20 | C22×C10 | C22×C10 | C23×C4 | C2×C10 | C22×C4 | C22×C4 | C24 | C2×C4 | C23 | C23 | C22 |
| # reps | 1 | 2 | 2 | 2 | 1 | 8 | 4 | 2 | 2 | 2 | 4 | 8 | 4 | 2 | 16 | 8 | 8 | 16 |
Matrix representation of C24.64D10 ►in GL5(𝔽41)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 0 | 18 | 0 |
| 0 | 0 | 0 | 0 | 16 |
| 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 |
| 0 | 0 | 0 | 18 | 0 |
G:=sub<GL(5,GF(41))| [1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,40],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,9,0,0,0,0,0,32,0,0,0,0,0,18,0,0,0,0,0,16],[9,0,0,0,0,0,0,9,0,0,0,32,0,0,0,0,0,0,0,18,0,0,0,16,0] >;
C24.64D10 in GAP, Magma, Sage, TeX
C_2^4._{64}D_{10} % in TeX
G:=Group("C2^4.64D10"); // GroupNames label
G:=SmallGroup(320,839);
// by ID
G=gap.SmallGroup(320,839);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,477,232,422,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^20=1,e^2=b,a*b=b*a,e*a*e^-1=a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations