metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.20D10, (C2×Dic5)⋊6D4, (C2×C20).302D4, (C22×D4).8D5, C10.73C22≀C2, C22.283(D4×D5), C2.25(C20⋊2D4), (C22×C10).110D4, (C22×C4).152D10, C2.6(C24⋊2D5), C5⋊5(C23.10D4), C23.30(C5⋊D4), C10.130(C4⋊D4), C10.48(C4.4D4), (C23×C10).48C22, C23.384(C22×D5), C10.10C42⋊45C2, C2.34(Dic5⋊D4), C2.14(C20.17D4), (C22×C20).395C22, (C22×C10).367C23, C22.106(D4⋊2D5), C10.84(C22.D4), (C22×Dic5).68C22, C2.17(C23.18D10), (D4×C2×C10).12C2, (C2×C10).556(C2×D4), (C2×C4).85(C5⋊D4), (C2×C23.D5)⋊11C2, (C2×C10.D4)⋊43C2, C22.218(C2×C5⋊D4), (C2×C10).163(C4○D4), SmallGroup(320,849)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.20D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=dc=cd, ab=ba, ac=ca, eae-1=ad=da, faf-1=abd, bc=cb, bd=db, be=eb, bf=fb, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce-1 >
Subgroups: 742 in 238 conjugacy classes, 65 normal (25 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C4 [×7], C22 [×3], C22 [×4], C22 [×20], C5, C2×C4 [×2], C2×C4 [×15], D4 [×8], C23, C23 [×4], C23 [×12], C10 [×3], C10 [×4], C10 [×4], C22⋊C4 [×8], C4⋊C4 [×2], C22×C4, C22×C4 [×4], C2×D4 [×6], C24 [×2], Dic5 [×5], C20 [×2], C2×C10 [×3], C2×C10 [×4], C2×C10 [×20], C2.C42, C2×C22⋊C4 [×4], C2×C4⋊C4, C22×D4, C2×Dic5 [×2], C2×Dic5 [×11], C2×C20 [×2], C2×C20 [×2], C5×D4 [×8], C22×C10, C22×C10 [×4], C22×C10 [×12], C23.10D4, C10.D4 [×2], C23.D5 [×8], C22×Dic5 [×2], C22×Dic5 [×2], C22×C20, D4×C10 [×6], C23×C10 [×2], C10.10C42, C2×C10.D4, C2×C23.D5 [×4], D4×C2×C10, C24.20D10
Quotients: C1, C2 [×7], C22 [×7], D4 [×8], C23, D5, C2×D4 [×4], C4○D4 [×3], D10 [×3], C22≀C2, C4⋊D4 [×3], C22.D4 [×2], C4.4D4, C5⋊D4 [×6], C22×D5, C23.10D4, D4×D5, D4⋊2D5 [×3], C2×C5⋊D4 [×3], C23.18D10 [×2], C20.17D4, C20⋊2D4, Dic5⋊D4 [×2], C24⋊2D5, C24.20D10
►On 160 points
Generators in S160
(2 64)(4 66)(6 68)(8 70)(10 62)(11 100)(13 92)(15 94)(17 96)(19 98)(21 72)(23 74)(25 76)(27 78)(29 80)(31 56)(33 58)(35 60)(37 52)(39 54)(41 114)(42 107)(43 116)(44 109)(45 118)(46 101)(47 120)(48 103)(49 112)(50 105)(81 160)(82 139)(83 152)(84 131)(85 154)(86 133)(87 156)(88 135)(89 158)(90 137)(102 127)(104 129)(106 121)(108 123)(110 125)(111 128)(113 130)(115 122)(117 124)(119 126)(132 144)(134 146)(136 148)(138 150)(140 142)(141 151)(143 153)(145 155)(147 157)(149 159)
(1 22)(2 23)(3 24)(4 25)(5 26)(6 27)(7 28)(8 29)(9 30)(10 21)(11 54)(12 55)(13 56)(14 57)(15 58)(16 59)(17 60)(18 51)(19 52)(20 53)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 91)(41 106)(42 107)(43 108)(44 109)(45 110)(46 101)(47 102)(48 103)(49 104)(50 105)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(81 138)(82 139)(83 140)(84 131)(85 132)(86 133)(87 134)(88 135)(89 136)(90 137)(111 128)(112 129)(113 130)(114 121)(115 122)(116 123)(117 124)(118 125)(119 126)(120 127)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)
(1 55)(2 56)(3 57)(4 58)(5 59)(6 60)(7 51)(8 52)(9 53)(10 54)(11 21)(12 22)(13 23)(14 24)(15 25)(16 26)(17 27)(18 28)(19 29)(20 30)(31 64)(32 65)(33 66)(34 67)(35 68)(36 69)(37 70)(38 61)(39 62)(40 63)(41 158)(42 159)(43 160)(44 151)(45 152)(46 153)(47 154)(48 155)(49 156)(50 157)(71 99)(72 100)(73 91)(74 92)(75 93)(76 94)(77 95)(78 96)(79 97)(80 98)(81 116)(82 117)(83 118)(84 119)(85 120)(86 111)(87 112)(88 113)(89 114)(90 115)(101 143)(102 144)(103 145)(104 146)(105 147)(106 148)(107 149)(108 150)(109 141)(110 142)(121 136)(122 137)(123 138)(124 139)(125 140)(126 131)(127 132)(128 133)(129 134)(130 135)
(1 63)(2 64)(3 65)(4 66)(5 67)(6 68)(7 69)(8 70)(9 61)(10 62)(11 100)(12 91)(13 92)(14 93)(15 94)(16 95)(17 96)(18 97)(19 98)(20 99)(21 72)(22 73)(23 74)(24 75)(25 76)(26 77)(27 78)(28 79)(29 80)(30 71)(31 56)(32 57)(33 58)(34 59)(35 60)(36 51)(37 52)(38 53)(39 54)(40 55)(41 121)(42 122)(43 123)(44 124)(45 125)(46 126)(47 127)(48 128)(49 129)(50 130)(81 150)(82 141)(83 142)(84 143)(85 144)(86 145)(87 146)(88 147)(89 148)(90 149)(101 119)(102 120)(103 111)(104 112)(105 113)(106 114)(107 115)(108 116)(109 117)(110 118)(131 153)(132 154)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 151)(140 152)
(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)
(1 104 40 87)(2 145 31 111)(3 102 32 85)(4 143 33 119)(5 110 34 83)(6 141 35 117)(7 108 36 81)(8 149 37 115)(9 106 38 89)(10 147 39 113)(11 50 72 135)(12 156 73 129)(13 48 74 133)(14 154 75 127)(15 46 76 131)(16 152 77 125)(17 44 78 139)(18 160 79 123)(19 42 80 137)(20 158 71 121)(21 157 100 130)(22 49 91 134)(23 155 92 128)(24 47 93 132)(25 153 94 126)(26 45 95 140)(27 151 96 124)(28 43 97 138)(29 159 98 122)(30 41 99 136)(51 150 69 116)(52 107 70 90)(53 148 61 114)(54 105 62 88)(55 146 63 112)(56 103 64 86)(57 144 65 120)(58 101 66 84)(59 142 67 118)(60 109 68 82)
G:=sub<Sym(160)| (2,64)(4,66)(6,68)(8,70)(10,62)(11,100)(13,92)(15,94)(17,96)(19,98)(21,72)(23,74)(25,76)(27,78)(29,80)(31,56)(33,58)(35,60)(37,52)(39,54)(41,114)(42,107)(43,116)(44,109)(45,118)(46,101)(47,120)(48,103)(49,112)(50,105)(81,160)(82,139)(83,152)(84,131)(85,154)(86,133)(87,156)(88,135)(89,158)(90,137)(102,127)(104,129)(106,121)(108,123)(110,125)(111,128)(113,130)(115,122)(117,124)(119,126)(132,144)(134,146)(136,148)(138,150)(140,142)(141,151)(143,153)(145,155)(147,157)(149,159), (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,21)(11,54)(12,55)(13,56)(14,57)(15,58)(16,59)(17,60)(18,51)(19,52)(20,53)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,91)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,138)(82,139)(83,140)(84,131)(85,132)(86,133)(87,134)(88,135)(89,136)(90,137)(111,128)(112,129)(113,130)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(120,127)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,51)(8,52)(9,53)(10,54)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,61)(39,62)(40,63)(41,158)(42,159)(43,160)(44,151)(45,152)(46,153)(47,154)(48,155)(49,156)(50,157)(71,99)(72,100)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,116)(82,117)(83,118)(84,119)(85,120)(86,111)(87,112)(88,113)(89,114)(90,115)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,141)(110,142)(121,136)(122,137)(123,138)(124,139)(125,140)(126,131)(127,132)(128,133)(129,134)(130,135), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,100)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,72)(22,73)(23,74)(24,75)(25,76)(26,77)(27,78)(28,79)(29,80)(30,71)(31,56)(32,57)(33,58)(34,59)(35,60)(36,51)(37,52)(38,53)(39,54)(40,55)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(81,150)(82,141)(83,142)(84,143)(85,144)(86,145)(87,146)(88,147)(89,148)(90,149)(101,119)(102,120)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,151)(140,152), (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), (1,104,40,87)(2,145,31,111)(3,102,32,85)(4,143,33,119)(5,110,34,83)(6,141,35,117)(7,108,36,81)(8,149,37,115)(9,106,38,89)(10,147,39,113)(11,50,72,135)(12,156,73,129)(13,48,74,133)(14,154,75,127)(15,46,76,131)(16,152,77,125)(17,44,78,139)(18,160,79,123)(19,42,80,137)(20,158,71,121)(21,157,100,130)(22,49,91,134)(23,155,92,128)(24,47,93,132)(25,153,94,126)(26,45,95,140)(27,151,96,124)(28,43,97,138)(29,159,98,122)(30,41,99,136)(51,150,69,116)(52,107,70,90)(53,148,61,114)(54,105,62,88)(55,146,63,112)(56,103,64,86)(57,144,65,120)(58,101,66,84)(59,142,67,118)(60,109,68,82)>;
G:=Group( (2,64)(4,66)(6,68)(8,70)(10,62)(11,100)(13,92)(15,94)(17,96)(19,98)(21,72)(23,74)(25,76)(27,78)(29,80)(31,56)(33,58)(35,60)(37,52)(39,54)(41,114)(42,107)(43,116)(44,109)(45,118)(46,101)(47,120)(48,103)(49,112)(50,105)(81,160)(82,139)(83,152)(84,131)(85,154)(86,133)(87,156)(88,135)(89,158)(90,137)(102,127)(104,129)(106,121)(108,123)(110,125)(111,128)(113,130)(115,122)(117,124)(119,126)(132,144)(134,146)(136,148)(138,150)(140,142)(141,151)(143,153)(145,155)(147,157)(149,159), (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,21)(11,54)(12,55)(13,56)(14,57)(15,58)(16,59)(17,60)(18,51)(19,52)(20,53)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,91)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,138)(82,139)(83,140)(84,131)(85,132)(86,133)(87,134)(88,135)(89,136)(90,137)(111,128)(112,129)(113,130)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(120,127)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,51)(8,52)(9,53)(10,54)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,61)(39,62)(40,63)(41,158)(42,159)(43,160)(44,151)(45,152)(46,153)(47,154)(48,155)(49,156)(50,157)(71,99)(72,100)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,116)(82,117)(83,118)(84,119)(85,120)(86,111)(87,112)(88,113)(89,114)(90,115)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,141)(110,142)(121,136)(122,137)(123,138)(124,139)(125,140)(126,131)(127,132)(128,133)(129,134)(130,135), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,100)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,72)(22,73)(23,74)(24,75)(25,76)(26,77)(27,78)(28,79)(29,80)(30,71)(31,56)(32,57)(33,58)(34,59)(35,60)(36,51)(37,52)(38,53)(39,54)(40,55)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(81,150)(82,141)(83,142)(84,143)(85,144)(86,145)(87,146)(88,147)(89,148)(90,149)(101,119)(102,120)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,151)(140,152), (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), (1,104,40,87)(2,145,31,111)(3,102,32,85)(4,143,33,119)(5,110,34,83)(6,141,35,117)(7,108,36,81)(8,149,37,115)(9,106,38,89)(10,147,39,113)(11,50,72,135)(12,156,73,129)(13,48,74,133)(14,154,75,127)(15,46,76,131)(16,152,77,125)(17,44,78,139)(18,160,79,123)(19,42,80,137)(20,158,71,121)(21,157,100,130)(22,49,91,134)(23,155,92,128)(24,47,93,132)(25,153,94,126)(26,45,95,140)(27,151,96,124)(28,43,97,138)(29,159,98,122)(30,41,99,136)(51,150,69,116)(52,107,70,90)(53,148,61,114)(54,105,62,88)(55,146,63,112)(56,103,64,86)(57,144,65,120)(58,101,66,84)(59,142,67,118)(60,109,68,82) );
G=PermutationGroup([(2,64),(4,66),(6,68),(8,70),(10,62),(11,100),(13,92),(15,94),(17,96),(19,98),(21,72),(23,74),(25,76),(27,78),(29,80),(31,56),(33,58),(35,60),(37,52),(39,54),(41,114),(42,107),(43,116),(44,109),(45,118),(46,101),(47,120),(48,103),(49,112),(50,105),(81,160),(82,139),(83,152),(84,131),(85,154),(86,133),(87,156),(88,135),(89,158),(90,137),(102,127),(104,129),(106,121),(108,123),(110,125),(111,128),(113,130),(115,122),(117,124),(119,126),(132,144),(134,146),(136,148),(138,150),(140,142),(141,151),(143,153),(145,155),(147,157),(149,159)], [(1,22),(2,23),(3,24),(4,25),(5,26),(6,27),(7,28),(8,29),(9,30),(10,21),(11,54),(12,55),(13,56),(14,57),(15,58),(16,59),(17,60),(18,51),(19,52),(20,53),(31,92),(32,93),(33,94),(34,95),(35,96),(36,97),(37,98),(38,99),(39,100),(40,91),(41,106),(42,107),(43,108),(44,109),(45,110),(46,101),(47,102),(48,103),(49,104),(50,105),(61,71),(62,72),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(81,138),(82,139),(83,140),(84,131),(85,132),(86,133),(87,134),(88,135),(89,136),(90,137),(111,128),(112,129),(113,130),(114,121),(115,122),(116,123),(117,124),(118,125),(119,126),(120,127),(141,151),(142,152),(143,153),(144,154),(145,155),(146,156),(147,157),(148,158),(149,159),(150,160)], [(1,55),(2,56),(3,57),(4,58),(5,59),(6,60),(7,51),(8,52),(9,53),(10,54),(11,21),(12,22),(13,23),(14,24),(15,25),(16,26),(17,27),(18,28),(19,29),(20,30),(31,64),(32,65),(33,66),(34,67),(35,68),(36,69),(37,70),(38,61),(39,62),(40,63),(41,158),(42,159),(43,160),(44,151),(45,152),(46,153),(47,154),(48,155),(49,156),(50,157),(71,99),(72,100),(73,91),(74,92),(75,93),(76,94),(77,95),(78,96),(79,97),(80,98),(81,116),(82,117),(83,118),(84,119),(85,120),(86,111),(87,112),(88,113),(89,114),(90,115),(101,143),(102,144),(103,145),(104,146),(105,147),(106,148),(107,149),(108,150),(109,141),(110,142),(121,136),(122,137),(123,138),(124,139),(125,140),(126,131),(127,132),(128,133),(129,134),(130,135)], [(1,63),(2,64),(3,65),(4,66),(5,67),(6,68),(7,69),(8,70),(9,61),(10,62),(11,100),(12,91),(13,92),(14,93),(15,94),(16,95),(17,96),(18,97),(19,98),(20,99),(21,72),(22,73),(23,74),(24,75),(25,76),(26,77),(27,78),(28,79),(29,80),(30,71),(31,56),(32,57),(33,58),(34,59),(35,60),(36,51),(37,52),(38,53),(39,54),(40,55),(41,121),(42,122),(43,123),(44,124),(45,125),(46,126),(47,127),(48,128),(49,129),(50,130),(81,150),(82,141),(83,142),(84,143),(85,144),(86,145),(87,146),(88,147),(89,148),(90,149),(101,119),(102,120),(103,111),(104,112),(105,113),(106,114),(107,115),(108,116),(109,117),(110,118),(131,153),(132,154),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,151),(140,152)], [(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)], [(1,104,40,87),(2,145,31,111),(3,102,32,85),(4,143,33,119),(5,110,34,83),(6,141,35,117),(7,108,36,81),(8,149,37,115),(9,106,38,89),(10,147,39,113),(11,50,72,135),(12,156,73,129),(13,48,74,133),(14,154,75,127),(15,46,76,131),(16,152,77,125),(17,44,78,139),(18,160,79,123),(19,42,80,137),(20,158,71,121),(21,157,100,130),(22,49,91,134),(23,155,92,128),(24,47,93,132),(25,153,94,126),(26,45,95,140),(27,151,96,124),(28,43,97,138),(29,159,98,122),(30,41,99,136),(51,150,69,116),(52,107,70,90),(53,148,61,114),(54,105,62,88),(55,146,63,112),(56,103,64,86),(57,144,65,120),(58,101,66,84),(59,142,67,118),(60,109,68,82)])
62 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | ··· | 4J | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | C4○D4 | D10 | D10 | C5⋊D4 | C5⋊D4 | D4×D5 | D4⋊2D5 |
| kernel | C24.20D10 | C10.10C42 | C2×C10.D4 | C2×C23.D5 | D4×C2×C10 | C2×Dic5 | C2×C20 | C22×C10 | C22×D4 | C2×C10 | C22×C4 | C24 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 1 | 1 | 4 | 1 | 2 | 2 | 4 | 2 | 6 | 2 | 4 | 8 | 16 | 2 | 6 |
Matrix representation of C24.20D10 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 23 | 40 |
| 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 |
| 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 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 37 | 0 |
| 0 | 0 | 0 | 0 | 28 | 31 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 21 |
| 0 | 0 | 0 | 0 | 19 | 16 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,23,0,0,0,0,0,40],[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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,37,28,0,0,0,0,0,31],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,25,19,0,0,0,0,21,16] >;
C24.20D10 in GAP, Magma, Sage, TeX
C_2^4._{20}D_{10} % in TeX
G:=Group("C2^4.20D10"); // GroupNames label
G:=SmallGroup(320,849);
// by ID
G=gap.SmallGroup(320,849);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,254,387,12550]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^10=1,f^2=d*c=c*d,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*b*d,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=c*e^-1>;
// generators/relations