metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.18D10, (D4×C10)⋊26C4, (C2×D4)⋊6Dic5, (C2×Dic5)⋊18D4, C10.131(C4×D4), C2.18(D4×Dic5), (C22×D4).6D5, C23⋊2(C2×Dic5), C10.67C22≀C2, (C23×Dic5)⋊2C2, C22.120(D4×D5), C2.5(C23⋊D10), (C22×C10).109D4, (C22×C4).151D10, C23.43(C5⋊D4), C5⋊6(C23.23D4), C10.128(C4⋊D4), C22⋊1(C23.D5), C2.7(Dic5⋊D4), (C23×C10).46C22, C23.305(C22×D5), C10.10C42⋊44C2, C22.61(D4⋊2D5), (C22×C10).365C23, (C22×C20).394C22, C22.51(C22×Dic5), C10.83(C22.D4), C2.5(C23.18D10), (C22×Dic5).219C22, (C2×C20)⋊35(C2×C4), (D4×C2×C10).11C2, (C2×C4)⋊3(C2×Dic5), (C2×C23.D5)⋊9C2, (C2×C10)⋊6(C22⋊C4), (C22×C10)⋊14(C2×C4), (C2×C10).377(C2×D4), C22.91(C2×C5⋊D4), C2.11(C2×C23.D5), C10.116(C2×C22⋊C4), (C2×C10).161(C4○D4), (C2×C10).297(C22×C4), SmallGroup(320,847)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.18D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=b, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e-1 >
Subgroups: 862 in 286 conjugacy classes, 91 normal (27 characteristic)
C1, C2 [×3], C2 [×4], C2 [×6], C4 [×8], C22 [×3], C22 [×8], C22 [×22], C5, C2×C4 [×2], C2×C4 [×24], D4 [×8], C23, C23 [×8], C23 [×10], C10 [×3], C10 [×4], C10 [×6], C22⋊C4 [×6], C22×C4, C22×C4 [×10], C2×D4 [×4], C2×D4 [×4], C24 [×2], Dic5 [×6], C20 [×2], C2×C10 [×3], C2×C10 [×8], C2×C10 [×22], C2.C42 [×2], C2×C22⋊C4 [×3], C23×C4, C22×D4, C2×Dic5 [×4], C2×Dic5 [×18], C2×C20 [×2], C2×C20 [×2], C5×D4 [×8], C22×C10, C22×C10 [×8], C22×C10 [×10], C23.23D4, C23.D5 [×6], C22×Dic5 [×4], C22×Dic5 [×6], C22×C20, D4×C10 [×4], D4×C10 [×4], C23×C10 [×2], C10.10C42 [×2], C2×C23.D5, C2×C23.D5 [×2], C23×Dic5, D4×C2×C10, C24.18D10
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], Dic5 [×4], D10 [×3], C2×C22⋊C4, C4×D4 [×2], C22≀C2, C4⋊D4 [×2], C22.D4, C2×Dic5 [×6], C5⋊D4 [×4], C22×D5, C23.23D4, C23.D5 [×4], D4×D5 [×2], D4⋊2D5 [×2], C22×Dic5, C2×C5⋊D4 [×2], D4×Dic5 [×2], C23.18D10, C23⋊D10, Dic5⋊D4 [×2], C2×C23.D5, C24.18D10
►On 160 points
Generators in S160
(2 64)(4 66)(6 68)(8 70)(10 62)(11 90)(13 82)(15 84)(17 86)(19 88)(21 74)(23 76)(25 78)(27 80)(29 72)(31 54)(33 56)(35 58)(37 60)(39 52)(41 106)(42 159)(43 108)(44 151)(45 110)(46 153)(47 102)(48 155)(49 104)(50 157)(91 133)(92 112)(93 135)(94 114)(95 137)(96 116)(97 139)(98 118)(99 131)(100 120)(101 128)(103 130)(105 122)(107 124)(109 126)(111 143)(113 145)(115 147)(117 149)(119 141)(121 156)(123 158)(125 160)(127 152)(129 154)(132 142)(134 144)(136 146)(138 148)(140 150)
(1 30)(2 21)(3 22)(4 23)(5 24)(6 25)(7 26)(8 27)(9 28)(10 29)(11 52)(12 53)(13 54)(14 55)(15 56)(16 57)(17 58)(18 59)(19 60)(20 51)(31 82)(32 83)(33 84)(34 85)(35 86)(36 87)(37 88)(38 89)(39 90)(40 81)(41 116)(42 117)(43 118)(44 119)(45 120)(46 111)(47 112)(48 113)(49 114)(50 115)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(91 101)(92 102)(93 103)(94 104)(95 105)(96 106)(97 107)(98 108)(99 109)(100 110)(121 136)(122 137)(123 138)(124 139)(125 140)(126 131)(127 132)(128 133)(129 134)(130 135)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)
(1 53)(2 54)(3 55)(4 56)(5 57)(6 58)(7 59)(8 60)(9 51)(10 52)(11 29)(12 30)(13 21)(14 22)(15 23)(16 24)(17 25)(18 26)(19 27)(20 28)(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 89)(72 90)(73 81)(74 82)(75 83)(76 84)(77 85)(78 86)(79 87)(80 88)(91 133)(92 134)(93 135)(94 136)(95 137)(96 138)(97 139)(98 140)(99 131)(100 132)(101 128)(102 129)(103 130)(104 121)(105 122)(106 123)(107 124)(108 125)(109 126)(110 127)(111 143)(112 144)(113 145)(114 146)(115 147)(116 148)(117 149)(118 150)(119 141)(120 142)
(1 63)(2 64)(3 65)(4 66)(5 67)(6 68)(7 69)(8 70)(9 61)(10 62)(11 90)(12 81)(13 82)(14 83)(15 84)(16 85)(17 86)(18 87)(19 88)(20 89)(21 74)(22 75)(23 76)(24 77)(25 78)(26 79)(27 80)(28 71)(29 72)(30 73)(31 54)(32 55)(33 56)(34 57)(35 58)(36 59)(37 60)(38 51)(39 52)(40 53)(41 123)(42 124)(43 125)(44 126)(45 127)(46 128)(47 129)(48 130)(49 121)(50 122)(91 143)(92 144)(93 145)(94 146)(95 147)(96 148)(97 149)(98 150)(99 141)(100 142)(101 153)(102 154)(103 155)(104 156)(105 157)(106 158)(107 159)(108 160)(109 151)(110 152)(111 133)(112 134)(113 135)(114 136)(115 137)(116 138)(117 139)(118 140)(119 131)(120 132)
(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 30 94)(2 103 21 93)(3 102 22 92)(4 101 23 91)(5 110 24 100)(6 109 25 99)(7 108 26 98)(8 107 27 97)(9 106 28 96)(10 105 29 95)(11 137 52 122)(12 136 53 121)(13 135 54 130)(14 134 55 129)(15 133 56 128)(16 132 57 127)(17 131 58 126)(18 140 59 125)(19 139 60 124)(20 138 51 123)(31 48 82 113)(32 47 83 112)(33 46 84 111)(34 45 85 120)(35 44 86 119)(36 43 87 118)(37 42 88 117)(38 41 89 116)(39 50 90 115)(40 49 81 114)(61 158 71 148)(62 157 72 147)(63 156 73 146)(64 155 74 145)(65 154 75 144)(66 153 76 143)(67 152 77 142)(68 151 78 141)(69 160 79 150)(70 159 80 149)
G:=sub<Sym(160)| (2,64)(4,66)(6,68)(8,70)(10,62)(11,90)(13,82)(15,84)(17,86)(19,88)(21,74)(23,76)(25,78)(27,80)(29,72)(31,54)(33,56)(35,58)(37,60)(39,52)(41,106)(42,159)(43,108)(44,151)(45,110)(46,153)(47,102)(48,155)(49,104)(50,157)(91,133)(92,112)(93,135)(94,114)(95,137)(96,116)(97,139)(98,118)(99,131)(100,120)(101,128)(103,130)(105,122)(107,124)(109,126)(111,143)(113,145)(115,147)(117,149)(119,141)(121,156)(123,158)(125,160)(127,152)(129,154)(132,142)(134,144)(136,146)(138,148)(140,150), (1,30)(2,21)(3,22)(4,23)(5,24)(6,25)(7,26)(8,27)(9,28)(10,29)(11,52)(12,53)(13,54)(14,55)(15,56)(16,57)(17,58)(18,59)(19,60)(20,51)(31,82)(32,83)(33,84)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,81)(41,116)(42,117)(43,118)(44,119)(45,120)(46,111)(47,112)(48,113)(49,114)(50,115)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(91,101)(92,102)(93,103)(94,104)(95,105)(96,106)(97,107)(98,108)(99,109)(100,110)(121,136)(122,137)(123,138)(124,139)(125,140)(126,131)(127,132)(128,133)(129,134)(130,135)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,51)(10,52)(11,29)(12,30)(13,21)(14,22)(15,23)(16,24)(17,25)(18,26)(19,27)(20,28)(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)(71,89)(72,90)(73,81)(74,82)(75,83)(76,84)(77,85)(78,86)(79,87)(80,88)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,131)(100,132)(101,128)(102,129)(103,130)(104,121)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,143)(112,144)(113,145)(114,146)(115,147)(116,148)(117,149)(118,150)(119,141)(120,142), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,90)(12,81)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,88)(20,89)(21,74)(22,75)(23,76)(24,77)(25,78)(26,79)(27,80)(28,71)(29,72)(30,73)(31,54)(32,55)(33,56)(34,57)(35,58)(36,59)(37,60)(38,51)(39,52)(40,53)(41,123)(42,124)(43,125)(44,126)(45,127)(46,128)(47,129)(48,130)(49,121)(50,122)(91,143)(92,144)(93,145)(94,146)(95,147)(96,148)(97,149)(98,150)(99,141)(100,142)(101,153)(102,154)(103,155)(104,156)(105,157)(106,158)(107,159)(108,160)(109,151)(110,152)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,131)(120,132), (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), (1,104,30,94)(2,103,21,93)(3,102,22,92)(4,101,23,91)(5,110,24,100)(6,109,25,99)(7,108,26,98)(8,107,27,97)(9,106,28,96)(10,105,29,95)(11,137,52,122)(12,136,53,121)(13,135,54,130)(14,134,55,129)(15,133,56,128)(16,132,57,127)(17,131,58,126)(18,140,59,125)(19,139,60,124)(20,138,51,123)(31,48,82,113)(32,47,83,112)(33,46,84,111)(34,45,85,120)(35,44,86,119)(36,43,87,118)(37,42,88,117)(38,41,89,116)(39,50,90,115)(40,49,81,114)(61,158,71,148)(62,157,72,147)(63,156,73,146)(64,155,74,145)(65,154,75,144)(66,153,76,143)(67,152,77,142)(68,151,78,141)(69,160,79,150)(70,159,80,149)>;
G:=Group( (2,64)(4,66)(6,68)(8,70)(10,62)(11,90)(13,82)(15,84)(17,86)(19,88)(21,74)(23,76)(25,78)(27,80)(29,72)(31,54)(33,56)(35,58)(37,60)(39,52)(41,106)(42,159)(43,108)(44,151)(45,110)(46,153)(47,102)(48,155)(49,104)(50,157)(91,133)(92,112)(93,135)(94,114)(95,137)(96,116)(97,139)(98,118)(99,131)(100,120)(101,128)(103,130)(105,122)(107,124)(109,126)(111,143)(113,145)(115,147)(117,149)(119,141)(121,156)(123,158)(125,160)(127,152)(129,154)(132,142)(134,144)(136,146)(138,148)(140,150), (1,30)(2,21)(3,22)(4,23)(5,24)(6,25)(7,26)(8,27)(9,28)(10,29)(11,52)(12,53)(13,54)(14,55)(15,56)(16,57)(17,58)(18,59)(19,60)(20,51)(31,82)(32,83)(33,84)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,81)(41,116)(42,117)(43,118)(44,119)(45,120)(46,111)(47,112)(48,113)(49,114)(50,115)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(91,101)(92,102)(93,103)(94,104)(95,105)(96,106)(97,107)(98,108)(99,109)(100,110)(121,136)(122,137)(123,138)(124,139)(125,140)(126,131)(127,132)(128,133)(129,134)(130,135)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,51)(10,52)(11,29)(12,30)(13,21)(14,22)(15,23)(16,24)(17,25)(18,26)(19,27)(20,28)(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)(71,89)(72,90)(73,81)(74,82)(75,83)(76,84)(77,85)(78,86)(79,87)(80,88)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,131)(100,132)(101,128)(102,129)(103,130)(104,121)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,143)(112,144)(113,145)(114,146)(115,147)(116,148)(117,149)(118,150)(119,141)(120,142), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,90)(12,81)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,88)(20,89)(21,74)(22,75)(23,76)(24,77)(25,78)(26,79)(27,80)(28,71)(29,72)(30,73)(31,54)(32,55)(33,56)(34,57)(35,58)(36,59)(37,60)(38,51)(39,52)(40,53)(41,123)(42,124)(43,125)(44,126)(45,127)(46,128)(47,129)(48,130)(49,121)(50,122)(91,143)(92,144)(93,145)(94,146)(95,147)(96,148)(97,149)(98,150)(99,141)(100,142)(101,153)(102,154)(103,155)(104,156)(105,157)(106,158)(107,159)(108,160)(109,151)(110,152)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,131)(120,132), (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), (1,104,30,94)(2,103,21,93)(3,102,22,92)(4,101,23,91)(5,110,24,100)(6,109,25,99)(7,108,26,98)(8,107,27,97)(9,106,28,96)(10,105,29,95)(11,137,52,122)(12,136,53,121)(13,135,54,130)(14,134,55,129)(15,133,56,128)(16,132,57,127)(17,131,58,126)(18,140,59,125)(19,139,60,124)(20,138,51,123)(31,48,82,113)(32,47,83,112)(33,46,84,111)(34,45,85,120)(35,44,86,119)(36,43,87,118)(37,42,88,117)(38,41,89,116)(39,50,90,115)(40,49,81,114)(61,158,71,148)(62,157,72,147)(63,156,73,146)(64,155,74,145)(65,154,75,144)(66,153,76,143)(67,152,77,142)(68,151,78,141)(69,160,79,150)(70,159,80,149) );
G=PermutationGroup([(2,64),(4,66),(6,68),(8,70),(10,62),(11,90),(13,82),(15,84),(17,86),(19,88),(21,74),(23,76),(25,78),(27,80),(29,72),(31,54),(33,56),(35,58),(37,60),(39,52),(41,106),(42,159),(43,108),(44,151),(45,110),(46,153),(47,102),(48,155),(49,104),(50,157),(91,133),(92,112),(93,135),(94,114),(95,137),(96,116),(97,139),(98,118),(99,131),(100,120),(101,128),(103,130),(105,122),(107,124),(109,126),(111,143),(113,145),(115,147),(117,149),(119,141),(121,156),(123,158),(125,160),(127,152),(129,154),(132,142),(134,144),(136,146),(138,148),(140,150)], [(1,30),(2,21),(3,22),(4,23),(5,24),(6,25),(7,26),(8,27),(9,28),(10,29),(11,52),(12,53),(13,54),(14,55),(15,56),(16,57),(17,58),(18,59),(19,60),(20,51),(31,82),(32,83),(33,84),(34,85),(35,86),(36,87),(37,88),(38,89),(39,90),(40,81),(41,116),(42,117),(43,118),(44,119),(45,120),(46,111),(47,112),(48,113),(49,114),(50,115),(61,71),(62,72),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(91,101),(92,102),(93,103),(94,104),(95,105),(96,106),(97,107),(98,108),(99,109),(100,110),(121,136),(122,137),(123,138),(124,139),(125,140),(126,131),(127,132),(128,133),(129,134),(130,135),(141,151),(142,152),(143,153),(144,154),(145,155),(146,156),(147,157),(148,158),(149,159),(150,160)], [(1,53),(2,54),(3,55),(4,56),(5,57),(6,58),(7,59),(8,60),(9,51),(10,52),(11,29),(12,30),(13,21),(14,22),(15,23),(16,24),(17,25),(18,26),(19,27),(20,28),(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),(71,89),(72,90),(73,81),(74,82),(75,83),(76,84),(77,85),(78,86),(79,87),(80,88),(91,133),(92,134),(93,135),(94,136),(95,137),(96,138),(97,139),(98,140),(99,131),(100,132),(101,128),(102,129),(103,130),(104,121),(105,122),(106,123),(107,124),(108,125),(109,126),(110,127),(111,143),(112,144),(113,145),(114,146),(115,147),(116,148),(117,149),(118,150),(119,141),(120,142)], [(1,63),(2,64),(3,65),(4,66),(5,67),(6,68),(7,69),(8,70),(9,61),(10,62),(11,90),(12,81),(13,82),(14,83),(15,84),(16,85),(17,86),(18,87),(19,88),(20,89),(21,74),(22,75),(23,76),(24,77),(25,78),(26,79),(27,80),(28,71),(29,72),(30,73),(31,54),(32,55),(33,56),(34,57),(35,58),(36,59),(37,60),(38,51),(39,52),(40,53),(41,123),(42,124),(43,125),(44,126),(45,127),(46,128),(47,129),(48,130),(49,121),(50,122),(91,143),(92,144),(93,145),(94,146),(95,147),(96,148),(97,149),(98,150),(99,141),(100,142),(101,153),(102,154),(103,155),(104,156),(105,157),(106,158),(107,159),(108,160),(109,151),(110,152),(111,133),(112,134),(113,135),(114,136),(115,137),(116,138),(117,139),(118,140),(119,131),(120,132)], [(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)], [(1,104,30,94),(2,103,21,93),(3,102,22,92),(4,101,23,91),(5,110,24,100),(6,109,25,99),(7,108,26,98),(8,107,27,97),(9,106,28,96),(10,105,29,95),(11,137,52,122),(12,136,53,121),(13,135,54,130),(14,134,55,129),(15,133,56,128),(16,132,57,127),(17,131,58,126),(18,140,59,125),(19,139,60,124),(20,138,51,123),(31,48,82,113),(32,47,83,112),(33,46,84,111),(34,45,85,120),(35,44,86,119),(36,43,87,118),(37,42,88,117),(38,41,89,116),(39,50,90,115),(40,49,81,114),(61,158,71,148),(62,157,72,147),(63,156,73,146),(64,155,74,145),(65,154,75,144),(66,153,76,143),(67,152,77,142),(68,151,78,141),(69,160,79,150),(70,159,80,149)])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 4A | 4B | 4C | ··· | 4J | 4K | 4L | 4M | 4N | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D5 | C4○D4 | D10 | Dic5 | D10 | C5⋊D4 | D4×D5 | D4⋊2D5 |
| kernel | C24.18D10 | C10.10C42 | C2×C23.D5 | C23×Dic5 | D4×C2×C10 | D4×C10 | C2×Dic5 | C22×C10 | C22×D4 | C2×C10 | C22×C4 | C2×D4 | C24 | C23 | C22 | C22 |
| # reps | 1 | 2 | 3 | 1 | 1 | 8 | 4 | 4 | 2 | 4 | 2 | 8 | 4 | 16 | 4 | 4 |
Matrix representation of C24.18D10 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 33 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 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 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 26 | 31 |
| 9 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 2 | 21 |
| 0 | 0 | 0 | 31 | 39 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,1,33,0,0,0,0,40],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[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],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,4,26,0,0,0,0,31],[9,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,2,31,0,0,0,21,39] >;
C24.18D10 in GAP, Magma, Sage, TeX
C_2^4._{18}D_{10} % in TeX
G:=Group("C2^4.18D10"); // GroupNames label
G:=SmallGroup(320,847);
// by ID
G=gap.SmallGroup(320,847);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,387,12550]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^10=1,f^2=b,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*c*d,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=e^-1>;
// generators/relations