direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C22⋊C4×C2×C10, C24⋊5C20, C25.3C10, (C23×C20)⋊5C2, (C23×C4)⋊2C10, C23⋊5(C2×C20), (C23×C10)⋊11C4, (C2×C20)⋊13C23, (C24×C10).2C2, C2.1(C23×C20), C23.58(C5×D4), C10.74(C23×C4), C24.28(C2×C10), C22⋊2(C22×C20), C22.57(D4×C10), (C2×C10).332C24, (C22×C20)⋊57C22, (C22×C10).219D4, C10.177(C22×D4), C22.5(C23×C10), C23.65(C22×C10), (C23×C10).88C22, (C22×C10).251C23, C2.1(D4×C2×C10), (C2×C4)⋊3(C22×C10), (C22×C4)⋊15(C2×C10), (C22×C10)⋊23(C2×C4), (C2×C10)⋊11(C22×C4), (C2×C10).679(C2×D4), SmallGroup(320,1514)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1010 in 674 conjugacy classes, 338 normal (12 characteristic)
C1, C2, C2 [×14], C2 [×8], C4 [×8], C22, C22 [×42], C22 [×56], C5, C2×C4 [×8], C2×C4 [×24], C23 [×43], C23 [×56], C10, C10 [×14], C10 [×8], C22⋊C4 [×16], C22×C4 [×12], C22×C4 [×8], C24, C24 [×14], C24 [×8], C20 [×8], C2×C10, C2×C10 [×42], C2×C10 [×56], C2×C22⋊C4 [×12], C23×C4 [×2], C25, C2×C20 [×8], C2×C20 [×24], C22×C10 [×43], C22×C10 [×56], C22×C22⋊C4, C5×C22⋊C4 [×16], C22×C20 [×12], C22×C20 [×8], C23×C10, C23×C10 [×14], C23×C10 [×8], C10×C22⋊C4 [×12], C23×C20 [×2], C24×C10, C22⋊C4×C2×C10
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C5, C2×C4 [×28], D4 [×8], C23 [×15], C10 [×15], C22⋊C4 [×16], C22×C4 [×14], C2×D4 [×12], C24, C20 [×8], C2×C10 [×35], C2×C22⋊C4 [×12], C23×C4, C22×D4 [×2], C2×C20 [×28], C5×D4 [×8], C22×C10 [×15], C22×C22⋊C4, C5×C22⋊C4 [×16], C22×C20 [×14], D4×C10 [×12], C23×C10, C10×C22⋊C4 [×12], C23×C20, D4×C2×C10 [×2], C22⋊C4×C2×C10
Generators and relations
G = < a,b,c,d,e | a2=b10=c2=d2=e4=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, ece-1=cd=dc, de=ed >
►On 160 points
Generators in S160
(1 86)(2 87)(3 88)(4 89)(5 90)(6 81)(7 82)(8 83)(9 84)(10 85)(11 120)(12 111)(13 112)(14 113)(15 114)(16 115)(17 116)(18 117)(19 118)(20 119)(21 145)(22 146)(23 147)(24 148)(25 149)(26 150)(27 141)(28 142)(29 143)(30 144)(31 127)(32 128)(33 129)(34 130)(35 121)(36 122)(37 123)(38 124)(39 125)(40 126)(41 106)(42 107)(43 108)(44 109)(45 110)(46 101)(47 102)(48 103)(49 104)(50 105)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(61 100)(62 91)(63 92)(64 93)(65 94)(66 95)(67 96)(68 97)(69 98)(70 99)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(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 56)(2 57)(3 58)(4 59)(5 60)(6 51)(7 52)(8 53)(9 54)(10 55)(11 160)(12 151)(13 152)(14 153)(15 154)(16 155)(17 156)(18 157)(19 158)(20 159)(21 34)(22 35)(23 36)(24 37)(25 38)(26 39)(27 40)(28 31)(29 32)(30 33)(41 62)(42 63)(43 64)(44 65)(45 66)(46 67)(47 68)(48 69)(49 70)(50 61)(71 81)(72 82)(73 83)(74 84)(75 85)(76 86)(77 87)(78 88)(79 89)(80 90)(91 106)(92 107)(93 108)(94 109)(95 110)(96 101)(97 102)(98 103)(99 104)(100 105)(111 131)(112 132)(113 133)(114 134)(115 135)(116 136)(117 137)(118 138)(119 139)(120 140)(121 146)(122 147)(123 148)(124 149)(125 150)(126 141)(127 142)(128 143)(129 144)(130 145)
(1 67)(2 68)(3 69)(4 70)(5 61)(6 62)(7 63)(8 64)(9 65)(10 66)(11 21)(12 22)(13 23)(14 24)(15 25)(16 26)(17 27)(18 28)(19 29)(20 30)(31 157)(32 158)(33 159)(34 160)(35 151)(36 152)(37 153)(38 154)(39 155)(40 156)(41 51)(42 52)(43 53)(44 54)(45 55)(46 56)(47 57)(48 58)(49 59)(50 60)(71 106)(72 107)(73 108)(74 109)(75 110)(76 101)(77 102)(78 103)(79 104)(80 105)(81 91)(82 92)(83 93)(84 94)(85 95)(86 96)(87 97)(88 98)(89 99)(90 100)(111 146)(112 147)(113 148)(114 149)(115 150)(116 141)(117 142)(118 143)(119 144)(120 145)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)
(1 12 51 40)(2 13 52 31)(3 14 53 32)(4 15 54 33)(5 16 55 34)(6 17 56 35)(7 18 57 36)(8 19 58 37)(9 20 59 38)(10 11 60 39)(21 50 155 66)(22 41 156 67)(23 42 157 68)(24 43 158 69)(25 44 159 70)(26 45 160 61)(27 46 151 62)(28 47 152 63)(29 48 153 64)(30 49 154 65)(71 126 86 111)(72 127 87 112)(73 128 88 113)(74 129 89 114)(75 130 90 115)(76 121 81 116)(77 122 82 117)(78 123 83 118)(79 124 84 119)(80 125 85 120)(91 141 101 131)(92 142 102 132)(93 143 103 133)(94 144 104 134)(95 145 105 135)(96 146 106 136)(97 147 107 137)(98 148 108 138)(99 149 109 139)(100 150 110 140)
G:=sub<Sym(160)| (1,86)(2,87)(3,88)(4,89)(5,90)(6,81)(7,82)(8,83)(9,84)(10,85)(11,120)(12,111)(13,112)(14,113)(15,114)(16,115)(17,116)(18,117)(19,118)(20,119)(21,145)(22,146)(23,147)(24,148)(25,149)(26,150)(27,141)(28,142)(29,143)(30,144)(31,127)(32,128)(33,129)(34,130)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(61,100)(62,91)(63,92)(64,93)(65,94)(66,95)(67,96)(68,97)(69,98)(70,99)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,56)(2,57)(3,58)(4,59)(5,60)(6,51)(7,52)(8,53)(9,54)(10,55)(11,160)(12,151)(13,152)(14,153)(15,154)(16,155)(17,156)(18,157)(19,158)(20,159)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)(28,31)(29,32)(30,33)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,61)(71,81)(72,82)(73,83)(74,84)(75,85)(76,86)(77,87)(78,88)(79,89)(80,90)(91,106)(92,107)(93,108)(94,109)(95,110)(96,101)(97,102)(98,103)(99,104)(100,105)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,138)(119,139)(120,140)(121,146)(122,147)(123,148)(124,149)(125,150)(126,141)(127,142)(128,143)(129,144)(130,145), (1,67)(2,68)(3,69)(4,70)(5,61)(6,62)(7,63)(8,64)(9,65)(10,66)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(31,157)(32,158)(33,159)(34,160)(35,151)(36,152)(37,153)(38,154)(39,155)(40,156)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(71,106)(72,107)(73,108)(74,109)(75,110)(76,101)(77,102)(78,103)(79,104)(80,105)(81,91)(82,92)(83,93)(84,94)(85,95)(86,96)(87,97)(88,98)(89,99)(90,100)(111,146)(112,147)(113,148)(114,149)(115,150)(116,141)(117,142)(118,143)(119,144)(120,145)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140), (1,12,51,40)(2,13,52,31)(3,14,53,32)(4,15,54,33)(5,16,55,34)(6,17,56,35)(7,18,57,36)(8,19,58,37)(9,20,59,38)(10,11,60,39)(21,50,155,66)(22,41,156,67)(23,42,157,68)(24,43,158,69)(25,44,159,70)(26,45,160,61)(27,46,151,62)(28,47,152,63)(29,48,153,64)(30,49,154,65)(71,126,86,111)(72,127,87,112)(73,128,88,113)(74,129,89,114)(75,130,90,115)(76,121,81,116)(77,122,82,117)(78,123,83,118)(79,124,84,119)(80,125,85,120)(91,141,101,131)(92,142,102,132)(93,143,103,133)(94,144,104,134)(95,145,105,135)(96,146,106,136)(97,147,107,137)(98,148,108,138)(99,149,109,139)(100,150,110,140)>;
G:=Group( (1,86)(2,87)(3,88)(4,89)(5,90)(6,81)(7,82)(8,83)(9,84)(10,85)(11,120)(12,111)(13,112)(14,113)(15,114)(16,115)(17,116)(18,117)(19,118)(20,119)(21,145)(22,146)(23,147)(24,148)(25,149)(26,150)(27,141)(28,142)(29,143)(30,144)(31,127)(32,128)(33,129)(34,130)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(61,100)(62,91)(63,92)(64,93)(65,94)(66,95)(67,96)(68,97)(69,98)(70,99)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,56)(2,57)(3,58)(4,59)(5,60)(6,51)(7,52)(8,53)(9,54)(10,55)(11,160)(12,151)(13,152)(14,153)(15,154)(16,155)(17,156)(18,157)(19,158)(20,159)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)(28,31)(29,32)(30,33)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,61)(71,81)(72,82)(73,83)(74,84)(75,85)(76,86)(77,87)(78,88)(79,89)(80,90)(91,106)(92,107)(93,108)(94,109)(95,110)(96,101)(97,102)(98,103)(99,104)(100,105)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,138)(119,139)(120,140)(121,146)(122,147)(123,148)(124,149)(125,150)(126,141)(127,142)(128,143)(129,144)(130,145), (1,67)(2,68)(3,69)(4,70)(5,61)(6,62)(7,63)(8,64)(9,65)(10,66)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(31,157)(32,158)(33,159)(34,160)(35,151)(36,152)(37,153)(38,154)(39,155)(40,156)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(71,106)(72,107)(73,108)(74,109)(75,110)(76,101)(77,102)(78,103)(79,104)(80,105)(81,91)(82,92)(83,93)(84,94)(85,95)(86,96)(87,97)(88,98)(89,99)(90,100)(111,146)(112,147)(113,148)(114,149)(115,150)(116,141)(117,142)(118,143)(119,144)(120,145)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140), (1,12,51,40)(2,13,52,31)(3,14,53,32)(4,15,54,33)(5,16,55,34)(6,17,56,35)(7,18,57,36)(8,19,58,37)(9,20,59,38)(10,11,60,39)(21,50,155,66)(22,41,156,67)(23,42,157,68)(24,43,158,69)(25,44,159,70)(26,45,160,61)(27,46,151,62)(28,47,152,63)(29,48,153,64)(30,49,154,65)(71,126,86,111)(72,127,87,112)(73,128,88,113)(74,129,89,114)(75,130,90,115)(76,121,81,116)(77,122,82,117)(78,123,83,118)(79,124,84,119)(80,125,85,120)(91,141,101,131)(92,142,102,132)(93,143,103,133)(94,144,104,134)(95,145,105,135)(96,146,106,136)(97,147,107,137)(98,148,108,138)(99,149,109,139)(100,150,110,140) );
G=PermutationGroup([(1,86),(2,87),(3,88),(4,89),(5,90),(6,81),(7,82),(8,83),(9,84),(10,85),(11,120),(12,111),(13,112),(14,113),(15,114),(16,115),(17,116),(18,117),(19,118),(20,119),(21,145),(22,146),(23,147),(24,148),(25,149),(26,150),(27,141),(28,142),(29,143),(30,144),(31,127),(32,128),(33,129),(34,130),(35,121),(36,122),(37,123),(38,124),(39,125),(40,126),(41,106),(42,107),(43,108),(44,109),(45,110),(46,101),(47,102),(48,103),(49,104),(50,105),(51,71),(52,72),(53,73),(54,74),(55,75),(56,76),(57,77),(58,78),(59,79),(60,80),(61,100),(62,91),(63,92),(64,93),(65,94),(66,95),(67,96),(68,97),(69,98),(70,99),(131,151),(132,152),(133,153),(134,154),(135,155),(136,156),(137,157),(138,158),(139,159),(140,160)], [(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)], [(1,56),(2,57),(3,58),(4,59),(5,60),(6,51),(7,52),(8,53),(9,54),(10,55),(11,160),(12,151),(13,152),(14,153),(15,154),(16,155),(17,156),(18,157),(19,158),(20,159),(21,34),(22,35),(23,36),(24,37),(25,38),(26,39),(27,40),(28,31),(29,32),(30,33),(41,62),(42,63),(43,64),(44,65),(45,66),(46,67),(47,68),(48,69),(49,70),(50,61),(71,81),(72,82),(73,83),(74,84),(75,85),(76,86),(77,87),(78,88),(79,89),(80,90),(91,106),(92,107),(93,108),(94,109),(95,110),(96,101),(97,102),(98,103),(99,104),(100,105),(111,131),(112,132),(113,133),(114,134),(115,135),(116,136),(117,137),(118,138),(119,139),(120,140),(121,146),(122,147),(123,148),(124,149),(125,150),(126,141),(127,142),(128,143),(129,144),(130,145)], [(1,67),(2,68),(3,69),(4,70),(5,61),(6,62),(7,63),(8,64),(9,65),(10,66),(11,21),(12,22),(13,23),(14,24),(15,25),(16,26),(17,27),(18,28),(19,29),(20,30),(31,157),(32,158),(33,159),(34,160),(35,151),(36,152),(37,153),(38,154),(39,155),(40,156),(41,51),(42,52),(43,53),(44,54),(45,55),(46,56),(47,57),(48,58),(49,59),(50,60),(71,106),(72,107),(73,108),(74,109),(75,110),(76,101),(77,102),(78,103),(79,104),(80,105),(81,91),(82,92),(83,93),(84,94),(85,95),(86,96),(87,97),(88,98),(89,99),(90,100),(111,146),(112,147),(113,148),(114,149),(115,150),(116,141),(117,142),(118,143),(119,144),(120,145),(121,131),(122,132),(123,133),(124,134),(125,135),(126,136),(127,137),(128,138),(129,139),(130,140)], [(1,12,51,40),(2,13,52,31),(3,14,53,32),(4,15,54,33),(5,16,55,34),(6,17,56,35),(7,18,57,36),(8,19,58,37),(9,20,59,38),(10,11,60,39),(21,50,155,66),(22,41,156,67),(23,42,157,68),(24,43,158,69),(25,44,159,70),(26,45,160,61),(27,46,151,62),(28,47,152,63),(29,48,153,64),(30,49,154,65),(71,126,86,111),(72,127,87,112),(73,128,88,113),(74,129,89,114),(75,130,90,115),(76,121,81,116),(77,122,82,117),(78,123,83,118),(79,124,84,119),(80,125,85,120),(91,141,101,131),(92,142,102,132),(93,143,103,133),(94,144,104,134),(95,145,105,135),(96,146,106,136),(97,147,107,137),(98,148,108,138),(99,149,109,139),(100,150,110,140)])
Matrix representation ►G ⊆ GL5(𝔽41)
| 40 | 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 | 1 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 37 | 0 |
| 0 | 0 | 0 | 0 | 37 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 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 | 32 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,37,0,0,0,0,0,37],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40],[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],[1,0,0,0,0,0,32,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0] >;
200 conjugacy classes
| class | 1 | 2A | ··· | 2O | 2P | ··· | 2W | 4A | ··· | 4P | 5A | 5B | 5C | 5D | 10A | ··· | 10BH | 10BI | ··· | 10CN | 20A | ··· | 20BL |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 5 | 5 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
200 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C5 | C10 | C10 | C10 | C20 | D4 | C5×D4 |
| kernel | C22⋊C4×C2×C10 | C10×C22⋊C4 | C23×C20 | C24×C10 | C23×C10 | C22×C22⋊C4 | C2×C22⋊C4 | C23×C4 | C25 | C24 | C22×C10 | C23 |
| # reps | 1 | 12 | 2 | 1 | 16 | 4 | 48 | 8 | 4 | 64 | 8 | 32 |
In GAP, Magma, Sage, TeX
C_2^2\rtimes C_4\times C_2\times C_{10} % in TeX
G:=Group("C2^2:C4xC2xC10"); // GroupNames label
G:=SmallGroup(320,1514);
// by ID
G=gap.SmallGroup(320,1514);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-2,1120,1149]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^10=c^2=d^2=e^4=1,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,e*c*e^-1=c*d=d*c,d*e=e*d>;
// generators/relations
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