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G = C24.47D10order 320 = 26·5

5th non-split extension by C24 of D10 acting via D10/D5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.47D10, C23.43D20, C23.11Dic10, C2.4(D4×Dic5), C10.116(C4×D4), C22⋊C44Dic5, C22.98(D4×D5), C10.31C22≀C2, C221(C4⋊Dic5), (C22×C4).90D10, C22.42(C2×D20), (C22×C10).63D4, C2.3(C22⋊D20), (C22×C10).14Q8, C54(C23.8Q8), (C2×Dic5).230D4, C10.17(C22⋊Q8), (C23×Dic5).5C2, C23.13(C2×Dic5), (C23×C10).33C22, (C22×C20).59C22, C22.25(C2×Dic10), C23.280(C22×D5), C10.10C4230C2, C22.46(D42D5), (C22×C10).325C23, C2.4(C22.D20), C22.39(C22×Dic5), C2.7(Dic5.14D4), C10.30(C22.D4), (C22×Dic5).207C22, (C2×C10)⋊6(C4⋊C4), (C2×C20)⋊19(C2×C4), C10.54(C2×C4⋊C4), (C2×C4)⋊2(C2×Dic5), C2.7(C2×C4⋊Dic5), (C5×C22⋊C4)⋊13C4, (C2×C4⋊Dic5)⋊10C2, (C2×C10).35(C2×Q8), (C2×C10).319(C2×D4), (C2×C22⋊C4).13D5, (C10×C22⋊C4).15C2, (C2×C23.D5).12C2, (C2×C10).142(C4○D4), (C2×C10).279(C22×C4), (C22×C10).118(C2×C4), SmallGroup(320,577)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C24.47D10
C1C5C10C2×C10C22×C10C22×Dic5C23×Dic5 — C24.47D10
C5C2×C10 — C24.47D10
C1C23C2×C22⋊C4

Generators and relations for C24.47D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=c, f2=b, ab=ba, ac=ca, eae-1=faf-1=ad=da, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce9 >

Subgroups: 734 in 234 conjugacy classes, 91 normal (25 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C4 [×10], C22 [×3], C22 [×8], C22 [×12], C5, C2×C4 [×4], C2×C4 [×26], C23, C23 [×6], C23 [×4], C10 [×3], C10 [×4], C10 [×4], C22⋊C4 [×4], C22⋊C4 [×2], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×10], C24, Dic5 [×6], C20 [×4], 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 [×4], C2×Dic5 [×18], C2×C20 [×4], C2×C20 [×4], C22×C10, C22×C10 [×6], C22×C10 [×4], C23.8Q8, C4⋊Dic5 [×4], C23.D5 [×2], C5×C22⋊C4 [×4], C22×Dic5 [×2], C22×Dic5 [×2], C22×Dic5 [×6], C22×C20 [×2], C23×C10, C10.10C42 [×2], C2×C4⋊Dic5 [×2], C2×C23.D5, C10×C22⋊C4, C23×Dic5, C24.47D10
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], Dic5 [×4], D10 [×3], C2×C4⋊C4, C4×D4 [×2], C22≀C2, C22⋊Q8 [×2], C22.D4, Dic10 [×2], D20 [×2], C2×Dic5 [×6], C22×D5, C23.8Q8, C4⋊Dic5 [×4], C2×Dic10, C2×D20, D4×D5 [×2], D42D5 [×2], C22×Dic5, Dic5.14D4 [×2], C22⋊D20, C22.D20, C2×C4⋊Dic5, D4×Dic5 [×2], C24.47D10

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

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

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

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

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○D4Dic5D10D10Dic10D20D4×D5D42D5
kernelC24.47D10C10.10C42C2×C4⋊Dic5C2×C23.D5C10×C22⋊C4C23×Dic5C5×C22⋊C4C2×Dic5C22×C10C22×C10C2×C22⋊C4C2×C10C22⋊C4C22×C4C24C23C23C22C22
# reps1221118422248428844

Matrix representation of C24.47D10 in GL5(𝔽41)

10000
040000
01100
000400
000040
,
400000
040000
004000
000400
000040
,
10000
01000
00100
000400
000040
,
10000
040000
004000
00010
00001
,
10000
0403900
00100
0002714
0002711
,
90000
0322300
00900
0001327
0001828

G:=sub<GL(5,GF(41))| [1,0,0,0,0,0,40,1,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,40,0,0,0,0,39,1,0,0,0,0,0,27,27,0,0,0,14,11],[9,0,0,0,0,0,32,0,0,0,0,23,9,0,0,0,0,0,13,18,0,0,0,27,28] >;

C24.47D10 in GAP, Magma, Sage, TeX

C_2^4._{47}D_{10}
% in TeX

G:=Group("C2^4.47D10");
// GroupNames label

G:=SmallGroup(320,577);
// by ID

G=gap.SmallGroup(320,577);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,387,100,12550]);
// Polycyclic

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

׿
×
𝔽