metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.62D10, C23.15Dic10, (C23×C4).4D5, (C2×C20).451D4, C10.114(C4×D4), (C23×C20).2C2, C23.D5⋊17C4, C23.37(C4×D5), C10.69C22≀C2, (C22×C10).25Q8, C5⋊6(C23.8Q8), (C22×C4).406D10, (C22×C10).191D4, C2.1(C24⋊2D5), C23.81(C5⋊D4), C10.67(C22⋊Q8), C2.4(C20.48D4), C22.61(C4○D20), C22⋊3(C10.D4), (C23×C10).97C22, C22.31(C2×Dic10), C23.301(C22×D5), C10.10C42⋊22C2, (C22×C20).482C22, (C22×C10).361C23, C10.67(C22.D4), C2.3(C23.23D10), (C22×Dic5).64C22, (C2×C10)⋊9(C4⋊C4), C10.78(C2×C4⋊C4), C2.28(C4×C5⋊D4), (C2×C10).43(C2×Q8), C22.149(C2×C4×D5), (C2×Dic5)⋊10(C2×C4), (C2×C10).547(C2×D4), C22.85(C2×C5⋊D4), (C2×C10).89(C4○D4), (C2×C10.D4)⋊15C2, (C2×C4).224(C5⋊D4), C2.20(C2×C10.D4), (C2×C23.D5).16C2, (C2×C10).243(C22×C4), (C22×C10).167(C2×C4), SmallGroup(320,837)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.62D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=f2=b, ab=ba, faf-1=ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=de9 >
Subgroups: 638 in 234 conjugacy classes, 87 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, 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×C4⋊C4, C23×C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C22×C10, C22×C10, C23.8Q8, C10.D4, C23.D5, C23.D5, C22×Dic5, C22×Dic5, C22×C20, C22×C20, C23×C10, C10.10C42, C2×C10.D4, C2×C23.D5, C23×C20, C24.62D10
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, C4○D20, C2×C5⋊D4, C2×C10.D4, C20.48D4, C4×C5⋊D4, C23.23D10, C24⋊2D5, C24.62D10
►On 160 points
Generators in S160
(1 127)(2 128)(3 129)(4 130)(5 131)(6 132)(7 133)(8 134)(9 135)(10 136)(11 137)(12 138)(13 139)(14 140)(15 121)(16 122)(17 123)(18 124)(19 125)(20 126)(21 106)(22 107)(23 108)(24 109)(25 110)(26 111)(27 112)(28 113)(29 114)(30 115)(31 116)(32 117)(33 118)(34 119)(35 120)(36 101)(37 102)(38 103)(39 104)(40 105)(41 99)(42 100)(43 81)(44 82)(45 83)(46 84)(47 85)(48 86)(49 87)(50 88)(51 89)(52 90)(53 91)(54 92)(55 93)(56 94)(57 95)(58 96)(59 97)(60 98)(61 146)(62 147)(63 148)(64 149)(65 150)(66 151)(67 152)(68 153)(69 154)(70 155)(71 156)(72 157)(73 158)(74 159)(75 160)(76 141)(77 142)(78 143)(79 144)(80 145)
(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 87)(2 88)(3 89)(4 90)(5 91)(6 92)(7 93)(8 94)(9 95)(10 96)(11 97)(12 98)(13 99)(14 100)(15 81)(16 82)(17 83)(18 84)(19 85)(20 86)(21 77)(22 78)(23 79)(24 80)(25 61)(26 62)(27 63)(28 64)(29 65)(30 66)(31 67)(32 68)(33 69)(34 70)(35 71)(36 72)(37 73)(38 74)(39 75)(40 76)(41 139)(42 140)(43 121)(44 122)(45 123)(46 124)(47 125)(48 126)(49 127)(50 128)(51 129)(52 130)(53 131)(54 132)(55 133)(56 134)(57 135)(58 136)(59 137)(60 138)(101 157)(102 158)(103 159)(104 160)(105 141)(106 142)(107 143)(108 144)(109 145)(110 146)(111 147)(112 148)(113 149)(114 150)(115 151)(116 152)(117 153)(118 154)(119 155)(120 156)
(1 127)(2 128)(3 129)(4 130)(5 131)(6 132)(7 133)(8 134)(9 135)(10 136)(11 137)(12 138)(13 139)(14 140)(15 121)(16 122)(17 123)(18 124)(19 125)(20 126)(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 99)(42 100)(43 81)(44 82)(45 83)(46 84)(47 85)(48 86)(49 87)(50 88)(51 89)(52 90)(53 91)(54 92)(55 93)(56 94)(57 95)(58 96)(59 97)(60 98)(61 110)(62 111)(63 112)(64 113)(65 114)(66 115)(67 116)(68 117)(69 118)(70 119)(71 120)(72 101)(73 102)(74 103)(75 104)(76 105)(77 106)(78 107)(79 108)(80 109)
(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)
(1 150 11 160)(2 38 12 28)(3 148 13 158)(4 36 14 26)(5 146 15 156)(6 34 16 24)(7 144 17 154)(8 32 18 22)(9 142 19 152)(10 30 20 40)(21 125 31 135)(23 123 33 133)(25 121 35 131)(27 139 37 129)(29 137 39 127)(41 73 51 63)(42 111 52 101)(43 71 53 61)(44 109 54 119)(45 69 55 79)(46 107 56 117)(47 67 57 77)(48 105 58 115)(49 65 59 75)(50 103 60 113)(62 90 72 100)(64 88 74 98)(66 86 76 96)(68 84 78 94)(70 82 80 92)(81 120 91 110)(83 118 93 108)(85 116 95 106)(87 114 97 104)(89 112 99 102)(122 145 132 155)(124 143 134 153)(126 141 136 151)(128 159 138 149)(130 157 140 147)
G:=sub<Sym(160)| (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,113)(29,114)(30,115)(31,116)(32,117)(33,118)(34,119)(35,120)(36,101)(37,102)(38,103)(39,104)(40,105)(41,99)(42,100)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,95)(58,96)(59,97)(60,98)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,155)(71,156)(72,157)(73,158)(74,159)(75,160)(76,141)(77,142)(78,143)(79,144)(80,145), (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), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,81)(16,82)(17,83)(18,84)(19,85)(20,86)(21,77)(22,78)(23,79)(24,80)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72)(37,73)(38,74)(39,75)(40,76)(41,139)(42,140)(43,121)(44,122)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(55,133)(56,134)(57,135)(58,136)(59,137)(60,138)(101,157)(102,158)(103,159)(104,160)(105,141)(106,142)(107,143)(108,144)(109,145)(110,146)(111,147)(112,148)(113,149)(114,150)(115,151)(116,152)(117,153)(118,154)(119,155)(120,156), (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(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)(41,99)(42,100)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,95)(58,96)(59,97)(60,98)(61,110)(62,111)(63,112)(64,113)(65,114)(66,115)(67,116)(68,117)(69,118)(70,119)(71,120)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109), (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), (1,150,11,160)(2,38,12,28)(3,148,13,158)(4,36,14,26)(5,146,15,156)(6,34,16,24)(7,144,17,154)(8,32,18,22)(9,142,19,152)(10,30,20,40)(21,125,31,135)(23,123,33,133)(25,121,35,131)(27,139,37,129)(29,137,39,127)(41,73,51,63)(42,111,52,101)(43,71,53,61)(44,109,54,119)(45,69,55,79)(46,107,56,117)(47,67,57,77)(48,105,58,115)(49,65,59,75)(50,103,60,113)(62,90,72,100)(64,88,74,98)(66,86,76,96)(68,84,78,94)(70,82,80,92)(81,120,91,110)(83,118,93,108)(85,116,95,106)(87,114,97,104)(89,112,99,102)(122,145,132,155)(124,143,134,153)(126,141,136,151)(128,159,138,149)(130,157,140,147)>;
G:=Group( (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,113)(29,114)(30,115)(31,116)(32,117)(33,118)(34,119)(35,120)(36,101)(37,102)(38,103)(39,104)(40,105)(41,99)(42,100)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,95)(58,96)(59,97)(60,98)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,155)(71,156)(72,157)(73,158)(74,159)(75,160)(76,141)(77,142)(78,143)(79,144)(80,145), (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), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,81)(16,82)(17,83)(18,84)(19,85)(20,86)(21,77)(22,78)(23,79)(24,80)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72)(37,73)(38,74)(39,75)(40,76)(41,139)(42,140)(43,121)(44,122)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(55,133)(56,134)(57,135)(58,136)(59,137)(60,138)(101,157)(102,158)(103,159)(104,160)(105,141)(106,142)(107,143)(108,144)(109,145)(110,146)(111,147)(112,148)(113,149)(114,150)(115,151)(116,152)(117,153)(118,154)(119,155)(120,156), (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(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)(41,99)(42,100)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,95)(58,96)(59,97)(60,98)(61,110)(62,111)(63,112)(64,113)(65,114)(66,115)(67,116)(68,117)(69,118)(70,119)(71,120)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109), (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), (1,150,11,160)(2,38,12,28)(3,148,13,158)(4,36,14,26)(5,146,15,156)(6,34,16,24)(7,144,17,154)(8,32,18,22)(9,142,19,152)(10,30,20,40)(21,125,31,135)(23,123,33,133)(25,121,35,131)(27,139,37,129)(29,137,39,127)(41,73,51,63)(42,111,52,101)(43,71,53,61)(44,109,54,119)(45,69,55,79)(46,107,56,117)(47,67,57,77)(48,105,58,115)(49,65,59,75)(50,103,60,113)(62,90,72,100)(64,88,74,98)(66,86,76,96)(68,84,78,94)(70,82,80,92)(81,120,91,110)(83,118,93,108)(85,116,95,106)(87,114,97,104)(89,112,99,102)(122,145,132,155)(124,143,134,153)(126,141,136,151)(128,159,138,149)(130,157,140,147) );
G=PermutationGroup([[(1,127),(2,128),(3,129),(4,130),(5,131),(6,132),(7,133),(8,134),(9,135),(10,136),(11,137),(12,138),(13,139),(14,140),(15,121),(16,122),(17,123),(18,124),(19,125),(20,126),(21,106),(22,107),(23,108),(24,109),(25,110),(26,111),(27,112),(28,113),(29,114),(30,115),(31,116),(32,117),(33,118),(34,119),(35,120),(36,101),(37,102),(38,103),(39,104),(40,105),(41,99),(42,100),(43,81),(44,82),(45,83),(46,84),(47,85),(48,86),(49,87),(50,88),(51,89),(52,90),(53,91),(54,92),(55,93),(56,94),(57,95),(58,96),(59,97),(60,98),(61,146),(62,147),(63,148),(64,149),(65,150),(66,151),(67,152),(68,153),(69,154),(70,155),(71,156),(72,157),(73,158),(74,159),(75,160),(76,141),(77,142),(78,143),(79,144),(80,145)], [(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)], [(1,87),(2,88),(3,89),(4,90),(5,91),(6,92),(7,93),(8,94),(9,95),(10,96),(11,97),(12,98),(13,99),(14,100),(15,81),(16,82),(17,83),(18,84),(19,85),(20,86),(21,77),(22,78),(23,79),(24,80),(25,61),(26,62),(27,63),(28,64),(29,65),(30,66),(31,67),(32,68),(33,69),(34,70),(35,71),(36,72),(37,73),(38,74),(39,75),(40,76),(41,139),(42,140),(43,121),(44,122),(45,123),(46,124),(47,125),(48,126),(49,127),(50,128),(51,129),(52,130),(53,131),(54,132),(55,133),(56,134),(57,135),(58,136),(59,137),(60,138),(101,157),(102,158),(103,159),(104,160),(105,141),(106,142),(107,143),(108,144),(109,145),(110,146),(111,147),(112,148),(113,149),(114,150),(115,151),(116,152),(117,153),(118,154),(119,155),(120,156)], [(1,127),(2,128),(3,129),(4,130),(5,131),(6,132),(7,133),(8,134),(9,135),(10,136),(11,137),(12,138),(13,139),(14,140),(15,121),(16,122),(17,123),(18,124),(19,125),(20,126),(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),(41,99),(42,100),(43,81),(44,82),(45,83),(46,84),(47,85),(48,86),(49,87),(50,88),(51,89),(52,90),(53,91),(54,92),(55,93),(56,94),(57,95),(58,96),(59,97),(60,98),(61,110),(62,111),(63,112),(64,113),(65,114),(66,115),(67,116),(68,117),(69,118),(70,119),(71,120),(72,101),(73,102),(74,103),(75,104),(76,105),(77,106),(78,107),(79,108),(80,109)], [(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)], [(1,150,11,160),(2,38,12,28),(3,148,13,158),(4,36,14,26),(5,146,15,156),(6,34,16,24),(7,144,17,154),(8,32,18,22),(9,142,19,152),(10,30,20,40),(21,125,31,135),(23,123,33,133),(25,121,35,131),(27,139,37,129),(29,137,39,127),(41,73,51,63),(42,111,52,101),(43,71,53,61),(44,109,54,119),(45,69,55,79),(46,107,56,117),(47,67,57,77),(48,105,58,115),(49,65,59,75),(50,103,60,113),(62,90,72,100),(64,88,74,98),(66,86,76,96),(68,84,78,94),(70,82,80,92),(81,120,91,110),(83,118,93,108),(85,116,95,106),(87,114,97,104),(89,112,99,102),(122,145,132,155),(124,143,134,153),(126,141,136,151),(128,159,138,149),(130,157,140,147)]])
92 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | ··· | 4P | 5A | 5B | 10A | ··· | 10AD | 20A | ··· | 20AF |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | - | + | + | + | - | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D5 | C4○D4 | D10 | D10 | C5⋊D4 | Dic10 | C4×D5 | C5⋊D4 | C4○D20 |
| kernel | C24.62D10 | C10.10C42 | C2×C10.D4 | C2×C23.D5 | C23×C20 | C23.D5 | C2×C20 | C22×C10 | C22×C10 | C23×C4 | C2×C10 | C22×C4 | C24 | C2×C4 | C23 | C23 | C23 | C22 |
| # reps | 1 | 2 | 2 | 2 | 1 | 8 | 4 | 2 | 2 | 2 | 4 | 4 | 2 | 16 | 8 | 8 | 8 | 16 |
Matrix representation of C24.62D10 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 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 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 32 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 |
| 0 | 0 | 33 | 0 | 0 |
| 0 | 0 | 0 | 10 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 37 |
| 0 | 0 | 0 | 10 | 0 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[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],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[32,0,0,0,0,0,5,0,0,0,0,0,33,0,0,0,0,0,10,0,0,0,0,0,4],[32,0,0,0,0,0,0,5,0,0,0,8,0,0,0,0,0,0,0,10,0,0,0,37,0] >;
C24.62D10 in GAP, Magma, Sage, TeX
C_2^4._{62}D_{10} % in TeX
G:=Group("C2^4.62D10"); // GroupNames label
G:=SmallGroup(320,837);
// by ID
G=gap.SmallGroup(320,837);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,758,58,12550]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^10=f^2=b,a*b=b*a,f*a*f^-1=a*c=c*a,a*d=d*a,a*e=e*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=d*e^9>;
// generators/relations