Copied to
clipboard

G = C24.21D10order 320 = 26·5

21st non-split extension by C24 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.21D10, (C2×C20)⋊23D4, (C2×Dic5)⋊7D4, (C22×D5)⋊5D4, (C22×D4)⋊2D5, (C22×C10)⋊8D4, C233(C5⋊D4), C53(C232D4), C10.68C22≀C2, C22.284(D4×D5), C2.26(C202D4), C2.27(C20⋊D4), C10.37(C41D4), (C22×C4).153D10, C2.7(C242D5), C2.35(C23⋊D10), C10.131(C4⋊D4), (C23×C10).49C22, (C23×D5).25C22, C23.385(C22×D5), C10.10C4246C2, C2.35(Dic5⋊D4), (C22×C20).396C22, (C22×C10).368C23, C22.107(D42D5), (C22×Dic5).69C22, (D4×C2×C10)⋊12C2, (C2×C4)⋊5(C5⋊D4), (C22×C5⋊D4)⋊2C2, (C2×C10).557(C2×D4), (C2×C23.D5)⋊12C2, (C2×D10⋊C4)⋊39C2, C22.219(C2×C5⋊D4), (C2×C10).164(C4○D4), SmallGroup(320,850)

Series: Derived Chief Lower central Upper central

C1C22×C10 — C24.21D10
C1C5C10C2×C10C22×C10C23×D5C22×C5⋊D4 — C24.21D10
C5C22×C10 — C24.21D10
C1C23C22×D4

Generators and relations for C24.21D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=c, ab=ba, ac=ca, eae-1=ad=da, faf-1=abd, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce-1 >

Subgroups: 1270 in 322 conjugacy classes, 69 normal (25 characteristic)
C1, C2 [×3], C2 [×4], C2 [×6], C4 [×7], C22 [×3], C22 [×4], C22 [×30], C5, C2×C4 [×2], C2×C4 [×13], D4 [×24], C23, C23 [×4], C23 [×20], D5 [×2], C10 [×3], C10 [×4], C10 [×4], C22⋊C4 [×6], C22×C4, C22×C4 [×3], C2×D4 [×18], C24 [×2], C24, Dic5 [×5], C20 [×2], D10 [×10], C2×C10 [×3], C2×C10 [×4], C2×C10 [×20], C2.C42, C2×C22⋊C4 [×3], C22×D4, C22×D4 [×2], C2×Dic5 [×4], C2×Dic5 [×7], C5⋊D4 [×16], C2×C20 [×2], C2×C20 [×2], C5×D4 [×8], C22×D5 [×2], C22×D5 [×6], C22×C10, C22×C10 [×4], C22×C10 [×12], C232D4, D10⋊C4 [×2], C23.D5 [×4], C22×Dic5, C22×Dic5 [×2], C2×C5⋊D4 [×12], C22×C20, D4×C10 [×6], C23×D5, C23×C10 [×2], C10.10C42, C2×D10⋊C4, C2×C23.D5 [×2], C22×C5⋊D4 [×2], D4×C2×C10, C24.21D10
Quotients: C1, C2 [×7], C22 [×7], D4 [×12], C23, D5, C2×D4 [×6], C4○D4, D10 [×3], C22≀C2 [×3], C4⋊D4 [×3], C41D4, C5⋊D4 [×6], C22×D5, C232D4, D4×D5 [×3], D42D5, C2×C5⋊D4 [×3], C23⋊D10 [×2], C202D4, Dic5⋊D4 [×2], C20⋊D4, C242D5, C24.21D10

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

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

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

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

62 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M4A4B4C···4H5A5B10A···10N10O···10AD20A···20H
order12···2222222444···45510···1010···1020···20
size11···1444420204420···20222···24···44···4

62 irreducible representations

dim111111222222222244
type++++++++++++++-
imageC1C2C2C2C2C2D4D4D4D4D5C4○D4D10D10C5⋊D4C5⋊D4D4×D5D42D5
kernelC24.21D10C10.10C42C2×D10⋊C4C2×C23.D5C22×C5⋊D4D4×C2×C10C2×Dic5C2×C20C22×D5C22×C10C22×D4C2×C10C22×C4C24C2×C4C23C22C22
# reps1112214224222481662

Matrix representation of C24.21D10 in GL6(𝔽41)

100000
010000
0017100
00402400
000010
00003640
,
100000
010000
0040000
0004000
000010
000001
,
4000000
0400000
001000
000100
0000400
0000040
,
100000
010000
001000
000100
0000400
0000040
,
24370000
31170000
0013400
0073400
0000920
00003732
,
1740000
30240000
001000
0074000
00003221
000009

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,40,0,0,0,0,1,24,0,0,0,0,0,0,1,36,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[24,31,0,0,0,0,37,17,0,0,0,0,0,0,1,7,0,0,0,0,34,34,0,0,0,0,0,0,9,37,0,0,0,0,20,32],[17,30,0,0,0,0,4,24,0,0,0,0,0,0,1,7,0,0,0,0,0,40,0,0,0,0,0,0,32,0,0,0,0,0,21,9] >;

C24.21D10 in GAP, Magma, Sage, TeX

C_2^4._{21}D_{10}
% in TeX

G:=Group("C2^4.21D10");
// GroupNames label

G:=SmallGroup(320,850);
// by ID

G=gap.SmallGroup(320,850);
# by ID

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

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^10=1,f^2=c,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*d=d*c,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

׿
×
𝔽