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G = C24.18D10order 320 = 26·5

18th non-split extension by C24 of D10 acting via D10/C5=C22

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, C232(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), C56(C23.23D4), C10.128(C4⋊D4), C221(C23.D5), C2.7(Dic5⋊D4), (C23×C10).46C22, C23.305(C22×D5), C10.10C4244C2, C22.61(D42D5), (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

C1C2×C10 — C24.18D10
C1C5C10C2×C10C22×C10C22×Dic5C23×Dic5 — C24.18D10
C5C2×C10 — C24.18D10
C1C23C22×D4

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], D42D5 [×2], C22×Dic5, C2×C5⋊D4 [×2], D4×Dic5 [×2], C23.18D10, C23⋊D10, Dic5⋊D4 [×2], C2×C23.D5, C24.18D10

Smallest permutation representation of 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···2G2H2I2J2K2L2M4A4B4C···4J4K4L4M4N5A5B10A···10N10O···10AD20A···20H
order12···2222222444···444445510···1010···1020···20
size11···12222444410···1020202020222···24···44···4

68 irreducible representations

dim1111112222222244
type+++++++++-++-
imageC1C2C2C2C2C4D4D4D5C4○D4D10Dic5D10C5⋊D4D4×D5D42D5
kernelC24.18D10C10.10C42C2×C23.D5C23×Dic5D4×C2×C10D4×C10C2×Dic5C22×C10C22×D4C2×C10C22×C4C2×D4C24C23C22C22
# reps12311844242841644

Matrix representation of C24.18D10 in GL5(𝔽41)

400000
01000
004000
00010
0003340
,
400000
01000
00100
000400
000040
,
10000
040000
004000
000400
000040
,
10000
040000
004000
00010
00001
,
400000
00100
01000
00040
0002631
,
90000
01000
00100
000221
0003139

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

׿
×
𝔽