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G = C24.46D10  order 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.D5⋊16C4, C22.97(D4×D5), C23.25(C4×D5), C10.35C22≀C2, (C22×C10).62D4, (C22×C4).26D10, C2.1(C23⋊D10), (C22×C10).11Q8, C5⋊3(C23.8Q8), (C2×Dic5).229D4, C23.51(C5⋊D4), C10.16(C22⋊Q8), (C23×Dic5).4C2, C22⋊2(C10.D4), (C23×C10).29C22, (C22×C20).23C22, C22.24(C2×Dic10), C23.279(C22×D5), C10.10C42⋊12C2, C2.26(Dic5⋊4D4), C22.45(D4⋊2D5), (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

Derived series
C1 — C2×C10 — C24.46D10
Chief series
C1 — C5 — C10 — C2×C10 — C22×C10 — C22×Dic5 — C23×Dic5 — C24.46D10
Lower central
C5 — C2×C10 — C24.46D10
Upper central
C1 — C23 — C2×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, C2, C2, C4, C22, C22, C22, C5, C2×C4, C23, C23, C23, C10, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic5, C20, C2×C10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C23×C4, C2×Dic5, C2×Dic5, C2×C20, C22×C10, C22×C10, C22×C10, C23.8Q8, C10.D4, C23.D5, C5×C22⋊C4, C22×Dic5, C22×Dic5, C22×C20, C23×C10, C10.10C42, C2×C10.D4, C2×C23.D5, C10×C22⋊C4, C23×Dic5, C24.46D10
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D10, C2×C4⋊C4, C4×D4, C22≀C2, C22⋊Q8, C22.D4, Dic10, C4×D5, C5⋊D4, C22×D5, C23.8Q8, C10.D4, C2×Dic10, C2×C4×D5, D4×D5, D4⋊2D5, C2×C5⋊D4, Dic5.14D4, Dic5⋊4D4, C2×C10.D4, C23.18D10, C23⋊D10, C24.46D10

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

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

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

(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)

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

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×D5D4⋊2D5
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
 

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