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G = C24.46D10order 320 = 26·5

4th non-split extension by C24 of D10 acting via D10/D5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.46D10, C23.10Dic10, C10.73(C4×D4), C23.D516C4, C22.97(D4×D5), C23.25(C4×D5), C10.35C22≀C2, (C22×C10).62D4, (C22×C4).26D10, C2.1(C23⋊D10), (C22×C10).11Q8, C53(C23.8Q8), (C2×Dic5).229D4, C23.51(C5⋊D4), C10.16(C22⋊Q8), (C23×Dic5).4C2, C222(C10.D4), (C23×C10).29C22, (C22×C20).23C22, C22.24(C2×Dic10), C23.279(C22×D5), C10.10C4212C2, C2.26(Dic54D4), C22.45(D42D5), (C22×C10).321C23, C2.6(Dic5.14D4), C2.3(C23.18D10), C10.72(C22.D4), (C22×Dic5).37C22, (C2×C10)⋊5(C4⋊C4), C10.53(C2×C4⋊C4), (C2×Dic5)⋊6(C2×C4), (C2×C22⋊C4).8D5, (C2×C10).31(C2×Q8), C22.125(C2×C4×D5), (C2×C10.D4)⋊8C2, (C2×C10).315(C2×D4), (C10×C22⋊C4).7C2, C2.6(C2×C10.D4), C22.49(C2×C5⋊D4), (C2×C23.D5).8C2, (C2×C10).141(C4○D4), (C2×C10).208(C22×C4), (C22×C10).117(C2×C4), SmallGroup(320,573)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C24.46D10
C1C5C10C2×C10C22×C10C22×Dic5C23×Dic5 — C24.46D10
C5C2×C10 — C24.46D10
C1C23C2×C22⋊C4

Generators and relations for C24.46D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=d, f2=b, ab=ba, eae-1=faf-1=ac=ca, ad=da, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=be9 >

Subgroups: 734 in 234 conjugacy classes, 83 normal (27 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C4 [×10], C22 [×3], C22 [×8], C22 [×12], C5, C2×C4 [×30], C23, C23 [×6], C23 [×4], C10 [×3], C10 [×4], C10 [×4], C22⋊C4 [×6], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×10], C24, Dic5 [×8], C20 [×2], C2×C10 [×3], C2×C10 [×8], C2×C10 [×12], C2.C42 [×2], C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4 [×2], C23×C4, C2×Dic5 [×8], C2×Dic5 [×16], C2×C20 [×6], C22×C10, C22×C10 [×6], C22×C10 [×4], C23.8Q8, C10.D4 [×4], C23.D5 [×4], C5×C22⋊C4 [×2], C22×Dic5 [×4], C22×Dic5 [×6], C22×C20 [×2], C23×C10, C10.10C42 [×2], C2×C10.D4 [×2], C2×C23.D5, C10×C22⋊C4, C23×Dic5, C24.46D10
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×6], Q8 [×2], C23, D5, C4⋊C4 [×4], C22×C4, C2×D4 [×3], C2×Q8, C4○D4 [×2], D10 [×3], C2×C4⋊C4, C4×D4 [×2], C22≀C2, C22⋊Q8 [×2], C22.D4, Dic10 [×2], C4×D5 [×2], C5⋊D4 [×2], C22×D5, C23.8Q8, C10.D4 [×4], C2×Dic10, C2×C4×D5, D4×D5 [×2], D42D5 [×2], C2×C5⋊D4, Dic5.14D4 [×2], Dic54D4 [×2], C2×C10.D4, C23.18D10, C23⋊D10, C24.46D10

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

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

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

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

68 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E···4L4M4N4O4P5A5B10A···10N10O···10V20A···20P
order12···2222244444···444445510···1010···1020···20
size11···12222444410···1020202020222···24···44···4

68 irreducible representations

dim1111111222222222244
type++++++++-+++-+-
imageC1C2C2C2C2C2C4D4D4Q8D5C4○D4D10D10Dic10C4×D5C5⋊D4D4×D5D42D5
kernelC24.46D10C10.10C42C2×C10.D4C2×C23.D5C10×C22⋊C4C23×Dic5C23.D5C2×Dic5C22×C10C22×C10C2×C22⋊C4C2×C10C22×C4C24C23C23C23C22C22
# reps1221118422244288844

Matrix representation of C24.46D10 in GL6(𝔽41)

100000
010000
0040000
0032100
0000400
0000040
,
100000
010000
0040000
0004000
0000400
0000040
,
100000
010000
0040000
0004000
000010
000001
,
4000000
0400000
0040000
0004000
0000400
0000040
,
28280000
13320000
0093900
0003200
00003027
00001414
,
350000
23380000
00402300
0032100
000033
00002438

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,32,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[28,13,0,0,0,0,28,32,0,0,0,0,0,0,9,0,0,0,0,0,39,32,0,0,0,0,0,0,30,14,0,0,0,0,27,14],[3,23,0,0,0,0,5,38,0,0,0,0,0,0,40,32,0,0,0,0,23,1,0,0,0,0,0,0,3,24,0,0,0,0,3,38] >;

C24.46D10 in GAP, Magma, Sage, TeX

C_2^4._{46}D_{10}
% in TeX

G:=Group("C2^4.46D10");
// GroupNames label

G:=SmallGroup(320,573);
// by ID

G=gap.SmallGroup(320,573);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,254,219,184,12550]);
// Polycyclic

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

׿
×
𝔽