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G = C24.9D10order 320 = 26·5

9th non-split extension by C24 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.9D10, (C2×Dic5).64D4, (C22×C10).64D4, (C22×C4).30D10, C22.240(D4×D5), C10.84(C4⋊D4), C23.17(C5⋊D4), C53(C23.11D4), C2.9(Dic5⋊D4), C10.33(C4.4D4), C22.97(C4○D20), (C22×C20).24C22, (C23×C10).35C22, C23.369(C22×D5), C10.10C4214C2, C10.15(C422C2), C22.95(D42D5), (C22×C10).327C23, C2.21(D10.12D4), C2.21(Dic5.5D4), C10.57(C22.D4), C2.13(C23.D10), C2.7(C23.18D10), C2.6(C23.23D10), (C22×Dic5).41C22, (C2×C22⋊C4).9D5, (C2×C10).431(C2×D4), (C10×C22⋊C4).8C2, (C2×C10.D4)⋊10C2, C22.125(C2×C5⋊D4), (C2×C23.D5).14C2, (C2×C10).143(C4○D4), SmallGroup(320,579)

Series: Derived Chief Lower central Upper central

C1C22×C10 — C24.9D10
C1C5C10C2×C10C22×C10C22×Dic5C2×C23.D5 — C24.9D10
C5C22×C10 — C24.9D10
C1C23C2×C22⋊C4

Generators and relations for C24.9D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=c, f2=bcd, 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=be9 >

Subgroups: 566 in 170 conjugacy classes, 57 normal (51 characteristic)
C1, C2 [×7], C2 [×2], C4 [×7], C22 [×7], C22 [×10], C5, C2×C4 [×19], C23, C23 [×2], C23 [×6], C10 [×7], C10 [×2], C22⋊C4 [×6], C4⋊C4 [×2], C22×C4 [×2], C22×C4 [×4], C24, Dic5 [×5], C20 [×2], C2×C10 [×7], C2×C10 [×10], C2.C42 [×3], C2×C22⋊C4, C2×C22⋊C4 [×2], C2×C4⋊C4, C2×Dic5 [×2], C2×Dic5 [×11], C2×C20 [×6], C22×C10, C22×C10 [×2], C22×C10 [×6], C23.11D4, C10.D4 [×2], C23.D5 [×4], C5×C22⋊C4 [×2], C22×Dic5 [×4], C22×C20 [×2], C23×C10, C10.10C42 [×3], C2×C10.D4, C2×C23.D5 [×2], C10×C22⋊C4, C24.9D10
Quotients: C1, C2 [×7], C22 [×7], D4 [×4], C23, D5, C2×D4 [×2], C4○D4 [×5], D10 [×3], C4⋊D4, C22.D4 [×3], C4.4D4, C422C2 [×2], C5⋊D4 [×2], C22×D5, C23.11D4, C4○D20 [×2], D4×D5, D42D5 [×3], C2×C5⋊D4, C23.D10 [×2], D10.12D4, Dic5.5D4, C23.23D10, C23.18D10, Dic5⋊D4, C24.9D10

Smallest permutation representation of C24.9D10
On 160 points
Generators in S160
(2 26)(4 28)(6 30)(8 32)(10 34)(12 36)(14 38)(16 40)(18 22)(20 24)(41 51)(42 92)(43 53)(44 94)(45 55)(46 96)(47 57)(48 98)(49 59)(50 100)(52 82)(54 84)(56 86)(58 88)(60 90)(61 122)(63 124)(65 126)(67 128)(69 130)(71 132)(73 134)(75 136)(77 138)(79 140)(81 91)(83 93)(85 95)(87 97)(89 99)(101 141)(102 112)(103 143)(104 114)(105 145)(106 116)(107 147)(108 118)(109 149)(110 120)(111 151)(113 153)(115 155)(117 157)(119 159)(142 152)(144 154)(146 156)(148 158)(150 160)
(1 80)(2 61)(3 62)(4 63)(5 64)(6 65)(7 66)(8 67)(9 68)(10 69)(11 70)(12 71)(13 72)(14 73)(15 74)(16 75)(17 76)(18 77)(19 78)(20 79)(21 137)(22 138)(23 139)(24 140)(25 121)(26 122)(27 123)(28 124)(29 125)(30 126)(31 127)(32 128)(33 129)(34 130)(35 131)(36 132)(37 133)(38 134)(39 135)(40 136)(41 114)(42 115)(43 116)(44 117)(45 118)(46 119)(47 120)(48 101)(49 102)(50 103)(51 104)(52 105)(53 106)(54 107)(55 108)(56 109)(57 110)(58 111)(59 112)(60 113)(81 144)(82 145)(83 146)(84 147)(85 148)(86 149)(87 150)(88 151)(89 152)(90 153)(91 154)(92 155)(93 156)(94 157)(95 158)(96 159)(97 160)(98 141)(99 142)(100 143)
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 31)(22 32)(23 33)(24 34)(25 35)(26 36)(27 37)(28 38)(29 39)(30 40)(41 51)(42 52)(43 53)(44 54)(45 55)(46 56)(47 57)(48 58)(49 59)(50 60)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(81 91)(82 92)(83 93)(84 94)(85 95)(86 96)(87 97)(88 98)(89 99)(90 100)(101 111)(102 112)(103 113)(104 114)(105 115)(106 116)(107 117)(108 118)(109 119)(110 120)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)
(1 25)(2 26)(3 27)(4 28)(5 29)(6 30)(7 31)(8 32)(9 33)(10 34)(11 35)(12 36)(13 37)(14 38)(15 39)(16 40)(17 21)(18 22)(19 23)(20 24)(41 81)(42 82)(43 83)(44 84)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)(57 97)(58 98)(59 99)(60 100)(61 122)(62 123)(63 124)(64 125)(65 126)(66 127)(67 128)(68 129)(69 130)(70 131)(71 132)(72 133)(73 134)(74 135)(75 136)(76 137)(77 138)(78 139)(79 140)(80 121)(101 151)(102 152)(103 153)(104 154)(105 155)(106 156)(107 157)(108 158)(109 159)(110 160)(111 141)(112 142)(113 143)(114 144)(115 145)(116 146)(117 147)(118 148)(119 149)(120 150)
(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 60 131 153)(2 102 132 99)(3 58 133 151)(4 120 134 97)(5 56 135 149)(6 118 136 95)(7 54 137 147)(8 116 138 93)(9 52 139 145)(10 114 140 91)(11 50 121 143)(12 112 122 89)(13 48 123 141)(14 110 124 87)(15 46 125 159)(16 108 126 85)(17 44 127 157)(18 106 128 83)(19 42 129 155)(20 104 130 81)(21 84 66 107)(22 156 67 43)(23 82 68 105)(24 154 69 41)(25 100 70 103)(26 152 71 59)(27 98 72 101)(28 150 73 57)(29 96 74 119)(30 148 75 55)(31 94 76 117)(32 146 77 53)(33 92 78 115)(34 144 79 51)(35 90 80 113)(36 142 61 49)(37 88 62 111)(38 160 63 47)(39 86 64 109)(40 158 65 45)

G:=sub<Sym(160)| (2,26)(4,28)(6,30)(8,32)(10,34)(12,36)(14,38)(16,40)(18,22)(20,24)(41,51)(42,92)(43,53)(44,94)(45,55)(46,96)(47,57)(48,98)(49,59)(50,100)(52,82)(54,84)(56,86)(58,88)(60,90)(61,122)(63,124)(65,126)(67,128)(69,130)(71,132)(73,134)(75,136)(77,138)(79,140)(81,91)(83,93)(85,95)(87,97)(89,99)(101,141)(102,112)(103,143)(104,114)(105,145)(106,116)(107,147)(108,118)(109,149)(110,120)(111,151)(113,153)(115,155)(117,157)(119,159)(142,152)(144,154)(146,156)(148,158)(150,160), (1,80)(2,61)(3,62)(4,63)(5,64)(6,65)(7,66)(8,67)(9,68)(10,69)(11,70)(12,71)(13,72)(14,73)(15,74)(16,75)(17,76)(18,77)(19,78)(20,79)(21,137)(22,138)(23,139)(24,140)(25,121)(26,122)(27,123)(28,124)(29,125)(30,126)(31,127)(32,128)(33,129)(34,130)(35,131)(36,132)(37,133)(38,134)(39,135)(40,136)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,108)(56,109)(57,110)(58,111)(59,112)(60,113)(81,144)(82,145)(83,146)(84,147)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,155)(93,156)(94,157)(95,158)(96,159)(97,160)(98,141)(99,142)(100,143), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,91)(82,92)(83,93)(84,94)(85,95)(86,96)(87,97)(88,98)(89,99)(90,100)(101,111)(102,112)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,21)(18,22)(19,23)(20,24)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(57,97)(58,98)(59,99)(60,100)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,121)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,141)(112,142)(113,143)(114,144)(115,145)(116,146)(117,147)(118,148)(119,149)(120,150), (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), (1,60,131,153)(2,102,132,99)(3,58,133,151)(4,120,134,97)(5,56,135,149)(6,118,136,95)(7,54,137,147)(8,116,138,93)(9,52,139,145)(10,114,140,91)(11,50,121,143)(12,112,122,89)(13,48,123,141)(14,110,124,87)(15,46,125,159)(16,108,126,85)(17,44,127,157)(18,106,128,83)(19,42,129,155)(20,104,130,81)(21,84,66,107)(22,156,67,43)(23,82,68,105)(24,154,69,41)(25,100,70,103)(26,152,71,59)(27,98,72,101)(28,150,73,57)(29,96,74,119)(30,148,75,55)(31,94,76,117)(32,146,77,53)(33,92,78,115)(34,144,79,51)(35,90,80,113)(36,142,61,49)(37,88,62,111)(38,160,63,47)(39,86,64,109)(40,158,65,45)>;

G:=Group( (2,26)(4,28)(6,30)(8,32)(10,34)(12,36)(14,38)(16,40)(18,22)(20,24)(41,51)(42,92)(43,53)(44,94)(45,55)(46,96)(47,57)(48,98)(49,59)(50,100)(52,82)(54,84)(56,86)(58,88)(60,90)(61,122)(63,124)(65,126)(67,128)(69,130)(71,132)(73,134)(75,136)(77,138)(79,140)(81,91)(83,93)(85,95)(87,97)(89,99)(101,141)(102,112)(103,143)(104,114)(105,145)(106,116)(107,147)(108,118)(109,149)(110,120)(111,151)(113,153)(115,155)(117,157)(119,159)(142,152)(144,154)(146,156)(148,158)(150,160), (1,80)(2,61)(3,62)(4,63)(5,64)(6,65)(7,66)(8,67)(9,68)(10,69)(11,70)(12,71)(13,72)(14,73)(15,74)(16,75)(17,76)(18,77)(19,78)(20,79)(21,137)(22,138)(23,139)(24,140)(25,121)(26,122)(27,123)(28,124)(29,125)(30,126)(31,127)(32,128)(33,129)(34,130)(35,131)(36,132)(37,133)(38,134)(39,135)(40,136)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,108)(56,109)(57,110)(58,111)(59,112)(60,113)(81,144)(82,145)(83,146)(84,147)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,155)(93,156)(94,157)(95,158)(96,159)(97,160)(98,141)(99,142)(100,143), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,91)(82,92)(83,93)(84,94)(85,95)(86,96)(87,97)(88,98)(89,99)(90,100)(101,111)(102,112)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,21)(18,22)(19,23)(20,24)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(57,97)(58,98)(59,99)(60,100)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,121)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,141)(112,142)(113,143)(114,144)(115,145)(116,146)(117,147)(118,148)(119,149)(120,150), (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), (1,60,131,153)(2,102,132,99)(3,58,133,151)(4,120,134,97)(5,56,135,149)(6,118,136,95)(7,54,137,147)(8,116,138,93)(9,52,139,145)(10,114,140,91)(11,50,121,143)(12,112,122,89)(13,48,123,141)(14,110,124,87)(15,46,125,159)(16,108,126,85)(17,44,127,157)(18,106,128,83)(19,42,129,155)(20,104,130,81)(21,84,66,107)(22,156,67,43)(23,82,68,105)(24,154,69,41)(25,100,70,103)(26,152,71,59)(27,98,72,101)(28,150,73,57)(29,96,74,119)(30,148,75,55)(31,94,76,117)(32,146,77,53)(33,92,78,115)(34,144,79,51)(35,90,80,113)(36,142,61,49)(37,88,62,111)(38,160,63,47)(39,86,64,109)(40,158,65,45) );

G=PermutationGroup([(2,26),(4,28),(6,30),(8,32),(10,34),(12,36),(14,38),(16,40),(18,22),(20,24),(41,51),(42,92),(43,53),(44,94),(45,55),(46,96),(47,57),(48,98),(49,59),(50,100),(52,82),(54,84),(56,86),(58,88),(60,90),(61,122),(63,124),(65,126),(67,128),(69,130),(71,132),(73,134),(75,136),(77,138),(79,140),(81,91),(83,93),(85,95),(87,97),(89,99),(101,141),(102,112),(103,143),(104,114),(105,145),(106,116),(107,147),(108,118),(109,149),(110,120),(111,151),(113,153),(115,155),(117,157),(119,159),(142,152),(144,154),(146,156),(148,158),(150,160)], [(1,80),(2,61),(3,62),(4,63),(5,64),(6,65),(7,66),(8,67),(9,68),(10,69),(11,70),(12,71),(13,72),(14,73),(15,74),(16,75),(17,76),(18,77),(19,78),(20,79),(21,137),(22,138),(23,139),(24,140),(25,121),(26,122),(27,123),(28,124),(29,125),(30,126),(31,127),(32,128),(33,129),(34,130),(35,131),(36,132),(37,133),(38,134),(39,135),(40,136),(41,114),(42,115),(43,116),(44,117),(45,118),(46,119),(47,120),(48,101),(49,102),(50,103),(51,104),(52,105),(53,106),(54,107),(55,108),(56,109),(57,110),(58,111),(59,112),(60,113),(81,144),(82,145),(83,146),(84,147),(85,148),(86,149),(87,150),(88,151),(89,152),(90,153),(91,154),(92,155),(93,156),(94,157),(95,158),(96,159),(97,160),(98,141),(99,142),(100,143)], [(1,11),(2,12),(3,13),(4,14),(5,15),(6,16),(7,17),(8,18),(9,19),(10,20),(21,31),(22,32),(23,33),(24,34),(25,35),(26,36),(27,37),(28,38),(29,39),(30,40),(41,51),(42,52),(43,53),(44,54),(45,55),(46,56),(47,57),(48,58),(49,59),(50,60),(61,71),(62,72),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(81,91),(82,92),(83,93),(84,94),(85,95),(86,96),(87,97),(88,98),(89,99),(90,100),(101,111),(102,112),(103,113),(104,114),(105,115),(106,116),(107,117),(108,118),(109,119),(110,120),(121,131),(122,132),(123,133),(124,134),(125,135),(126,136),(127,137),(128,138),(129,139),(130,140),(141,151),(142,152),(143,153),(144,154),(145,155),(146,156),(147,157),(148,158),(149,159),(150,160)], [(1,25),(2,26),(3,27),(4,28),(5,29),(6,30),(7,31),(8,32),(9,33),(10,34),(11,35),(12,36),(13,37),(14,38),(15,39),(16,40),(17,21),(18,22),(19,23),(20,24),(41,81),(42,82),(43,83),(44,84),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(51,91),(52,92),(53,93),(54,94),(55,95),(56,96),(57,97),(58,98),(59,99),(60,100),(61,122),(62,123),(63,124),(64,125),(65,126),(66,127),(67,128),(68,129),(69,130),(70,131),(71,132),(72,133),(73,134),(74,135),(75,136),(76,137),(77,138),(78,139),(79,140),(80,121),(101,151),(102,152),(103,153),(104,154),(105,155),(106,156),(107,157),(108,158),(109,159),(110,160),(111,141),(112,142),(113,143),(114,144),(115,145),(116,146),(117,147),(118,148),(119,149),(120,150)], [(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)], [(1,60,131,153),(2,102,132,99),(3,58,133,151),(4,120,134,97),(5,56,135,149),(6,118,136,95),(7,54,137,147),(8,116,138,93),(9,52,139,145),(10,114,140,91),(11,50,121,143),(12,112,122,89),(13,48,123,141),(14,110,124,87),(15,46,125,159),(16,108,126,85),(17,44,127,157),(18,106,128,83),(19,42,129,155),(20,104,130,81),(21,84,66,107),(22,156,67,43),(23,82,68,105),(24,154,69,41),(25,100,70,103),(26,152,71,59),(27,98,72,101),(28,150,73,57),(29,96,74,119),(30,148,75,55),(31,94,76,117),(32,146,77,53),(33,92,78,115),(34,144,79,51),(35,90,80,113),(36,142,61,49),(37,88,62,111),(38,160,63,47),(39,86,64,109),(40,158,65,45)])

62 conjugacy classes

class 1 2A···2G2H2I4A4B4C4D4E···4L5A5B10A···10N10O···10V20A···20P
order12···22244444···45510···1010···1020···20
size11···144444420···20222···24···44···4

62 irreducible representations

dim111112222222244
type+++++++++++-
imageC1C2C2C2C2D4D4D5C4○D4D10D10C5⋊D4C4○D20D4×D5D42D5
kernelC24.9D10C10.10C42C2×C10.D4C2×C23.D5C10×C22⋊C4C2×Dic5C22×C10C2×C22⋊C4C2×C10C22×C4C24C23C22C22C22
# reps13121222104281626

Matrix representation of C24.9D10 in GL6(𝔽41)

100000
0400000
001000
00304000
000010
000001
,
100000
010000
0040000
0004000
0000400
0000040
,
4000000
0400000
0040000
0004000
000010
000001
,
4000000
0400000
001000
000100
000010
000001
,
010000
4000000
008000
00313600
0000310
0000037
,
100000
010000
0037300
0036400
000004
0000100

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,30,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,8,31,0,0,0,0,0,36,0,0,0,0,0,0,31,0,0,0,0,0,0,37],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,37,36,0,0,0,0,3,4,0,0,0,0,0,0,0,10,0,0,0,0,4,0] >;

C24.9D10 in GAP, Magma, Sage, TeX

C_2^4._9D_{10}
% in TeX

G:=Group("C2^4.9D10");
// GroupNames label

G:=SmallGroup(320,579);
// by ID

G=gap.SmallGroup(320,579);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,254,387,100,12550]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^10=c,f^2=b*c*d,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=b*e^9>;
// generators/relations

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