metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.47D10, C23.43D20, C23.11Dic10, C2.4(D4×Dic5), C10.116(C4×D4), C22⋊C4⋊4Dic5, C22.98(D4×D5), C10.31C22≀C2, C22⋊1(C4⋊Dic5), (C22×C4).90D10, C22.42(C2×D20), (C22×C10).63D4, C2.3(C22⋊D20), (C22×C10).14Q8, C5⋊4(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), C10.10C42⋊30C2, C22.46(D4⋊2D5), (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
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, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, C23, C23, C23, C10, C10, C10, C22⋊C4, 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, C2×C20, C22×C10, C22×C10, C22×C10, C23.8Q8, C4⋊Dic5, C23.D5, C5×C22⋊C4, C22×Dic5, C22×Dic5, C22×Dic5, C22×C20, C23×C10, C10.10C42, C2×C4⋊Dic5, C2×C23.D5, C10×C22⋊C4, C23×Dic5, C24.47D10
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, D10, C2×C4⋊C4, C4×D4, C22≀C2, C22⋊Q8, C22.D4, Dic10, D20, C2×Dic5, C22×D5, C23.8Q8, C4⋊Dic5, C2×Dic10, C2×D20, D4×D5, D4⋊2D5, C22×Dic5, Dic5.14D4, C22⋊D20, C22.D20, C2×C4⋊Dic5, D4×Dic5, C24.47D10
►On 160 points
Generators in S160
(1 154)(2 85)(3 156)(4 87)(5 158)(6 89)(7 160)(8 91)(9 142)(10 93)(11 144)(12 95)(13 146)(14 97)(15 148)(16 99)(17 150)(18 81)(19 152)(20 83)(21 117)(22 126)(23 119)(24 128)(25 101)(26 130)(27 103)(28 132)(29 105)(30 134)(31 107)(32 136)(33 109)(34 138)(35 111)(36 140)(37 113)(38 122)(39 115)(40 124)(41 110)(42 139)(43 112)(44 121)(45 114)(46 123)(47 116)(48 125)(49 118)(50 127)(51 120)(52 129)(53 102)(54 131)(55 104)(56 133)(57 106)(58 135)(59 108)(60 137)(61 147)(62 98)(63 149)(64 100)(65 151)(66 82)(67 153)(68 84)(69 155)(70 86)(71 157)(72 88)(73 159)(74 90)(75 141)(76 92)(77 143)(78 94)(79 145)(80 96)
(1 154)(2 155)(3 156)(4 157)(5 158)(6 159)(7 160)(8 141)(9 142)(10 143)(11 144)(12 145)(13 146)(14 147)(15 148)(16 149)(17 150)(18 151)(19 152)(20 153)(21 125)(22 126)(23 127)(24 128)(25 129)(26 130)(27 131)(28 132)(29 133)(30 134)(31 135)(32 136)(33 137)(34 138)(35 139)(36 140)(37 121)(38 122)(39 123)(40 124)(41 110)(42 111)(43 112)(44 113)(45 114)(46 115)(47 116)(48 117)(49 118)(50 119)(51 120)(52 101)(53 102)(54 103)(55 104)(56 105)(57 106)(58 107)(59 108)(60 109)(61 97)(62 98)(63 99)(64 100)(65 81)(66 82)(67 83)(68 84)(69 85)(70 86)(71 87)(72 88)(73 89)(74 90)(75 91)(76 92)(77 93)(78 94)(79 95)(80 96)
(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 68)(2 69)(3 70)(4 71)(5 72)(6 73)(7 74)(8 75)(9 76)(10 77)(11 78)(12 79)(13 80)(14 61)(15 62)(16 63)(17 64)(18 65)(19 66)(20 67)(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)(81 151)(82 152)(83 153)(84 154)(85 155)(86 156)(87 157)(88 158)(89 159)(90 160)(91 141)(92 142)(93 143)(94 144)(95 145)(96 146)(97 147)(98 148)(99 149)(100 150)(101 129)(102 130)(103 131)(104 132)(105 133)(106 134)(107 135)(108 136)(109 137)(110 138)(111 139)(112 140)(113 121)(114 122)(115 123)(116 124)(117 125)(118 126)(119 127)(120 128)
(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 37 154 121)(2 36 155 140)(3 35 156 139)(4 34 157 138)(5 33 158 137)(6 32 159 136)(7 31 160 135)(8 30 141 134)(9 29 142 133)(10 28 143 132)(11 27 144 131)(12 26 145 130)(13 25 146 129)(14 24 147 128)(15 23 148 127)(16 22 149 126)(17 21 150 125)(18 40 151 124)(19 39 152 123)(20 38 153 122)(41 87 110 71)(42 86 111 70)(43 85 112 69)(44 84 113 68)(45 83 114 67)(46 82 115 66)(47 81 116 65)(48 100 117 64)(49 99 118 63)(50 98 119 62)(51 97 120 61)(52 96 101 80)(53 95 102 79)(54 94 103 78)(55 93 104 77)(56 92 105 76)(57 91 106 75)(58 90 107 74)(59 89 108 73)(60 88 109 72)
G:=sub<Sym(160)| (1,154)(2,85)(3,156)(4,87)(5,158)(6,89)(7,160)(8,91)(9,142)(10,93)(11,144)(12,95)(13,146)(14,97)(15,148)(16,99)(17,150)(18,81)(19,152)(20,83)(21,117)(22,126)(23,119)(24,128)(25,101)(26,130)(27,103)(28,132)(29,105)(30,134)(31,107)(32,136)(33,109)(34,138)(35,111)(36,140)(37,113)(38,122)(39,115)(40,124)(41,110)(42,139)(43,112)(44,121)(45,114)(46,123)(47,116)(48,125)(49,118)(50,127)(51,120)(52,129)(53,102)(54,131)(55,104)(56,133)(57,106)(58,135)(59,108)(60,137)(61,147)(62,98)(63,149)(64,100)(65,151)(66,82)(67,153)(68,84)(69,155)(70,86)(71,157)(72,88)(73,159)(74,90)(75,141)(76,92)(77,143)(78,94)(79,145)(80,96), (1,154)(2,155)(3,156)(4,157)(5,158)(6,159)(7,160)(8,141)(9,142)(10,143)(11,144)(12,145)(13,146)(14,147)(15,148)(16,149)(17,150)(18,151)(19,152)(20,153)(21,125)(22,126)(23,127)(24,128)(25,129)(26,130)(27,131)(28,132)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,121)(38,122)(39,123)(40,124)(41,110)(42,111)(43,112)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,101)(53,102)(54,103)(55,104)(56,105)(57,106)(58,107)(59,108)(60,109)(61,97)(62,98)(63,99)(64,100)(65,81)(66,82)(67,83)(68,84)(69,85)(70,86)(71,87)(72,88)(73,89)(74,90)(75,91)(76,92)(77,93)(78,94)(79,95)(80,96), (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), (1,68)(2,69)(3,70)(4,71)(5,72)(6,73)(7,74)(8,75)(9,76)(10,77)(11,78)(12,79)(13,80)(14,61)(15,62)(16,63)(17,64)(18,65)(19,66)(20,67)(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)(81,151)(82,152)(83,153)(84,154)(85,155)(86,156)(87,157)(88,158)(89,159)(90,160)(91,141)(92,142)(93,143)(94,144)(95,145)(96,146)(97,147)(98,148)(99,149)(100,150)(101,129)(102,130)(103,131)(104,132)(105,133)(106,134)(107,135)(108,136)(109,137)(110,138)(111,139)(112,140)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128), (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), (1,37,154,121)(2,36,155,140)(3,35,156,139)(4,34,157,138)(5,33,158,137)(6,32,159,136)(7,31,160,135)(8,30,141,134)(9,29,142,133)(10,28,143,132)(11,27,144,131)(12,26,145,130)(13,25,146,129)(14,24,147,128)(15,23,148,127)(16,22,149,126)(17,21,150,125)(18,40,151,124)(19,39,152,123)(20,38,153,122)(41,87,110,71)(42,86,111,70)(43,85,112,69)(44,84,113,68)(45,83,114,67)(46,82,115,66)(47,81,116,65)(48,100,117,64)(49,99,118,63)(50,98,119,62)(51,97,120,61)(52,96,101,80)(53,95,102,79)(54,94,103,78)(55,93,104,77)(56,92,105,76)(57,91,106,75)(58,90,107,74)(59,89,108,73)(60,88,109,72)>;
G:=Group( (1,154)(2,85)(3,156)(4,87)(5,158)(6,89)(7,160)(8,91)(9,142)(10,93)(11,144)(12,95)(13,146)(14,97)(15,148)(16,99)(17,150)(18,81)(19,152)(20,83)(21,117)(22,126)(23,119)(24,128)(25,101)(26,130)(27,103)(28,132)(29,105)(30,134)(31,107)(32,136)(33,109)(34,138)(35,111)(36,140)(37,113)(38,122)(39,115)(40,124)(41,110)(42,139)(43,112)(44,121)(45,114)(46,123)(47,116)(48,125)(49,118)(50,127)(51,120)(52,129)(53,102)(54,131)(55,104)(56,133)(57,106)(58,135)(59,108)(60,137)(61,147)(62,98)(63,149)(64,100)(65,151)(66,82)(67,153)(68,84)(69,155)(70,86)(71,157)(72,88)(73,159)(74,90)(75,141)(76,92)(77,143)(78,94)(79,145)(80,96), (1,154)(2,155)(3,156)(4,157)(5,158)(6,159)(7,160)(8,141)(9,142)(10,143)(11,144)(12,145)(13,146)(14,147)(15,148)(16,149)(17,150)(18,151)(19,152)(20,153)(21,125)(22,126)(23,127)(24,128)(25,129)(26,130)(27,131)(28,132)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,121)(38,122)(39,123)(40,124)(41,110)(42,111)(43,112)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,101)(53,102)(54,103)(55,104)(56,105)(57,106)(58,107)(59,108)(60,109)(61,97)(62,98)(63,99)(64,100)(65,81)(66,82)(67,83)(68,84)(69,85)(70,86)(71,87)(72,88)(73,89)(74,90)(75,91)(76,92)(77,93)(78,94)(79,95)(80,96), (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), (1,68)(2,69)(3,70)(4,71)(5,72)(6,73)(7,74)(8,75)(9,76)(10,77)(11,78)(12,79)(13,80)(14,61)(15,62)(16,63)(17,64)(18,65)(19,66)(20,67)(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)(81,151)(82,152)(83,153)(84,154)(85,155)(86,156)(87,157)(88,158)(89,159)(90,160)(91,141)(92,142)(93,143)(94,144)(95,145)(96,146)(97,147)(98,148)(99,149)(100,150)(101,129)(102,130)(103,131)(104,132)(105,133)(106,134)(107,135)(108,136)(109,137)(110,138)(111,139)(112,140)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128), (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), (1,37,154,121)(2,36,155,140)(3,35,156,139)(4,34,157,138)(5,33,158,137)(6,32,159,136)(7,31,160,135)(8,30,141,134)(9,29,142,133)(10,28,143,132)(11,27,144,131)(12,26,145,130)(13,25,146,129)(14,24,147,128)(15,23,148,127)(16,22,149,126)(17,21,150,125)(18,40,151,124)(19,39,152,123)(20,38,153,122)(41,87,110,71)(42,86,111,70)(43,85,112,69)(44,84,113,68)(45,83,114,67)(46,82,115,66)(47,81,116,65)(48,100,117,64)(49,99,118,63)(50,98,119,62)(51,97,120,61)(52,96,101,80)(53,95,102,79)(54,94,103,78)(55,93,104,77)(56,92,105,76)(57,91,106,75)(58,90,107,74)(59,89,108,73)(60,88,109,72) );
G=PermutationGroup([[(1,154),(2,85),(3,156),(4,87),(5,158),(6,89),(7,160),(8,91),(9,142),(10,93),(11,144),(12,95),(13,146),(14,97),(15,148),(16,99),(17,150),(18,81),(19,152),(20,83),(21,117),(22,126),(23,119),(24,128),(25,101),(26,130),(27,103),(28,132),(29,105),(30,134),(31,107),(32,136),(33,109),(34,138),(35,111),(36,140),(37,113),(38,122),(39,115),(40,124),(41,110),(42,139),(43,112),(44,121),(45,114),(46,123),(47,116),(48,125),(49,118),(50,127),(51,120),(52,129),(53,102),(54,131),(55,104),(56,133),(57,106),(58,135),(59,108),(60,137),(61,147),(62,98),(63,149),(64,100),(65,151),(66,82),(67,153),(68,84),(69,155),(70,86),(71,157),(72,88),(73,159),(74,90),(75,141),(76,92),(77,143),(78,94),(79,145),(80,96)], [(1,154),(2,155),(3,156),(4,157),(5,158),(6,159),(7,160),(8,141),(9,142),(10,143),(11,144),(12,145),(13,146),(14,147),(15,148),(16,149),(17,150),(18,151),(19,152),(20,153),(21,125),(22,126),(23,127),(24,128),(25,129),(26,130),(27,131),(28,132),(29,133),(30,134),(31,135),(32,136),(33,137),(34,138),(35,139),(36,140),(37,121),(38,122),(39,123),(40,124),(41,110),(42,111),(43,112),(44,113),(45,114),(46,115),(47,116),(48,117),(49,118),(50,119),(51,120),(52,101),(53,102),(54,103),(55,104),(56,105),(57,106),(58,107),(59,108),(60,109),(61,97),(62,98),(63,99),(64,100),(65,81),(66,82),(67,83),(68,84),(69,85),(70,86),(71,87),(72,88),(73,89),(74,90),(75,91),(76,92),(77,93),(78,94),(79,95),(80,96)], [(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)], [(1,68),(2,69),(3,70),(4,71),(5,72),(6,73),(7,74),(8,75),(9,76),(10,77),(11,78),(12,79),(13,80),(14,61),(15,62),(16,63),(17,64),(18,65),(19,66),(20,67),(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),(81,151),(82,152),(83,153),(84,154),(85,155),(86,156),(87,157),(88,158),(89,159),(90,160),(91,141),(92,142),(93,143),(94,144),(95,145),(96,146),(97,147),(98,148),(99,149),(100,150),(101,129),(102,130),(103,131),(104,132),(105,133),(106,134),(107,135),(108,136),(109,137),(110,138),(111,139),(112,140),(113,121),(114,122),(115,123),(116,124),(117,125),(118,126),(119,127),(120,128)], [(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)], [(1,37,154,121),(2,36,155,140),(3,35,156,139),(4,34,157,138),(5,33,158,137),(6,32,159,136),(7,31,160,135),(8,30,141,134),(9,29,142,133),(10,28,143,132),(11,27,144,131),(12,26,145,130),(13,25,146,129),(14,24,147,128),(15,23,148,127),(16,22,149,126),(17,21,150,125),(18,40,151,124),(19,39,152,123),(20,38,153,122),(41,87,110,71),(42,86,111,70),(43,85,112,69),(44,84,113,68),(45,83,114,67),(46,82,115,66),(47,81,116,65),(48,100,117,64),(49,99,118,63),(50,98,119,62),(51,97,120,61),(52,96,101,80),(53,95,102,79),(54,94,103,78),(55,93,104,77),(56,92,105,76),(57,91,106,75),(58,90,107,74),(59,89,108,73),(60,88,109,72)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 4M | 4N | 4O | 4P | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10V | 20A | ··· | 20P |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | - | + | + | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D5 | C4○D4 | Dic5 | D10 | D10 | Dic10 | D20 | D4×D5 | D4⋊2D5 |
| kernel | C24.47D10 | C10.10C42 | C2×C4⋊Dic5 | C2×C23.D5 | C10×C22⋊C4 | C23×Dic5 | C5×C22⋊C4 | C2×Dic5 | C22×C10 | C22×C10 | C2×C22⋊C4 | C2×C10 | C22⋊C4 | C22×C4 | C24 | C23 | C23 | C22 | C22 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 4 | 2 | 2 | 2 | 4 | 8 | 4 | 2 | 8 | 8 | 4 | 4 |
Matrix representation of C24.47D10 ►in GL5(𝔽41)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 1 | 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 | 39 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 27 | 14 |
| 0 | 0 | 0 | 27 | 11 |
| 9 | 0 | 0 | 0 | 0 |
| 0 | 32 | 23 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 13 | 27 |
| 0 | 0 | 0 | 18 | 28 |
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