direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C4○D20, C10.4C25, D20⋊14C23, C20.77C24, D10.1C24, C24.73D10, Dic5.2C24, Dic10⋊13C23, (C23×C4)⋊8D5, (C4×D5)⋊8C23, C5⋊D4⋊7C23, C2.5(D5×C24), (C23×C20)⋊11C2, (C2×C20)⋊15C23, (C22×C4)⋊46D10, C4.76(C23×D5), (C22×D20)⋊25C2, (C2×D20)⋊66C22, C22.7(C23×D5), (C2×C10).326C24, (C22×C20)⋊62C22, (C22×Dic10)⋊26C2, (C2×Dic10)⋊77C22, C23.347(C22×D5), (C22×C10).433C23, (C23×C10).116C22, (C2×Dic5).306C23, (C22×D5).255C23, (C23×D5).128C22, (C22×Dic5).262C22, C10⋊1(C2×C4○D4), C5⋊1(C22×C4○D4), (C2×C4×D5)⋊72C22, (D5×C22×C4)⋊26C2, (C2×C4)⋊12(C22×D5), (C2×C10)⋊13(C4○D4), (C22×C5⋊D4)⋊22C2, (C2×C5⋊D4)⋊56C22, SmallGroup(320,1611)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 2558 in 890 conjugacy classes, 463 normal (17 characteristic)
C1, C2, C2 [×6], C2 [×12], C4 [×8], C4 [×8], C22 [×11], C22 [×44], C5, C2×C4 [×28], C2×C4 [×44], D4 [×48], Q8 [×16], C23, C23 [×6], C23 [×24], D5 [×8], C10, C10 [×6], C10 [×4], C22×C4 [×2], C22×C4 [×12], C22×C4 [×26], C2×D4 [×36], C2×Q8 [×12], C4○D4 [×64], C24, C24 [×2], Dic5 [×8], C20 [×8], D10 [×8], D10 [×24], C2×C10 [×11], C2×C10 [×12], C23×C4, C23×C4 [×2], C22×D4 [×3], C22×Q8, C2×C4○D4 [×24], Dic10 [×16], C4×D5 [×32], D20 [×16], C2×Dic5 [×12], C5⋊D4 [×32], C2×C20 [×28], C22×D5 [×12], C22×D5 [×8], C22×C10, C22×C10 [×6], C22×C10 [×4], C22×C4○D4, C2×Dic10 [×12], C2×C4×D5 [×24], C2×D20 [×12], C4○D20 [×64], C22×Dic5 [×2], C2×C5⋊D4 [×24], C22×C20 [×2], C22×C20 [×12], C23×D5 [×2], C23×C10, C22×Dic10, D5×C22×C4 [×2], C22×D20, C2×C4○D20 [×24], C22×C5⋊D4 [×2], C23×C20, C22×C4○D20
Quotients:
C1, C2 [×31], C22 [×155], C23 [×155], D5, C4○D4 [×4], C24 [×31], D10 [×15], C2×C4○D4 [×6], C25, C22×D5 [×35], C22×C4○D4, C4○D20 [×4], C23×D5 [×15], C2×C4○D20 [×6], D5×C24, C22×C4○D20
Generators and relations
G = < a,b,c,d,e | a2=b2=c4=e2=1, d10=c2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede=c2d9 >
►On 160 points
Generators in S160
(1 71)(2 72)(3 73)(4 74)(5 75)(6 76)(7 77)(8 78)(9 79)(10 80)(11 61)(12 62)(13 63)(14 64)(15 65)(16 66)(17 67)(18 68)(19 69)(20 70)(21 85)(22 86)(23 87)(24 88)(25 89)(26 90)(27 91)(28 92)(29 93)(30 94)(31 95)(32 96)(33 97)(34 98)(35 99)(36 100)(37 81)(38 82)(39 83)(40 84)(41 120)(42 101)(43 102)(44 103)(45 104)(46 105)(47 106)(48 107)(49 108)(50 109)(51 110)(52 111)(53 112)(54 113)(55 114)(56 115)(57 116)(58 117)(59 118)(60 119)(121 159)(122 160)(123 141)(124 142)(125 143)(126 144)(127 145)(128 146)(129 147)(130 148)(131 149)(132 150)(133 151)(134 152)(135 153)(136 154)(137 155)(138 156)(139 157)(140 158)
(1 104)(2 105)(3 106)(4 107)(5 108)(6 109)(7 110)(8 111)(9 112)(10 113)(11 114)(12 115)(13 116)(14 117)(15 118)(16 119)(17 120)(18 101)(19 102)(20 103)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 121)(30 122)(31 123)(32 124)(33 125)(34 126)(35 127)(36 128)(37 129)(38 130)(39 131)(40 132)(41 67)(42 68)(43 69)(44 70)(45 71)(46 72)(47 73)(48 74)(49 75)(50 76)(51 77)(52 78)(53 79)(54 80)(55 61)(56 62)(57 63)(58 64)(59 65)(60 66)(81 147)(82 148)(83 149)(84 150)(85 151)(86 152)(87 153)(88 154)(89 155)(90 156)(91 157)(92 158)(93 159)(94 160)(95 141)(96 142)(97 143)(98 144)(99 145)(100 146)
(1 148 11 158)(2 149 12 159)(3 150 13 160)(4 151 14 141)(5 152 15 142)(6 153 16 143)(7 154 17 144)(8 155 18 145)(9 156 19 146)(10 157 20 147)(21 58 31 48)(22 59 32 49)(23 60 33 50)(24 41 34 51)(25 42 35 52)(26 43 36 53)(27 44 37 54)(28 45 38 55)(29 46 39 56)(30 47 40 57)(61 140 71 130)(62 121 72 131)(63 122 73 132)(64 123 74 133)(65 124 75 134)(66 125 76 135)(67 126 77 136)(68 127 78 137)(69 128 79 138)(70 129 80 139)(81 113 91 103)(82 114 92 104)(83 115 93 105)(84 116 94 106)(85 117 95 107)(86 118 96 108)(87 119 97 109)(88 120 98 110)(89 101 99 111)(90 102 100 112)
(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 44)(2 43)(3 42)(4 41)(5 60)(6 59)(7 58)(8 57)(9 56)(10 55)(11 54)(12 53)(13 52)(14 51)(15 50)(16 49)(17 48)(18 47)(19 46)(20 45)(21 144)(22 143)(23 142)(24 141)(25 160)(26 159)(27 158)(28 157)(29 156)(30 155)(31 154)(32 153)(33 152)(34 151)(35 150)(36 149)(37 148)(38 147)(39 146)(40 145)(61 113)(62 112)(63 111)(64 110)(65 109)(66 108)(67 107)(68 106)(69 105)(70 104)(71 103)(72 102)(73 101)(74 120)(75 119)(76 118)(77 117)(78 116)(79 115)(80 114)(81 130)(82 129)(83 128)(84 127)(85 126)(86 125)(87 124)(88 123)(89 122)(90 121)(91 140)(92 139)(93 138)(94 137)(95 136)(96 135)(97 134)(98 133)(99 132)(100 131)
G:=sub<Sym(160)| (1,71)(2,72)(3,73)(4,74)(5,75)(6,76)(7,77)(8,78)(9,79)(10,80)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,91)(28,92)(29,93)(30,94)(31,95)(32,96)(33,97)(34,98)(35,99)(36,100)(37,81)(38,82)(39,83)(40,84)(41,120)(42,101)(43,102)(44,103)(45,104)(46,105)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118)(60,119)(121,159)(122,160)(123,141)(124,142)(125,143)(126,144)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,155)(138,156)(139,157)(140,158), (1,104)(2,105)(3,106)(4,107)(5,108)(6,109)(7,110)(8,111)(9,112)(10,113)(11,114)(12,115)(13,116)(14,117)(15,118)(16,119)(17,120)(18,101)(19,102)(20,103)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,131)(40,132)(41,67)(42,68)(43,69)(44,70)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(53,79)(54,80)(55,61)(56,62)(57,63)(58,64)(59,65)(60,66)(81,147)(82,148)(83,149)(84,150)(85,151)(86,152)(87,153)(88,154)(89,155)(90,156)(91,157)(92,158)(93,159)(94,160)(95,141)(96,142)(97,143)(98,144)(99,145)(100,146), (1,148,11,158)(2,149,12,159)(3,150,13,160)(4,151,14,141)(5,152,15,142)(6,153,16,143)(7,154,17,144)(8,155,18,145)(9,156,19,146)(10,157,20,147)(21,58,31,48)(22,59,32,49)(23,60,33,50)(24,41,34,51)(25,42,35,52)(26,43,36,53)(27,44,37,54)(28,45,38,55)(29,46,39,56)(30,47,40,57)(61,140,71,130)(62,121,72,131)(63,122,73,132)(64,123,74,133)(65,124,75,134)(66,125,76,135)(67,126,77,136)(68,127,78,137)(69,128,79,138)(70,129,80,139)(81,113,91,103)(82,114,92,104)(83,115,93,105)(84,116,94,106)(85,117,95,107)(86,118,96,108)(87,119,97,109)(88,120,98,110)(89,101,99,111)(90,102,100,112), (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), (1,44)(2,43)(3,42)(4,41)(5,60)(6,59)(7,58)(8,57)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,144)(22,143)(23,142)(24,141)(25,160)(26,159)(27,158)(28,157)(29,156)(30,155)(31,154)(32,153)(33,152)(34,151)(35,150)(36,149)(37,148)(38,147)(39,146)(40,145)(61,113)(62,112)(63,111)(64,110)(65,109)(66,108)(67,107)(68,106)(69,105)(70,104)(71,103)(72,102)(73,101)(74,120)(75,119)(76,118)(77,117)(78,116)(79,115)(80,114)(81,130)(82,129)(83,128)(84,127)(85,126)(86,125)(87,124)(88,123)(89,122)(90,121)(91,140)(92,139)(93,138)(94,137)(95,136)(96,135)(97,134)(98,133)(99,132)(100,131)>;
G:=Group( (1,71)(2,72)(3,73)(4,74)(5,75)(6,76)(7,77)(8,78)(9,79)(10,80)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,91)(28,92)(29,93)(30,94)(31,95)(32,96)(33,97)(34,98)(35,99)(36,100)(37,81)(38,82)(39,83)(40,84)(41,120)(42,101)(43,102)(44,103)(45,104)(46,105)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118)(60,119)(121,159)(122,160)(123,141)(124,142)(125,143)(126,144)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,155)(138,156)(139,157)(140,158), (1,104)(2,105)(3,106)(4,107)(5,108)(6,109)(7,110)(8,111)(9,112)(10,113)(11,114)(12,115)(13,116)(14,117)(15,118)(16,119)(17,120)(18,101)(19,102)(20,103)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,131)(40,132)(41,67)(42,68)(43,69)(44,70)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(53,79)(54,80)(55,61)(56,62)(57,63)(58,64)(59,65)(60,66)(81,147)(82,148)(83,149)(84,150)(85,151)(86,152)(87,153)(88,154)(89,155)(90,156)(91,157)(92,158)(93,159)(94,160)(95,141)(96,142)(97,143)(98,144)(99,145)(100,146), (1,148,11,158)(2,149,12,159)(3,150,13,160)(4,151,14,141)(5,152,15,142)(6,153,16,143)(7,154,17,144)(8,155,18,145)(9,156,19,146)(10,157,20,147)(21,58,31,48)(22,59,32,49)(23,60,33,50)(24,41,34,51)(25,42,35,52)(26,43,36,53)(27,44,37,54)(28,45,38,55)(29,46,39,56)(30,47,40,57)(61,140,71,130)(62,121,72,131)(63,122,73,132)(64,123,74,133)(65,124,75,134)(66,125,76,135)(67,126,77,136)(68,127,78,137)(69,128,79,138)(70,129,80,139)(81,113,91,103)(82,114,92,104)(83,115,93,105)(84,116,94,106)(85,117,95,107)(86,118,96,108)(87,119,97,109)(88,120,98,110)(89,101,99,111)(90,102,100,112), (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), (1,44)(2,43)(3,42)(4,41)(5,60)(6,59)(7,58)(8,57)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,144)(22,143)(23,142)(24,141)(25,160)(26,159)(27,158)(28,157)(29,156)(30,155)(31,154)(32,153)(33,152)(34,151)(35,150)(36,149)(37,148)(38,147)(39,146)(40,145)(61,113)(62,112)(63,111)(64,110)(65,109)(66,108)(67,107)(68,106)(69,105)(70,104)(71,103)(72,102)(73,101)(74,120)(75,119)(76,118)(77,117)(78,116)(79,115)(80,114)(81,130)(82,129)(83,128)(84,127)(85,126)(86,125)(87,124)(88,123)(89,122)(90,121)(91,140)(92,139)(93,138)(94,137)(95,136)(96,135)(97,134)(98,133)(99,132)(100,131) );
G=PermutationGroup([(1,71),(2,72),(3,73),(4,74),(5,75),(6,76),(7,77),(8,78),(9,79),(10,80),(11,61),(12,62),(13,63),(14,64),(15,65),(16,66),(17,67),(18,68),(19,69),(20,70),(21,85),(22,86),(23,87),(24,88),(25,89),(26,90),(27,91),(28,92),(29,93),(30,94),(31,95),(32,96),(33,97),(34,98),(35,99),(36,100),(37,81),(38,82),(39,83),(40,84),(41,120),(42,101),(43,102),(44,103),(45,104),(46,105),(47,106),(48,107),(49,108),(50,109),(51,110),(52,111),(53,112),(54,113),(55,114),(56,115),(57,116),(58,117),(59,118),(60,119),(121,159),(122,160),(123,141),(124,142),(125,143),(126,144),(127,145),(128,146),(129,147),(130,148),(131,149),(132,150),(133,151),(134,152),(135,153),(136,154),(137,155),(138,156),(139,157),(140,158)], [(1,104),(2,105),(3,106),(4,107),(5,108),(6,109),(7,110),(8,111),(9,112),(10,113),(11,114),(12,115),(13,116),(14,117),(15,118),(16,119),(17,120),(18,101),(19,102),(20,103),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,121),(30,122),(31,123),(32,124),(33,125),(34,126),(35,127),(36,128),(37,129),(38,130),(39,131),(40,132),(41,67),(42,68),(43,69),(44,70),(45,71),(46,72),(47,73),(48,74),(49,75),(50,76),(51,77),(52,78),(53,79),(54,80),(55,61),(56,62),(57,63),(58,64),(59,65),(60,66),(81,147),(82,148),(83,149),(84,150),(85,151),(86,152),(87,153),(88,154),(89,155),(90,156),(91,157),(92,158),(93,159),(94,160),(95,141),(96,142),(97,143),(98,144),(99,145),(100,146)], [(1,148,11,158),(2,149,12,159),(3,150,13,160),(4,151,14,141),(5,152,15,142),(6,153,16,143),(7,154,17,144),(8,155,18,145),(9,156,19,146),(10,157,20,147),(21,58,31,48),(22,59,32,49),(23,60,33,50),(24,41,34,51),(25,42,35,52),(26,43,36,53),(27,44,37,54),(28,45,38,55),(29,46,39,56),(30,47,40,57),(61,140,71,130),(62,121,72,131),(63,122,73,132),(64,123,74,133),(65,124,75,134),(66,125,76,135),(67,126,77,136),(68,127,78,137),(69,128,79,138),(70,129,80,139),(81,113,91,103),(82,114,92,104),(83,115,93,105),(84,116,94,106),(85,117,95,107),(86,118,96,108),(87,119,97,109),(88,120,98,110),(89,101,99,111),(90,102,100,112)], [(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)], [(1,44),(2,43),(3,42),(4,41),(5,60),(6,59),(7,58),(8,57),(9,56),(10,55),(11,54),(12,53),(13,52),(14,51),(15,50),(16,49),(17,48),(18,47),(19,46),(20,45),(21,144),(22,143),(23,142),(24,141),(25,160),(26,159),(27,158),(28,157),(29,156),(30,155),(31,154),(32,153),(33,152),(34,151),(35,150),(36,149),(37,148),(38,147),(39,146),(40,145),(61,113),(62,112),(63,111),(64,110),(65,109),(66,108),(67,107),(68,106),(69,105),(70,104),(71,103),(72,102),(73,101),(74,120),(75,119),(76,118),(77,117),(78,116),(79,115),(80,114),(81,130),(82,129),(83,128),(84,127),(85,126),(86,125),(87,124),(88,123),(89,122),(90,121),(91,140),(92,139),(93,138),(94,137),(95,136),(96,135),(97,134),(98,133),(99,132),(100,131)])
Matrix representation ►G ⊆ GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 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 | 9 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 6 | 1 |
| 0 | 0 | 0 | 40 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 35 |
| 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[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],[1,0,0,0,0,0,9,0,0,0,0,0,9,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,0,9,0,0,0,9,0,0,0,0,0,0,6,40,0,0,0,1,0],[1,0,0,0,0,0,0,32,0,0,0,9,0,0,0,0,0,0,40,0,0,0,0,35,1] >;
104 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | ··· | 2S | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4T | 5A | 5B | 10A | ··· | 10AD | 20A | ··· | 20AF |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 10 | ··· | 10 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | D10 | D10 | C4○D20 |
| kernel | C22×C4○D20 | C22×Dic10 | D5×C22×C4 | C22×D20 | C2×C4○D20 | C22×C5⋊D4 | C23×C20 | C23×C4 | C2×C10 | C22×C4 | C24 | C22 |
| # reps | 1 | 1 | 2 | 1 | 24 | 2 | 1 | 2 | 8 | 28 | 2 | 32 |
In GAP, Magma, Sage, TeX
C_2^2\times C_4\circ D_{20} % in TeX
G:=Group("C2^2xC4oD20"); // GroupNames label
G:=SmallGroup(320,1611);
// by ID
G=gap.SmallGroup(320,1611);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,136,1684,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^4=e^2=1,d^10=c^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=c^2*d^9>;
// generators/relations
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