metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.14D10, (C2×Dic5)⋊4D4, C10.39C22≀C2, (C22×D5).39D4, C22.241(D4×D5), (C22×C10).69D4, (C22×C4).34D10, C2.7(C23⋊D10), C10.32(C4⋊D4), C23.18(C5⋊D4), C5⋊2(C23.10D4), C2.33(D10⋊D4), C10.35(C4.4D4), C22.99(C4○D20), (C22×C20).27C22, (C23×C10).42C22, (C23×D5).15C22, C23.371(C22×D5), C10.10C42⋊17C2, C2.10(Dic5⋊D4), C22.97(D4⋊2D5), (C22×C10).333C23, C2.22(D10.12D4), C2.22(Dic5.5D4), C10.34(C22.D4), C2.7(C23.23D10), (C22×Dic5).45C22, (C2×C22⋊C4)⋊6D5, (C10×C22⋊C4)⋊4C2, (C2×C23.D5)⋊5C2, (C2×D10⋊C4)⋊7C2, (C2×C10).434(C2×D4), (C22×C5⋊D4).5C2, (C2×C10.D4)⋊12C2, C22.127(C2×C5⋊D4), (C2×C10).148(C4○D4), SmallGroup(320,586)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.14D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=c, f2=cb=bc, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=be9 >
Subgroups: 998 in 238 conjugacy classes, 61 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C5, C2×C4, D4, C23, C23, C23, D5, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, C24, Dic5, C20, D10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C22×D4, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C22×D5, C22×D5, C22×C10, C22×C10, C22×C10, C23.10D4, C10.D4, D10⋊C4, C23.D5, C5×C22⋊C4, C22×Dic5, C2×C5⋊D4, C22×C20, C23×D5, C23×C10, C10.10C42, C2×C10.D4, C2×D10⋊C4, C2×C23.D5, C10×C22⋊C4, C22×C5⋊D4, C24.14D10
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, D10, C22≀C2, C4⋊D4, C22.D4, C4.4D4, C5⋊D4, C22×D5, C23.10D4, C4○D20, D4×D5, D4⋊2D5, C2×C5⋊D4, D10.12D4, D10⋊D4, Dic5.5D4, C23.23D10, C23⋊D10, Dic5⋊D4, C24.14D10
►On 160 points
Generators in S160
(1 43)(2 105)(3 45)(4 107)(5 47)(6 109)(7 49)(8 111)(9 51)(10 113)(11 53)(12 115)(13 55)(14 117)(15 57)(16 119)(17 59)(18 101)(19 41)(20 103)(21 98)(22 154)(23 100)(24 156)(25 82)(26 158)(27 84)(28 160)(29 86)(30 142)(31 88)(32 144)(33 90)(34 146)(35 92)(36 148)(37 94)(38 150)(39 96)(40 152)(42 124)(44 126)(46 128)(48 130)(50 132)(52 134)(54 136)(56 138)(58 140)(60 122)(61 85)(62 141)(63 87)(64 143)(65 89)(66 145)(67 91)(68 147)(69 93)(70 149)(71 95)(72 151)(73 97)(74 153)(75 99)(76 155)(77 81)(78 157)(79 83)(80 159)(102 123)(104 125)(106 127)(108 129)(110 131)(112 133)(114 135)(116 137)(118 139)(120 121)
(1 78)(2 79)(3 80)(4 61)(5 62)(6 63)(7 64)(8 65)(9 66)(10 67)(11 68)(12 69)(13 70)(14 71)(15 72)(16 73)(17 74)(18 75)(19 76)(20 77)(21 121)(22 122)(23 123)(24 124)(25 125)(26 126)(27 127)(28 128)(29 129)(30 130)(31 131)(32 132)(33 133)(34 134)(35 135)(36 136)(37 137)(38 138)(39 139)(40 140)(41 155)(42 156)(43 157)(44 158)(45 159)(46 160)(47 141)(48 142)(49 143)(50 144)(51 145)(52 146)(53 147)(54 148)(55 149)(56 150)(57 151)(58 152)(59 153)(60 154)(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)
(1 125)(2 126)(3 127)(4 128)(5 129)(6 130)(7 131)(8 132)(9 133)(10 134)(11 135)(12 136)(13 137)(14 138)(15 139)(16 140)(17 121)(18 122)(19 123)(20 124)(21 74)(22 75)(23 76)(24 77)(25 78)(26 79)(27 80)(28 61)(29 62)(30 63)(31 64)(32 65)(33 66)(34 67)(35 68)(36 69)(37 70)(38 71)(39 72)(40 73)(41 102)(42 103)(43 104)(44 105)(45 106)(46 107)(47 108)(48 109)(49 110)(50 111)(51 112)(52 113)(53 114)(54 115)(55 116)(56 117)(57 118)(58 119)(59 120)(60 101)(81 156)(82 157)(83 158)(84 159)(85 160)(86 141)(87 142)(88 143)(89 144)(90 145)(91 146)(92 147)(93 148)(94 149)(95 150)(96 151)(97 152)(98 153)(99 154)(100 155)
(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 10 68 77)(2 76 69 9)(3 8 70 75)(4 74 71 7)(5 6 72 73)(11 20 78 67)(12 66 79 19)(13 18 80 65)(14 64 61 17)(15 16 62 63)(21 38 131 128)(22 127 132 37)(23 36 133 126)(24 125 134 35)(25 34 135 124)(26 123 136 33)(27 32 137 122)(28 121 138 31)(29 30 139 140)(39 40 129 130)(41 44 145 148)(42 147 146 43)(45 60 149 144)(46 143 150 59)(47 58 151 142)(48 141 152 57)(49 56 153 160)(50 159 154 55)(51 54 155 158)(52 157 156 53)(81 114 113 82)(83 112 115 100)(84 99 116 111)(85 110 117 98)(86 97 118 109)(87 108 119 96)(88 95 120 107)(89 106 101 94)(90 93 102 105)(91 104 103 92)
G:=sub<Sym(160)| (1,43)(2,105)(3,45)(4,107)(5,47)(6,109)(7,49)(8,111)(9,51)(10,113)(11,53)(12,115)(13,55)(14,117)(15,57)(16,119)(17,59)(18,101)(19,41)(20,103)(21,98)(22,154)(23,100)(24,156)(25,82)(26,158)(27,84)(28,160)(29,86)(30,142)(31,88)(32,144)(33,90)(34,146)(35,92)(36,148)(37,94)(38,150)(39,96)(40,152)(42,124)(44,126)(46,128)(48,130)(50,132)(52,134)(54,136)(56,138)(58,140)(60,122)(61,85)(62,141)(63,87)(64,143)(65,89)(66,145)(67,91)(68,147)(69,93)(70,149)(71,95)(72,151)(73,97)(74,153)(75,99)(76,155)(77,81)(78,157)(79,83)(80,159)(102,123)(104,125)(106,127)(108,129)(110,131)(112,133)(114,135)(116,137)(118,139)(120,121), (1,78)(2,79)(3,80)(4,61)(5,62)(6,63)(7,64)(8,65)(9,66)(10,67)(11,68)(12,69)(13,70)(14,71)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,121)(22,122)(23,123)(24,124)(25,125)(26,126)(27,127)(28,128)(29,129)(30,130)(31,131)(32,132)(33,133)(34,134)(35,135)(36,136)(37,137)(38,138)(39,139)(40,140)(41,155)(42,156)(43,157)(44,158)(45,159)(46,160)(47,141)(48,142)(49,143)(50,144)(51,145)(52,146)(53,147)(54,148)(55,149)(56,150)(57,151)(58,152)(59,153)(60,154)(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), (1,125)(2,126)(3,127)(4,128)(5,129)(6,130)(7,131)(8,132)(9,133)(10,134)(11,135)(12,136)(13,137)(14,138)(15,139)(16,140)(17,121)(18,122)(19,123)(20,124)(21,74)(22,75)(23,76)(24,77)(25,78)(26,79)(27,80)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,102)(42,103)(43,104)(44,105)(45,106)(46,107)(47,108)(48,109)(49,110)(50,111)(51,112)(52,113)(53,114)(54,115)(55,116)(56,117)(57,118)(58,119)(59,120)(60,101)(81,156)(82,157)(83,158)(84,159)(85,160)(86,141)(87,142)(88,143)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,152)(98,153)(99,154)(100,155), (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), (1,10,68,77)(2,76,69,9)(3,8,70,75)(4,74,71,7)(5,6,72,73)(11,20,78,67)(12,66,79,19)(13,18,80,65)(14,64,61,17)(15,16,62,63)(21,38,131,128)(22,127,132,37)(23,36,133,126)(24,125,134,35)(25,34,135,124)(26,123,136,33)(27,32,137,122)(28,121,138,31)(29,30,139,140)(39,40,129,130)(41,44,145,148)(42,147,146,43)(45,60,149,144)(46,143,150,59)(47,58,151,142)(48,141,152,57)(49,56,153,160)(50,159,154,55)(51,54,155,158)(52,157,156,53)(81,114,113,82)(83,112,115,100)(84,99,116,111)(85,110,117,98)(86,97,118,109)(87,108,119,96)(88,95,120,107)(89,106,101,94)(90,93,102,105)(91,104,103,92)>;
G:=Group( (1,43)(2,105)(3,45)(4,107)(5,47)(6,109)(7,49)(8,111)(9,51)(10,113)(11,53)(12,115)(13,55)(14,117)(15,57)(16,119)(17,59)(18,101)(19,41)(20,103)(21,98)(22,154)(23,100)(24,156)(25,82)(26,158)(27,84)(28,160)(29,86)(30,142)(31,88)(32,144)(33,90)(34,146)(35,92)(36,148)(37,94)(38,150)(39,96)(40,152)(42,124)(44,126)(46,128)(48,130)(50,132)(52,134)(54,136)(56,138)(58,140)(60,122)(61,85)(62,141)(63,87)(64,143)(65,89)(66,145)(67,91)(68,147)(69,93)(70,149)(71,95)(72,151)(73,97)(74,153)(75,99)(76,155)(77,81)(78,157)(79,83)(80,159)(102,123)(104,125)(106,127)(108,129)(110,131)(112,133)(114,135)(116,137)(118,139)(120,121), (1,78)(2,79)(3,80)(4,61)(5,62)(6,63)(7,64)(8,65)(9,66)(10,67)(11,68)(12,69)(13,70)(14,71)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,121)(22,122)(23,123)(24,124)(25,125)(26,126)(27,127)(28,128)(29,129)(30,130)(31,131)(32,132)(33,133)(34,134)(35,135)(36,136)(37,137)(38,138)(39,139)(40,140)(41,155)(42,156)(43,157)(44,158)(45,159)(46,160)(47,141)(48,142)(49,143)(50,144)(51,145)(52,146)(53,147)(54,148)(55,149)(56,150)(57,151)(58,152)(59,153)(60,154)(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), (1,125)(2,126)(3,127)(4,128)(5,129)(6,130)(7,131)(8,132)(9,133)(10,134)(11,135)(12,136)(13,137)(14,138)(15,139)(16,140)(17,121)(18,122)(19,123)(20,124)(21,74)(22,75)(23,76)(24,77)(25,78)(26,79)(27,80)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,102)(42,103)(43,104)(44,105)(45,106)(46,107)(47,108)(48,109)(49,110)(50,111)(51,112)(52,113)(53,114)(54,115)(55,116)(56,117)(57,118)(58,119)(59,120)(60,101)(81,156)(82,157)(83,158)(84,159)(85,160)(86,141)(87,142)(88,143)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,152)(98,153)(99,154)(100,155), (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), (1,10,68,77)(2,76,69,9)(3,8,70,75)(4,74,71,7)(5,6,72,73)(11,20,78,67)(12,66,79,19)(13,18,80,65)(14,64,61,17)(15,16,62,63)(21,38,131,128)(22,127,132,37)(23,36,133,126)(24,125,134,35)(25,34,135,124)(26,123,136,33)(27,32,137,122)(28,121,138,31)(29,30,139,140)(39,40,129,130)(41,44,145,148)(42,147,146,43)(45,60,149,144)(46,143,150,59)(47,58,151,142)(48,141,152,57)(49,56,153,160)(50,159,154,55)(51,54,155,158)(52,157,156,53)(81,114,113,82)(83,112,115,100)(84,99,116,111)(85,110,117,98)(86,97,118,109)(87,108,119,96)(88,95,120,107)(89,106,101,94)(90,93,102,105)(91,104,103,92) );
G=PermutationGroup([[(1,43),(2,105),(3,45),(4,107),(5,47),(6,109),(7,49),(8,111),(9,51),(10,113),(11,53),(12,115),(13,55),(14,117),(15,57),(16,119),(17,59),(18,101),(19,41),(20,103),(21,98),(22,154),(23,100),(24,156),(25,82),(26,158),(27,84),(28,160),(29,86),(30,142),(31,88),(32,144),(33,90),(34,146),(35,92),(36,148),(37,94),(38,150),(39,96),(40,152),(42,124),(44,126),(46,128),(48,130),(50,132),(52,134),(54,136),(56,138),(58,140),(60,122),(61,85),(62,141),(63,87),(64,143),(65,89),(66,145),(67,91),(68,147),(69,93),(70,149),(71,95),(72,151),(73,97),(74,153),(75,99),(76,155),(77,81),(78,157),(79,83),(80,159),(102,123),(104,125),(106,127),(108,129),(110,131),(112,133),(114,135),(116,137),(118,139),(120,121)], [(1,78),(2,79),(3,80),(4,61),(5,62),(6,63),(7,64),(8,65),(9,66),(10,67),(11,68),(12,69),(13,70),(14,71),(15,72),(16,73),(17,74),(18,75),(19,76),(20,77),(21,121),(22,122),(23,123),(24,124),(25,125),(26,126),(27,127),(28,128),(29,129),(30,130),(31,131),(32,132),(33,133),(34,134),(35,135),(36,136),(37,137),(38,138),(39,139),(40,140),(41,155),(42,156),(43,157),(44,158),(45,159),(46,160),(47,141),(48,142),(49,143),(50,144),(51,145),(52,146),(53,147),(54,148),(55,149),(56,150),(57,151),(58,152),(59,153),(60,154),(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)], [(1,125),(2,126),(3,127),(4,128),(5,129),(6,130),(7,131),(8,132),(9,133),(10,134),(11,135),(12,136),(13,137),(14,138),(15,139),(16,140),(17,121),(18,122),(19,123),(20,124),(21,74),(22,75),(23,76),(24,77),(25,78),(26,79),(27,80),(28,61),(29,62),(30,63),(31,64),(32,65),(33,66),(34,67),(35,68),(36,69),(37,70),(38,71),(39,72),(40,73),(41,102),(42,103),(43,104),(44,105),(45,106),(46,107),(47,108),(48,109),(49,110),(50,111),(51,112),(52,113),(53,114),(54,115),(55,116),(56,117),(57,118),(58,119),(59,120),(60,101),(81,156),(82,157),(83,158),(84,159),(85,160),(86,141),(87,142),(88,143),(89,144),(90,145),(91,146),(92,147),(93,148),(94,149),(95,150),(96,151),(97,152),(98,153),(99,154),(100,155)], [(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)], [(1,10,68,77),(2,76,69,9),(3,8,70,75),(4,74,71,7),(5,6,72,73),(11,20,78,67),(12,66,79,19),(13,18,80,65),(14,64,61,17),(15,16,62,63),(21,38,131,128),(22,127,132,37),(23,36,133,126),(24,125,134,35),(25,34,135,124),(26,123,136,33),(27,32,137,122),(28,121,138,31),(29,30,139,140),(39,40,129,130),(41,44,145,148),(42,147,146,43),(45,60,149,144),(46,143,150,59),(47,58,151,142),(48,141,152,57),(49,56,153,160),(50,159,154,55),(51,54,155,158),(52,157,156,53),(81,114,113,82),(83,112,115,100),(84,99,116,111),(85,110,117,98),(86,97,118,109),(87,108,119,96),(88,95,120,107),(89,106,101,94),(90,93,102,105),(91,104,103,92)]])
62 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | ··· | 4J | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10V | 20A | ··· | 20P |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 20 | 20 | 4 | 4 | 4 | 4 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | C4○D4 | D10 | D10 | C5⋊D4 | C4○D20 | D4×D5 | D4⋊2D5 |
| kernel | C24.14D10 | C10.10C42 | C2×C10.D4 | C2×D10⋊C4 | C2×C23.D5 | C10×C22⋊C4 | C22×C5⋊D4 | C2×Dic5 | C22×D5 | C22×C10 | C2×C22⋊C4 | C2×C10 | C22×C4 | C24 | C23 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 6 | 4 | 2 | 8 | 16 | 6 | 2 |
Matrix representation of C24.14D10 ►in GL6(𝔽41)
| 23 | 6 | 0 | 0 | 0 | 0 |
| 35 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 21 |
| 0 | 0 | 0 | 0 | 4 | 9 |
| 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 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 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 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 25 | 16 | 0 | 0 | 0 | 0 |
| 25 | 39 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 21 | 0 | 0 |
| 0 | 0 | 20 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 21 |
| 0 | 0 | 0 | 0 | 0 | 9 |
| 16 | 25 | 0 | 0 | 0 | 0 |
| 39 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 21 | 0 | 0 |
| 0 | 0 | 18 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 20 |
| 0 | 0 | 0 | 0 | 37 | 32 |
G:=sub<GL(6,GF(41))| [23,35,0,0,0,0,6,18,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,32,4,0,0,0,0,21,9],[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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[25,25,0,0,0,0,16,39,0,0,0,0,0,0,20,20,0,0,0,0,21,23,0,0,0,0,0,0,32,0,0,0,0,0,21,9],[16,39,0,0,0,0,25,25,0,0,0,0,0,0,20,18,0,0,0,0,21,21,0,0,0,0,0,0,9,37,0,0,0,0,20,32] >;
C24.14D10 in GAP, Magma, Sage, TeX
C_2^4._{14}D_{10} % in TeX
G:=Group("C2^4.14D10"); // GroupNames label
G:=SmallGroup(320,586);
// by ID
G=gap.SmallGroup(320,586);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,254,387,100,12550]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^10=c,f^2=c*b=b*c,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*c*d,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