metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.28D20, C24.65D10, (C2×C20)⋊35D4, (C23×C4)⋊1D5, (C23×C20)⋊1C2, C10.115(C4×D4), C23.38(C4×D5), C10.70C22≀C2, C2.5(C20⋊7D4), C22.61(C2×D20), C10.80(C4⋊D4), (C22×C4).408D10, (C22×C10).193D4, C2.2(C24⋊2D5), C23.83(C5⋊D4), C5⋊5(C23.23D4), C22⋊2(D10⋊C4), C22.64(C4○D20), (C23×D5).24C22, C23.304(C22×D5), C10.10C42⋊25C2, (C22×C10).364C23, (C23×C10).100C22, (C22×C20).485C22, C10.69(C22.D4), C2.5(C23.23D10), (C22×Dic5).67C22, (C2×C5⋊D4)⋊12C4, C2.29(C4×C5⋊D4), (C2×C4)⋊15(C5⋊D4), (C22×D5)⋊7(C2×C4), (C2×C23.D5)⋊7C2, C22.150(C2×C4×D5), (C2×C10)⋊8(C22⋊C4), (C2×Dic5)⋊11(C2×C4), (C2×C10).550(C2×D4), (C2×D10⋊C4)⋊11C2, (C22×C5⋊D4).7C2, C22.88(C2×C5⋊D4), (C2×C10).92(C4○D4), C2.36(C2×D10⋊C4), C10.106(C2×C22⋊C4), (C2×C10).244(C22×C4), (C22×C10).168(C2×C4), SmallGroup(320,840)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.28D20
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=bd-1 >
Subgroups: 1022 in 286 conjugacy classes, 87 normal (25 characteristic)
C1, C2 [×3], C2 [×4], C2 [×6], C4 [×8], C22 [×3], C22 [×8], C22 [×22], C5, C2×C4 [×4], C2×C4 [×22], D4 [×8], C23, C23 [×6], C23 [×12], D5 [×2], C10 [×3], C10 [×4], C10 [×4], C22⋊C4 [×6], C22×C4 [×2], C22×C4 [×9], C2×D4 [×8], C24, C24, Dic5 [×4], C20 [×4], D10 [×10], C2×C10 [×3], C2×C10 [×8], C2×C10 [×12], C2.C42 [×2], C2×C22⋊C4 [×3], C23×C4, C22×D4, C2×Dic5 [×2], C2×Dic5 [×8], C5⋊D4 [×8], C2×C20 [×4], C2×C20 [×12], C22×D5 [×2], C22×D5 [×6], C22×C10, C22×C10 [×6], C22×C10 [×4], C23.23D4, D10⋊C4 [×4], C23.D5 [×2], C22×Dic5, C22×Dic5 [×2], C2×C5⋊D4 [×4], C2×C5⋊D4 [×4], C22×C20 [×2], C22×C20 [×6], C23×D5, C23×C10, C10.10C42 [×2], C2×D10⋊C4 [×2], C2×C23.D5, C22×C5⋊D4, C23×C20, C23.28D20
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×8], C23, D5, C22⋊C4 [×4], C22×C4, C2×D4 [×4], C4○D4 [×2], D10 [×3], C2×C22⋊C4, C4×D4 [×2], C22≀C2, C4⋊D4 [×2], C22.D4, C4×D5 [×2], D20 [×2], C5⋊D4 [×6], C22×D5, C23.23D4, D10⋊C4 [×4], C2×C4×D5, C2×D20, C4○D20 [×2], C2×C5⋊D4 [×3], C2×D10⋊C4, C4×C5⋊D4 [×2], C23.23D10, C20⋊7D4 [×2], C24⋊2D5, C23.28D20
►On 160 points
Generators in S160
(1 31)(2 32)(3 33)(4 34)(5 35)(6 36)(7 37)(8 38)(9 39)(10 40)(11 21)(12 22)(13 23)(14 24)(15 25)(16 26)(17 27)(18 28)(19 29)(20 30)(41 76)(42 77)(43 78)(44 79)(45 80)(46 61)(47 62)(48 63)(49 64)(50 65)(51 66)(52 67)(53 68)(54 69)(55 70)(56 71)(57 72)(58 73)(59 74)(60 75)(81 102)(82 103)(83 104)(84 105)(85 106)(86 107)(87 108)(88 109)(89 110)(90 111)(91 112)(92 113)(93 114)(94 115)(95 116)(96 117)(97 118)(98 119)(99 120)(100 101)(121 158)(122 159)(123 160)(124 141)(125 142)(126 143)(127 144)(128 145)(129 146)(130 147)(131 148)(132 149)(133 150)(134 151)(135 152)(136 153)(137 154)(138 155)(139 156)(140 157)
(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)(21 146)(22 147)(23 148)(24 149)(25 150)(26 151)(27 152)(28 153)(29 154)(30 155)(31 156)(32 157)(33 158)(34 159)(35 160)(36 141)(37 142)(38 143)(39 144)(40 145)(41 101)(42 102)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(61 85)(62 86)(63 87)(64 88)(65 89)(66 90)(67 91)(68 92)(69 93)(70 94)(71 95)(72 96)(73 97)(74 98)(75 99)(76 100)(77 81)(78 82)(79 83)(80 84)
(1 73)(2 74)(3 75)(4 76)(5 77)(6 78)(7 79)(8 80)(9 61)(10 62)(11 63)(12 64)(13 65)(14 66)(15 67)(16 68)(17 69)(18 70)(19 71)(20 72)(21 48)(22 49)(23 50)(24 51)(25 52)(26 53)(27 54)(28 55)(29 56)(30 57)(31 58)(32 59)(33 60)(34 41)(35 42)(36 43)(37 44)(38 45)(39 46)(40 47)(81 123)(82 124)(83 125)(84 126)(85 127)(86 128)(87 129)(88 130)(89 131)(90 132)(91 133)(92 134)(93 135)(94 136)(95 137)(96 138)(97 139)(98 140)(99 121)(100 122)(101 159)(102 160)(103 141)(104 142)(105 143)(106 144)(107 145)(108 146)(109 147)(110 148)(111 149)(112 150)(113 151)(114 152)(115 153)(116 154)(117 155)(118 156)(119 157)(120 158)
(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)
(1 138 139 20)(2 19 140 137)(3 136 121 18)(4 17 122 135)(5 134 123 16)(6 15 124 133)(7 132 125 14)(8 13 126 131)(9 130 127 12)(10 11 128 129)(21 107 146 47)(22 46 147 106)(23 105 148 45)(24 44 149 104)(25 103 150 43)(26 42 151 102)(27 101 152 41)(28 60 153 120)(29 119 154 59)(30 58 155 118)(31 117 156 57)(32 56 157 116)(33 115 158 55)(34 54 159 114)(35 113 160 53)(36 52 141 112)(37 111 142 51)(38 50 143 110)(39 109 144 49)(40 48 145 108)(61 88 85 64)(62 63 86 87)(65 84 89 80)(66 79 90 83)(67 82 91 78)(68 77 92 81)(69 100 93 76)(70 75 94 99)(71 98 95 74)(72 73 96 97)
G:=sub<Sym(160)| (1,31)(2,32)(3,33)(4,34)(5,35)(6,36)(7,37)(8,38)(9,39)(10,40)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(41,76)(42,77)(43,78)(44,79)(45,80)(46,61)(47,62)(48,63)(49,64)(50,65)(51,66)(52,67)(53,68)(54,69)(55,70)(56,71)(57,72)(58,73)(59,74)(60,75)(81,102)(82,103)(83,104)(84,105)(85,106)(86,107)(87,108)(88,109)(89,110)(90,111)(91,112)(92,113)(93,114)(94,115)(95,116)(96,117)(97,118)(98,119)(99,120)(100,101)(121,158)(122,159)(123,160)(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)(133,150)(134,151)(135,152)(136,153)(137,154)(138,155)(139,156)(140,157), (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)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,141)(37,142)(38,143)(39,144)(40,145)(41,101)(42,102)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,97)(74,98)(75,99)(76,100)(77,81)(78,82)(79,83)(80,84), (1,73)(2,74)(3,75)(4,76)(5,77)(6,78)(7,79)(8,80)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,70)(19,71)(20,72)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(81,123)(82,124)(83,125)(84,126)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,121)(100,122)(101,159)(102,160)(103,141)(104,142)(105,143)(106,144)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150)(113,151)(114,152)(115,153)(116,154)(117,155)(118,156)(119,157)(120,158), (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), (1,138,139,20)(2,19,140,137)(3,136,121,18)(4,17,122,135)(5,134,123,16)(6,15,124,133)(7,132,125,14)(8,13,126,131)(9,130,127,12)(10,11,128,129)(21,107,146,47)(22,46,147,106)(23,105,148,45)(24,44,149,104)(25,103,150,43)(26,42,151,102)(27,101,152,41)(28,60,153,120)(29,119,154,59)(30,58,155,118)(31,117,156,57)(32,56,157,116)(33,115,158,55)(34,54,159,114)(35,113,160,53)(36,52,141,112)(37,111,142,51)(38,50,143,110)(39,109,144,49)(40,48,145,108)(61,88,85,64)(62,63,86,87)(65,84,89,80)(66,79,90,83)(67,82,91,78)(68,77,92,81)(69,100,93,76)(70,75,94,99)(71,98,95,74)(72,73,96,97)>;
G:=Group( (1,31)(2,32)(3,33)(4,34)(5,35)(6,36)(7,37)(8,38)(9,39)(10,40)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(41,76)(42,77)(43,78)(44,79)(45,80)(46,61)(47,62)(48,63)(49,64)(50,65)(51,66)(52,67)(53,68)(54,69)(55,70)(56,71)(57,72)(58,73)(59,74)(60,75)(81,102)(82,103)(83,104)(84,105)(85,106)(86,107)(87,108)(88,109)(89,110)(90,111)(91,112)(92,113)(93,114)(94,115)(95,116)(96,117)(97,118)(98,119)(99,120)(100,101)(121,158)(122,159)(123,160)(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)(133,150)(134,151)(135,152)(136,153)(137,154)(138,155)(139,156)(140,157), (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)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,141)(37,142)(38,143)(39,144)(40,145)(41,101)(42,102)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,97)(74,98)(75,99)(76,100)(77,81)(78,82)(79,83)(80,84), (1,73)(2,74)(3,75)(4,76)(5,77)(6,78)(7,79)(8,80)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,70)(19,71)(20,72)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(81,123)(82,124)(83,125)(84,126)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,121)(100,122)(101,159)(102,160)(103,141)(104,142)(105,143)(106,144)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150)(113,151)(114,152)(115,153)(116,154)(117,155)(118,156)(119,157)(120,158), (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), (1,138,139,20)(2,19,140,137)(3,136,121,18)(4,17,122,135)(5,134,123,16)(6,15,124,133)(7,132,125,14)(8,13,126,131)(9,130,127,12)(10,11,128,129)(21,107,146,47)(22,46,147,106)(23,105,148,45)(24,44,149,104)(25,103,150,43)(26,42,151,102)(27,101,152,41)(28,60,153,120)(29,119,154,59)(30,58,155,118)(31,117,156,57)(32,56,157,116)(33,115,158,55)(34,54,159,114)(35,113,160,53)(36,52,141,112)(37,111,142,51)(38,50,143,110)(39,109,144,49)(40,48,145,108)(61,88,85,64)(62,63,86,87)(65,84,89,80)(66,79,90,83)(67,82,91,78)(68,77,92,81)(69,100,93,76)(70,75,94,99)(71,98,95,74)(72,73,96,97) );
G=PermutationGroup([(1,31),(2,32),(3,33),(4,34),(5,35),(6,36),(7,37),(8,38),(9,39),(10,40),(11,21),(12,22),(13,23),(14,24),(15,25),(16,26),(17,27),(18,28),(19,29),(20,30),(41,76),(42,77),(43,78),(44,79),(45,80),(46,61),(47,62),(48,63),(49,64),(50,65),(51,66),(52,67),(53,68),(54,69),(55,70),(56,71),(57,72),(58,73),(59,74),(60,75),(81,102),(82,103),(83,104),(84,105),(85,106),(86,107),(87,108),(88,109),(89,110),(90,111),(91,112),(92,113),(93,114),(94,115),(95,116),(96,117),(97,118),(98,119),(99,120),(100,101),(121,158),(122,159),(123,160),(124,141),(125,142),(126,143),(127,144),(128,145),(129,146),(130,147),(131,148),(132,149),(133,150),(134,151),(135,152),(136,153),(137,154),(138,155),(139,156),(140,157)], [(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),(21,146),(22,147),(23,148),(24,149),(25,150),(26,151),(27,152),(28,153),(29,154),(30,155),(31,156),(32,157),(33,158),(34,159),(35,160),(36,141),(37,142),(38,143),(39,144),(40,145),(41,101),(42,102),(43,103),(44,104),(45,105),(46,106),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,113),(54,114),(55,115),(56,116),(57,117),(58,118),(59,119),(60,120),(61,85),(62,86),(63,87),(64,88),(65,89),(66,90),(67,91),(68,92),(69,93),(70,94),(71,95),(72,96),(73,97),(74,98),(75,99),(76,100),(77,81),(78,82),(79,83),(80,84)], [(1,73),(2,74),(3,75),(4,76),(5,77),(6,78),(7,79),(8,80),(9,61),(10,62),(11,63),(12,64),(13,65),(14,66),(15,67),(16,68),(17,69),(18,70),(19,71),(20,72),(21,48),(22,49),(23,50),(24,51),(25,52),(26,53),(27,54),(28,55),(29,56),(30,57),(31,58),(32,59),(33,60),(34,41),(35,42),(36,43),(37,44),(38,45),(39,46),(40,47),(81,123),(82,124),(83,125),(84,126),(85,127),(86,128),(87,129),(88,130),(89,131),(90,132),(91,133),(92,134),(93,135),(94,136),(95,137),(96,138),(97,139),(98,140),(99,121),(100,122),(101,159),(102,160),(103,141),(104,142),(105,143),(106,144),(107,145),(108,146),(109,147),(110,148),(111,149),(112,150),(113,151),(114,152),(115,153),(116,154),(117,155),(118,156),(119,157),(120,158)], [(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)], [(1,138,139,20),(2,19,140,137),(3,136,121,18),(4,17,122,135),(5,134,123,16),(6,15,124,133),(7,132,125,14),(8,13,126,131),(9,130,127,12),(10,11,128,129),(21,107,146,47),(22,46,147,106),(23,105,148,45),(24,44,149,104),(25,103,150,43),(26,42,151,102),(27,101,152,41),(28,60,153,120),(29,119,154,59),(30,58,155,118),(31,117,156,57),(32,56,157,116),(33,115,158,55),(34,54,159,114),(35,113,160,53),(36,52,141,112),(37,111,142,51),(38,50,143,110),(39,109,144,49),(40,48,145,108),(61,88,85,64),(62,63,86,87),(65,84,89,80),(66,79,90,83),(67,82,91,78),(68,77,92,81),(69,100,93,76),(70,75,94,99),(71,98,95,74),(72,73,96,97)])
92 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 4A | ··· | 4H | 4I | ··· | 4N | 5A | 5B | 10A | ··· | 10AD | 20A | ··· | 20AF |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 20 | 20 | 2 | ··· | 2 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D5 | C4○D4 | D10 | D10 | C5⋊D4 | C4×D5 | D20 | C5⋊D4 | C4○D20 |
| kernel | C23.28D20 | C10.10C42 | C2×D10⋊C4 | C2×C23.D5 | C22×C5⋊D4 | C23×C20 | C2×C5⋊D4 | C2×C20 | C22×C10 | C23×C4 | C2×C10 | C22×C4 | C24 | C2×C4 | C23 | C23 | C23 | C22 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 4 | 4 | 2 | 4 | 4 | 2 | 16 | 8 | 8 | 8 | 16 |
Matrix representation of C23.28D20 ►in GL6(𝔽41)
| 23 | 6 | 0 | 0 | 0 | 0 |
| 35 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 6 | 0 | 0 |
| 0 | 0 | 35 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 1 |
| 0 | 0 | 0 | 0 | 5 | 23 |
| 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 |
| 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 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 1 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 32 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 11 |
| 0 | 0 | 0 | 0 | 14 | 39 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 11 |
| 0 | 0 | 0 | 0 | 37 | 39 |
G:=sub<GL(6,GF(41))| [23,35,0,0,0,0,6,18,0,0,0,0,0,0,23,35,0,0,0,0,6,18,0,0,0,0,0,0,18,5,0,0,0,0,1,23],[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],[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],[0,1,0,0,0,0,40,35,0,0,0,0,0,0,0,32,0,0,0,0,9,13,0,0,0,0,0,0,25,14,0,0,0,0,11,39],[0,40,0,0,0,0,40,0,0,0,0,0,0,0,0,9,0,0,0,0,9,0,0,0,0,0,0,0,2,37,0,0,0,0,11,39] >;
C23.28D20 in GAP, Magma, Sage, TeX
C_2^3._{28}D_{20} % in TeX
G:=Group("C2^3.28D20"); // GroupNames label
G:=SmallGroup(320,840);
// by ID
G=gap.SmallGroup(320,840);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,758,58,12550]);
// 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=b*d^-1>;
// generators/relations