metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.20D10, (C2×Dic5)⋊6D4, (C2×C20).302D4, (C22×D4).8D5, C10.73C22≀C2, C22.283(D4×D5), C2.25(C20⋊2D4), (C22×C10).110D4, (C22×C4).152D10, C2.6(C24⋊2D5), C5⋊5(C23.10D4), C23.30(C5⋊D4), C10.130(C4⋊D4), C10.48(C4.4D4), (C23×C10).48C22, C23.384(C22×D5), C10.10C42⋊45C2, C2.34(Dic5⋊D4), C2.14(C20.17D4), (C22×C20).395C22, (C22×C10).367C23, C22.106(D4⋊2D5), C10.84(C22.D4), (C22×Dic5).68C22, C2.17(C23.18D10), (D4×C2×C10).12C2, (C2×C10).556(C2×D4), (C2×C4).85(C5⋊D4), (C2×C23.D5)⋊11C2, (C2×C10.D4)⋊43C2, C22.218(C2×C5⋊D4), (C2×C10).163(C4○D4), SmallGroup(320,849)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.20D10
G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=dc=cd, ab=ba, ac=ca, eae-1=ad=da, faf-1=abd, bc=cb, bd=db, be=eb, bf=fb, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce-1 >
Subgroups: 742 in 238 conjugacy classes, 65 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, C10, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic5, C20, C2×C10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C22×D4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C22×C10, C23.10D4, C10.D4, C23.D5, C22×Dic5, C22×Dic5, C22×C20, D4×C10, C23×C10, C10.10C42, C2×C10.D4, C2×C23.D5, D4×C2×C10, C24.20D10
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, D4×D5, D4⋊2D5, C2×C5⋊D4, C23.18D10, C20.17D4, C20⋊2D4, Dic5⋊D4, C24⋊2D5, C24.20D10
►On 160 points
Generators in S160
(2 64)(4 66)(6 68)(8 70)(10 62)(12 74)(14 76)(16 78)(18 80)(20 72)(21 33)(23 35)(25 37)(27 39)(29 31)(41 136)(42 107)(43 138)(44 109)(45 140)(46 101)(47 132)(48 103)(49 134)(50 105)(52 98)(54 100)(56 92)(58 94)(60 96)(81 119)(82 144)(83 111)(84 146)(85 113)(86 148)(87 115)(88 150)(89 117)(90 142)(102 125)(104 127)(106 129)(108 121)(110 123)(112 156)(114 158)(116 160)(118 152)(120 154)(122 139)(124 131)(126 133)(128 135)(130 137)(141 151)(143 153)(145 155)(147 157)(149 159)
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 58)(22 59)(23 60)(24 51)(25 52)(26 53)(27 54)(28 55)(29 56)(30 57)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 91)(41 106)(42 107)(43 108)(44 109)(45 110)(46 101)(47 102)(48 103)(49 104)(50 105)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(81 119)(82 120)(83 111)(84 112)(85 113)(86 114)(87 115)(88 116)(89 117)(90 118)(121 138)(122 139)(123 140)(124 131)(125 132)(126 133)(127 134)(128 135)(129 136)(130 137)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)
(1 28)(2 29)(3 30)(4 21)(5 22)(6 23)(7 24)(8 25)(9 26)(10 27)(11 55)(12 56)(13 57)(14 58)(15 59)(16 60)(17 51)(18 52)(19 53)(20 54)(31 64)(32 65)(33 66)(34 67)(35 68)(36 69)(37 70)(38 61)(39 62)(40 63)(41 158)(42 159)(43 160)(44 151)(45 152)(46 153)(47 154)(48 155)(49 156)(50 157)(71 99)(72 100)(73 91)(74 92)(75 93)(76 94)(77 95)(78 96)(79 97)(80 98)(81 124)(82 125)(83 126)(84 127)(85 128)(86 129)(87 130)(88 121)(89 122)(90 123)(101 143)(102 144)(103 145)(104 146)(105 147)(106 148)(107 149)(108 150)(109 141)(110 142)(111 133)(112 134)(113 135)(114 136)(115 137)(116 138)(117 139)(118 140)(119 131)(120 132)
(1 63)(2 64)(3 65)(4 66)(5 67)(6 68)(7 69)(8 70)(9 61)(10 62)(11 73)(12 74)(13 75)(14 76)(15 77)(16 78)(17 79)(18 80)(19 71)(20 72)(21 33)(22 34)(23 35)(24 36)(25 37)(26 38)(27 39)(28 40)(29 31)(30 32)(41 129)(42 130)(43 121)(44 122)(45 123)(46 124)(47 125)(48 126)(49 127)(50 128)(51 97)(52 98)(53 99)(54 100)(55 91)(56 92)(57 93)(58 94)(59 95)(60 96)(81 153)(82 154)(83 155)(84 156)(85 157)(86 158)(87 159)(88 160)(89 151)(90 152)(101 131)(102 132)(103 133)(104 134)(105 135)(106 136)(107 137)(108 138)(109 139)(110 140)(111 145)(112 146)(113 147)(114 148)(115 149)(116 150)(117 141)(118 142)(119 143)(120 144)
(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)
(1 104 40 112)(2 145 31 133)(3 102 32 120)(4 143 33 131)(5 110 34 118)(6 141 35 139)(7 108 36 116)(8 149 37 137)(9 106 38 114)(10 147 39 135)(11 49 91 84)(12 155 92 126)(13 47 93 82)(14 153 94 124)(15 45 95 90)(16 151 96 122)(17 43 97 88)(18 159 98 130)(19 41 99 86)(20 157 100 128)(21 101 66 119)(22 142 67 140)(23 109 68 117)(24 150 69 138)(25 107 70 115)(26 148 61 136)(27 105 62 113)(28 146 63 134)(29 103 64 111)(30 144 65 132)(42 80 87 52)(44 78 89 60)(46 76 81 58)(48 74 83 56)(50 72 85 54)(51 160 79 121)(53 158 71 129)(55 156 73 127)(57 154 75 125)(59 152 77 123)
G:=sub<Sym(160)| (2,64)(4,66)(6,68)(8,70)(10,62)(12,74)(14,76)(16,78)(18,80)(20,72)(21,33)(23,35)(25,37)(27,39)(29,31)(41,136)(42,107)(43,138)(44,109)(45,140)(46,101)(47,132)(48,103)(49,134)(50,105)(52,98)(54,100)(56,92)(58,94)(60,96)(81,119)(82,144)(83,111)(84,146)(85,113)(86,148)(87,115)(88,150)(89,117)(90,142)(102,125)(104,127)(106,129)(108,121)(110,123)(112,156)(114,158)(116,160)(118,152)(120,154)(122,139)(124,131)(126,133)(128,135)(130,137)(141,151)(143,153)(145,155)(147,157)(149,159), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,58)(22,59)(23,60)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(30,57)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,91)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,119)(82,120)(83,111)(84,112)(85,113)(86,114)(87,115)(88,116)(89,117)(90,118)(121,138)(122,139)(123,140)(124,131)(125,132)(126,133)(127,134)(128,135)(129,136)(130,137)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,28)(2,29)(3,30)(4,21)(5,22)(6,23)(7,24)(8,25)(9,26)(10,27)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,51)(18,52)(19,53)(20,54)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,61)(39,62)(40,63)(41,158)(42,159)(43,160)(44,151)(45,152)(46,153)(47,154)(48,155)(49,156)(50,157)(71,99)(72,100)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,124)(82,125)(83,126)(84,127)(85,128)(86,129)(87,130)(88,121)(89,122)(90,123)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,141)(110,142)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,131)(120,132), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,73)(12,74)(13,75)(14,76)(15,77)(16,78)(17,79)(18,80)(19,71)(20,72)(21,33)(22,34)(23,35)(24,36)(25,37)(26,38)(27,39)(28,40)(29,31)(30,32)(41,129)(42,130)(43,121)(44,122)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,97)(52,98)(53,99)(54,100)(55,91)(56,92)(57,93)(58,94)(59,95)(60,96)(81,153)(82,154)(83,155)(84,156)(85,157)(86,158)(87,159)(88,160)(89,151)(90,152)(101,131)(102,132)(103,133)(104,134)(105,135)(106,136)(107,137)(108,138)(109,139)(110,140)(111,145)(112,146)(113,147)(114,148)(115,149)(116,150)(117,141)(118,142)(119,143)(120,144), (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), (1,104,40,112)(2,145,31,133)(3,102,32,120)(4,143,33,131)(5,110,34,118)(6,141,35,139)(7,108,36,116)(8,149,37,137)(9,106,38,114)(10,147,39,135)(11,49,91,84)(12,155,92,126)(13,47,93,82)(14,153,94,124)(15,45,95,90)(16,151,96,122)(17,43,97,88)(18,159,98,130)(19,41,99,86)(20,157,100,128)(21,101,66,119)(22,142,67,140)(23,109,68,117)(24,150,69,138)(25,107,70,115)(26,148,61,136)(27,105,62,113)(28,146,63,134)(29,103,64,111)(30,144,65,132)(42,80,87,52)(44,78,89,60)(46,76,81,58)(48,74,83,56)(50,72,85,54)(51,160,79,121)(53,158,71,129)(55,156,73,127)(57,154,75,125)(59,152,77,123)>;
G:=Group( (2,64)(4,66)(6,68)(8,70)(10,62)(12,74)(14,76)(16,78)(18,80)(20,72)(21,33)(23,35)(25,37)(27,39)(29,31)(41,136)(42,107)(43,138)(44,109)(45,140)(46,101)(47,132)(48,103)(49,134)(50,105)(52,98)(54,100)(56,92)(58,94)(60,96)(81,119)(82,144)(83,111)(84,146)(85,113)(86,148)(87,115)(88,150)(89,117)(90,142)(102,125)(104,127)(106,129)(108,121)(110,123)(112,156)(114,158)(116,160)(118,152)(120,154)(122,139)(124,131)(126,133)(128,135)(130,137)(141,151)(143,153)(145,155)(147,157)(149,159), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,58)(22,59)(23,60)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(30,57)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,91)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,119)(82,120)(83,111)(84,112)(85,113)(86,114)(87,115)(88,116)(89,117)(90,118)(121,138)(122,139)(123,140)(124,131)(125,132)(126,133)(127,134)(128,135)(129,136)(130,137)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,28)(2,29)(3,30)(4,21)(5,22)(6,23)(7,24)(8,25)(9,26)(10,27)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,51)(18,52)(19,53)(20,54)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,61)(39,62)(40,63)(41,158)(42,159)(43,160)(44,151)(45,152)(46,153)(47,154)(48,155)(49,156)(50,157)(71,99)(72,100)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,124)(82,125)(83,126)(84,127)(85,128)(86,129)(87,130)(88,121)(89,122)(90,123)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,141)(110,142)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,131)(120,132), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,73)(12,74)(13,75)(14,76)(15,77)(16,78)(17,79)(18,80)(19,71)(20,72)(21,33)(22,34)(23,35)(24,36)(25,37)(26,38)(27,39)(28,40)(29,31)(30,32)(41,129)(42,130)(43,121)(44,122)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,97)(52,98)(53,99)(54,100)(55,91)(56,92)(57,93)(58,94)(59,95)(60,96)(81,153)(82,154)(83,155)(84,156)(85,157)(86,158)(87,159)(88,160)(89,151)(90,152)(101,131)(102,132)(103,133)(104,134)(105,135)(106,136)(107,137)(108,138)(109,139)(110,140)(111,145)(112,146)(113,147)(114,148)(115,149)(116,150)(117,141)(118,142)(119,143)(120,144), (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), (1,104,40,112)(2,145,31,133)(3,102,32,120)(4,143,33,131)(5,110,34,118)(6,141,35,139)(7,108,36,116)(8,149,37,137)(9,106,38,114)(10,147,39,135)(11,49,91,84)(12,155,92,126)(13,47,93,82)(14,153,94,124)(15,45,95,90)(16,151,96,122)(17,43,97,88)(18,159,98,130)(19,41,99,86)(20,157,100,128)(21,101,66,119)(22,142,67,140)(23,109,68,117)(24,150,69,138)(25,107,70,115)(26,148,61,136)(27,105,62,113)(28,146,63,134)(29,103,64,111)(30,144,65,132)(42,80,87,52)(44,78,89,60)(46,76,81,58)(48,74,83,56)(50,72,85,54)(51,160,79,121)(53,158,71,129)(55,156,73,127)(57,154,75,125)(59,152,77,123) );
G=PermutationGroup([[(2,64),(4,66),(6,68),(8,70),(10,62),(12,74),(14,76),(16,78),(18,80),(20,72),(21,33),(23,35),(25,37),(27,39),(29,31),(41,136),(42,107),(43,138),(44,109),(45,140),(46,101),(47,132),(48,103),(49,134),(50,105),(52,98),(54,100),(56,92),(58,94),(60,96),(81,119),(82,144),(83,111),(84,146),(85,113),(86,148),(87,115),(88,150),(89,117),(90,142),(102,125),(104,127),(106,129),(108,121),(110,123),(112,156),(114,158),(116,160),(118,152),(120,154),(122,139),(124,131),(126,133),(128,135),(130,137),(141,151),(143,153),(145,155),(147,157),(149,159)], [(1,11),(2,12),(3,13),(4,14),(5,15),(6,16),(7,17),(8,18),(9,19),(10,20),(21,58),(22,59),(23,60),(24,51),(25,52),(26,53),(27,54),(28,55),(29,56),(30,57),(31,92),(32,93),(33,94),(34,95),(35,96),(36,97),(37,98),(38,99),(39,100),(40,91),(41,106),(42,107),(43,108),(44,109),(45,110),(46,101),(47,102),(48,103),(49,104),(50,105),(61,71),(62,72),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(81,119),(82,120),(83,111),(84,112),(85,113),(86,114),(87,115),(88,116),(89,117),(90,118),(121,138),(122,139),(123,140),(124,131),(125,132),(126,133),(127,134),(128,135),(129,136),(130,137),(141,151),(142,152),(143,153),(144,154),(145,155),(146,156),(147,157),(148,158),(149,159),(150,160)], [(1,28),(2,29),(3,30),(4,21),(5,22),(6,23),(7,24),(8,25),(9,26),(10,27),(11,55),(12,56),(13,57),(14,58),(15,59),(16,60),(17,51),(18,52),(19,53),(20,54),(31,64),(32,65),(33,66),(34,67),(35,68),(36,69),(37,70),(38,61),(39,62),(40,63),(41,158),(42,159),(43,160),(44,151),(45,152),(46,153),(47,154),(48,155),(49,156),(50,157),(71,99),(72,100),(73,91),(74,92),(75,93),(76,94),(77,95),(78,96),(79,97),(80,98),(81,124),(82,125),(83,126),(84,127),(85,128),(86,129),(87,130),(88,121),(89,122),(90,123),(101,143),(102,144),(103,145),(104,146),(105,147),(106,148),(107,149),(108,150),(109,141),(110,142),(111,133),(112,134),(113,135),(114,136),(115,137),(116,138),(117,139),(118,140),(119,131),(120,132)], [(1,63),(2,64),(3,65),(4,66),(5,67),(6,68),(7,69),(8,70),(9,61),(10,62),(11,73),(12,74),(13,75),(14,76),(15,77),(16,78),(17,79),(18,80),(19,71),(20,72),(21,33),(22,34),(23,35),(24,36),(25,37),(26,38),(27,39),(28,40),(29,31),(30,32),(41,129),(42,130),(43,121),(44,122),(45,123),(46,124),(47,125),(48,126),(49,127),(50,128),(51,97),(52,98),(53,99),(54,100),(55,91),(56,92),(57,93),(58,94),(59,95),(60,96),(81,153),(82,154),(83,155),(84,156),(85,157),(86,158),(87,159),(88,160),(89,151),(90,152),(101,131),(102,132),(103,133),(104,134),(105,135),(106,136),(107,137),(108,138),(109,139),(110,140),(111,145),(112,146),(113,147),(114,148),(115,149),(116,150),(117,141),(118,142),(119,143),(120,144)], [(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)], [(1,104,40,112),(2,145,31,133),(3,102,32,120),(4,143,33,131),(5,110,34,118),(6,141,35,139),(7,108,36,116),(8,149,37,137),(9,106,38,114),(10,147,39,135),(11,49,91,84),(12,155,92,126),(13,47,93,82),(14,153,94,124),(15,45,95,90),(16,151,96,122),(17,43,97,88),(18,159,98,130),(19,41,99,86),(20,157,100,128),(21,101,66,119),(22,142,67,140),(23,109,68,117),(24,150,69,138),(25,107,70,115),(26,148,61,136),(27,105,62,113),(28,146,63,134),(29,103,64,111),(30,144,65,132),(42,80,87,52),(44,78,89,60),(46,76,81,58),(48,74,83,56),(50,72,85,54),(51,160,79,121),(53,158,71,129),(55,156,73,127),(57,154,75,125),(59,152,77,123)]])
62 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | ··· | 4J | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | C4○D4 | D10 | D10 | C5⋊D4 | C5⋊D4 | D4×D5 | D4⋊2D5 |
| kernel | C24.20D10 | C10.10C42 | C2×C10.D4 | C2×C23.D5 | D4×C2×C10 | C2×Dic5 | C2×C20 | C22×C10 | C22×D4 | C2×C10 | C22×C4 | C24 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 1 | 1 | 4 | 1 | 2 | 2 | 4 | 2 | 6 | 2 | 4 | 8 | 16 | 2 | 6 |
Matrix representation of C24.20D10 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 23 | 40 |
| 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 |
| 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 |
| 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 37 | 0 |
| 0 | 0 | 0 | 0 | 28 | 31 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 21 |
| 0 | 0 | 0 | 0 | 19 | 16 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,23,0,0,0,0,0,40],[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],[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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,37,28,0,0,0,0,0,31],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,25,19,0,0,0,0,21,16] >;
C24.20D10 in GAP, Magma, Sage, TeX
C_2^4._{20}D_{10} % in TeX
G:=Group("C2^4.20D10"); // GroupNames label
G:=SmallGroup(320,849);
// by ID
G=gap.SmallGroup(320,849);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,254,387,12550]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^10=1,f^2=d*c=c*d,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*b*d,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=c*e^-1>;
// generators/relations