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, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, C10, C10, C10, C22⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, Dic5, C20, C2×C10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C23×C4, C22×D4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C22×C10, C23.23D4, C23.D5, C22×Dic5, C22×Dic5, C22×C20, D4×C10, D4×C10, C23×C10, C10.10C42, C2×C23.D5, C2×C23.D5, C23×Dic5, D4×C2×C10, C24.18D10
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22⋊C4, C22×C4, C2×D4, C4○D4, Dic5, D10, C2×C22⋊C4, C4×D4, C22≀C2, C4⋊D4, C22.D4, C2×Dic5, C5⋊D4, C22×D5, C23.23D4, C23.D5, D4×D5, D4⋊2D5, C22×Dic5, C2×C5⋊D4, D4×Dic5, C23.18D10, C23⋊D10, Dic5⋊D4, 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 72)(23 74)(25 76)(27 78)(29 80)(31 56)(33 58)(35 60)(37 52)(39 54)(41 104)(42 159)(43 106)(44 151)(45 108)(46 153)(47 110)(48 155)(49 102)(50 157)(91 133)(92 114)(93 135)(94 116)(95 137)(96 118)(97 139)(98 120)(99 131)(100 112)(101 128)(103 130)(105 122)(107 124)(109 126)(111 143)(113 145)(115 147)(117 149)(119 141)(121 158)(123 160)(125 152)(127 154)(129 156)(132 144)(134 146)(136 148)(138 150)(140 142)
(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 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 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 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 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)(91 145)(92 146)(93 147)(94 148)(95 149)(96 150)(97 141)(98 142)(99 143)(100 144)(101 155)(102 156)(103 157)(104 158)(105 159)(106 160)(107 151)(108 152)(109 153)(110 154)(111 131)(112 132)(113 133)(114 134)(115 135)(116 136)(117 137)(118 138)(119 139)(120 140)
(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)
(1 102 22 92)(2 101 23 91)(3 110 24 100)(4 109 25 99)(5 108 26 98)(6 107 27 97)(7 106 28 96)(8 105 29 95)(9 104 30 94)(10 103 21 93)(11 135 54 130)(12 134 55 129)(13 133 56 128)(14 132 57 127)(15 131 58 126)(16 140 59 125)(17 139 60 124)(18 138 51 123)(19 137 52 122)(20 136 53 121)(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)(21,72)(23,74)(25,76)(27,78)(29,80)(31,56)(33,58)(35,60)(37,52)(39,54)(41,104)(42,159)(43,106)(44,151)(45,108)(46,153)(47,110)(48,155)(49,102)(50,157)(91,133)(92,114)(93,135)(94,116)(95,137)(96,118)(97,139)(98,120)(99,131)(100,112)(101,128)(103,130)(105,122)(107,124)(109,126)(111,143)(113,145)(115,147)(117,149)(119,141)(121,158)(123,160)(125,152)(127,154)(129,156)(132,144)(134,146)(136,148)(138,150)(140,142), (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)(31,82)(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), (1,55)(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)(71,89)(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)(21,72)(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)(91,145)(92,146)(93,147)(94,148)(95,149)(96,150)(97,141)(98,142)(99,143)(100,144)(101,155)(102,156)(103,157)(104,158)(105,159)(106,160)(107,151)(108,152)(109,153)(110,154)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,138)(119,139)(120,140), (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), (1,102,22,92)(2,101,23,91)(3,110,24,100)(4,109,25,99)(5,108,26,98)(6,107,27,97)(7,106,28,96)(8,105,29,95)(9,104,30,94)(10,103,21,93)(11,135,54,130)(12,134,55,129)(13,133,56,128)(14,132,57,127)(15,131,58,126)(16,140,59,125)(17,139,60,124)(18,138,51,123)(19,137,52,122)(20,136,53,121)(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)(21,72)(23,74)(25,76)(27,78)(29,80)(31,56)(33,58)(35,60)(37,52)(39,54)(41,104)(42,159)(43,106)(44,151)(45,108)(46,153)(47,110)(48,155)(49,102)(50,157)(91,133)(92,114)(93,135)(94,116)(95,137)(96,118)(97,139)(98,120)(99,131)(100,112)(101,128)(103,130)(105,122)(107,124)(109,126)(111,143)(113,145)(115,147)(117,149)(119,141)(121,158)(123,160)(125,152)(127,154)(129,156)(132,144)(134,146)(136,148)(138,150)(140,142), (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)(31,82)(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), (1,55)(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)(71,89)(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)(21,72)(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)(91,145)(92,146)(93,147)(94,148)(95,149)(96,150)(97,141)(98,142)(99,143)(100,144)(101,155)(102,156)(103,157)(104,158)(105,159)(106,160)(107,151)(108,152)(109,153)(110,154)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,138)(119,139)(120,140), (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), (1,102,22,92)(2,101,23,91)(3,110,24,100)(4,109,25,99)(5,108,26,98)(6,107,27,97)(7,106,28,96)(8,105,29,95)(9,104,30,94)(10,103,21,93)(11,135,54,130)(12,134,55,129)(13,133,56,128)(14,132,57,127)(15,131,58,126)(16,140,59,125)(17,139,60,124)(18,138,51,123)(19,137,52,122)(20,136,53,121)(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),(21,72),(23,74),(25,76),(27,78),(29,80),(31,56),(33,58),(35,60),(37,52),(39,54),(41,104),(42,159),(43,106),(44,151),(45,108),(46,153),(47,110),(48,155),(49,102),(50,157),(91,133),(92,114),(93,135),(94,116),(95,137),(96,118),(97,139),(98,120),(99,131),(100,112),(101,128),(103,130),(105,122),(107,124),(109,126),(111,143),(113,145),(115,147),(117,149),(119,141),(121,158),(123,160),(125,152),(127,154),(129,156),(132,144),(134,146),(136,148),(138,150),(140,142)], [(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),(31,82),(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)], [(1,55),(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),(71,89),(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),(21,72),(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),(91,145),(92,146),(93,147),(94,148),(95,149),(96,150),(97,141),(98,142),(99,143),(100,144),(101,155),(102,156),(103,157),(104,158),(105,159),(106,160),(107,151),(108,152),(109,153),(110,154),(111,131),(112,132),(113,133),(114,134),(115,135),(116,136),(117,137),(118,138),(119,139),(120,140)], [(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)], [(1,102,22,92),(2,101,23,91),(3,110,24,100),(4,109,25,99),(5,108,26,98),(6,107,27,97),(7,106,28,96),(8,105,29,95),(9,104,30,94),(10,103,21,93),(11,135,54,130),(12,134,55,129),(13,133,56,128),(14,132,57,127),(15,131,58,126),(16,140,59,125),(17,139,60,124),(18,138,51,123),(19,137,52,122),(20,136,53,121),(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