direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D5×C4⋊C4, C20⋊5(C22×C4), D10.29(C2×Q8), D10.105(C2×D4), C22.32(Q8×D5), (C2×C10).45C24, C10.32(C23×C4), C4⋊Dic5⋊69C22, Dic5⋊5(C22×C4), C10.40(C22×D4), C22.130(D4×D5), (C22×D5).25Q8, C10.23(C22×Q8), (C2×C20).577C23, D10.51(C22×C4), (C22×D5).157D4, (C22×C4).316D10, C22.21(C23×D5), C10.D4⋊60C22, C23.324(C22×D5), (C22×C20).357C22, (C22×C10).394C23, (C2×Dic5).194C23, (C22×D5).290C23, (C23×D5).144C22, (C22×Dic5).232C22, C4⋊4(C2×C4×D5), (C2×C4×D5)⋊8C4, C10⋊2(C2×C4⋊C4), C2.3(C2×D4×D5), C2.2(C2×Q8×D5), C5⋊2(C22×C4⋊C4), (C10×C4⋊C4)⋊7C2, (C2×C4)⋊15(C4×D5), (C2×C20)⋊20(C2×C4), (C4×D5)⋊15(C2×C4), (D5×C22×C4).3C2, C22.71(C2×C4×D5), (C5×C4⋊C4)⋊42C22, C2.13(D5×C22×C4), (C2×C4⋊Dic5)⋊37C2, (C2×C10).92(C2×Q8), (C2×Dic5)⋊31(C2×C4), (C2×C10).386(C2×D4), (C2×C4×D5).312C22, (C2×C10.D4)⋊37C2, (C2×C4).264(C22×D5), (C2×C10).251(C22×C4), (C22×D5).141(C2×C4), SmallGroup(320,1173)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D5×C4⋊C4
G = < a,b,c,d,e | a2=b5=c2=d4=e4=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 1278 in 418 conjugacy classes, 207 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C23, C23, D5, C10, C10, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic5, Dic5, C20, C20, D10, C2×C10, C2×C10, C2×C4⋊C4, C2×C4⋊C4, C23×C4, C4×D5, C4×D5, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, C22×C10, C22×C4⋊C4, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×C4×D5, C2×C4×D5, C22×Dic5, C22×Dic5, C22×C20, C22×C20, C23×D5, D5×C4⋊C4, C2×C10.D4, C2×C4⋊Dic5, C10×C4⋊C4, D5×C22×C4, D5×C22×C4, C2×D5×C4⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, C22×C4, C2×D4, C2×Q8, C24, D10, C2×C4⋊C4, C23×C4, C22×D4, C22×Q8, C4×D5, C22×D5, C22×C4⋊C4, C2×C4×D5, D4×D5, Q8×D5, C23×D5, D5×C4⋊C4, D5×C22×C4, C2×D4×D5, C2×Q8×D5, C2×D5×C4⋊C4
►On 160 points
Generators in S160
(1 89)(2 90)(3 86)(4 87)(5 88)(6 81)(7 82)(8 83)(9 84)(10 85)(11 96)(12 97)(13 98)(14 99)(15 100)(16 91)(17 92)(18 93)(19 94)(20 95)(21 106)(22 107)(23 108)(24 109)(25 110)(26 101)(27 102)(28 103)(29 104)(30 105)(31 116)(32 117)(33 118)(34 119)(35 120)(36 111)(37 112)(38 113)(39 114)(40 115)(41 126)(42 127)(43 128)(44 129)(45 130)(46 121)(47 122)(48 123)(49 124)(50 125)(51 136)(52 137)(53 138)(54 139)(55 140)(56 131)(57 132)(58 133)(59 134)(60 135)(61 146)(62 147)(63 148)(64 149)(65 150)(66 141)(67 142)(68 143)(69 144)(70 145)(71 156)(72 157)(73 158)(74 159)(75 160)(76 151)(77 152)(78 153)(79 154)(80 155)
(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 5)(2 4)(7 10)(8 9)(12 15)(13 14)(17 20)(18 19)(22 25)(23 24)(27 30)(28 29)(32 35)(33 34)(37 40)(38 39)(42 45)(43 44)(47 50)(48 49)(52 55)(53 54)(57 60)(58 59)(62 65)(63 64)(67 70)(68 69)(72 75)(73 74)(77 80)(78 79)(82 85)(83 84)(87 90)(88 89)(92 95)(93 94)(97 100)(98 99)(102 105)(103 104)(107 110)(108 109)(112 115)(113 114)(117 120)(118 119)(122 125)(123 124)(127 130)(128 129)(132 135)(133 134)(137 140)(138 139)(142 145)(143 144)(147 150)(148 149)(152 155)(153 154)(157 160)(158 159)
(1 139 9 134)(2 140 10 135)(3 136 6 131)(4 137 7 132)(5 138 8 133)(11 126 16 121)(12 127 17 122)(13 128 18 123)(14 129 19 124)(15 130 20 125)(21 156 26 151)(22 157 27 152)(23 158 28 153)(24 159 29 154)(25 160 30 155)(31 146 36 141)(32 147 37 142)(33 148 38 143)(34 149 39 144)(35 150 40 145)(41 91 46 96)(42 92 47 97)(43 93 48 98)(44 94 49 99)(45 95 50 100)(51 81 56 86)(52 82 57 87)(53 83 58 88)(54 84 59 89)(55 85 60 90)(61 111 66 116)(62 112 67 117)(63 113 68 118)(64 114 69 119)(65 115 70 120)(71 101 76 106)(72 102 77 107)(73 103 78 108)(74 104 79 109)(75 105 80 110)
(1 34 14 24)(2 35 15 25)(3 31 11 21)(4 32 12 22)(5 33 13 23)(6 36 16 26)(7 37 17 27)(8 38 18 28)(9 39 19 29)(10 40 20 30)(41 76 51 66)(42 77 52 67)(43 78 53 68)(44 79 54 69)(45 80 55 70)(46 71 56 61)(47 72 57 62)(48 73 58 63)(49 74 59 64)(50 75 60 65)(81 111 91 101)(82 112 92 102)(83 113 93 103)(84 114 94 104)(85 115 95 105)(86 116 96 106)(87 117 97 107)(88 118 98 108)(89 119 99 109)(90 120 100 110)(121 156 131 146)(122 157 132 147)(123 158 133 148)(124 159 134 149)(125 160 135 150)(126 151 136 141)(127 152 137 142)(128 153 138 143)(129 154 139 144)(130 155 140 145)
G:=sub<Sym(160)| (1,89)(2,90)(3,86)(4,87)(5,88)(6,81)(7,82)(8,83)(9,84)(10,85)(11,96)(12,97)(13,98)(14,99)(15,100)(16,91)(17,92)(18,93)(19,94)(20,95)(21,106)(22,107)(23,108)(24,109)(25,110)(26,101)(27,102)(28,103)(29,104)(30,105)(31,116)(32,117)(33,118)(34,119)(35,120)(36,111)(37,112)(38,113)(39,114)(40,115)(41,126)(42,127)(43,128)(44,129)(45,130)(46,121)(47,122)(48,123)(49,124)(50,125)(51,136)(52,137)(53,138)(54,139)(55,140)(56,131)(57,132)(58,133)(59,134)(60,135)(61,146)(62,147)(63,148)(64,149)(65,150)(66,141)(67,142)(68,143)(69,144)(70,145)(71,156)(72,157)(73,158)(74,159)(75,160)(76,151)(77,152)(78,153)(79,154)(80,155), (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), (1,5)(2,4)(7,10)(8,9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74)(77,80)(78,79)(82,85)(83,84)(87,90)(88,89)(92,95)(93,94)(97,100)(98,99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159), (1,139,9,134)(2,140,10,135)(3,136,6,131)(4,137,7,132)(5,138,8,133)(11,126,16,121)(12,127,17,122)(13,128,18,123)(14,129,19,124)(15,130,20,125)(21,156,26,151)(22,157,27,152)(23,158,28,153)(24,159,29,154)(25,160,30,155)(31,146,36,141)(32,147,37,142)(33,148,38,143)(34,149,39,144)(35,150,40,145)(41,91,46,96)(42,92,47,97)(43,93,48,98)(44,94,49,99)(45,95,50,100)(51,81,56,86)(52,82,57,87)(53,83,58,88)(54,84,59,89)(55,85,60,90)(61,111,66,116)(62,112,67,117)(63,113,68,118)(64,114,69,119)(65,115,70,120)(71,101,76,106)(72,102,77,107)(73,103,78,108)(74,104,79,109)(75,105,80,110), (1,34,14,24)(2,35,15,25)(3,31,11,21)(4,32,12,22)(5,33,13,23)(6,36,16,26)(7,37,17,27)(8,38,18,28)(9,39,19,29)(10,40,20,30)(41,76,51,66)(42,77,52,67)(43,78,53,68)(44,79,54,69)(45,80,55,70)(46,71,56,61)(47,72,57,62)(48,73,58,63)(49,74,59,64)(50,75,60,65)(81,111,91,101)(82,112,92,102)(83,113,93,103)(84,114,94,104)(85,115,95,105)(86,116,96,106)(87,117,97,107)(88,118,98,108)(89,119,99,109)(90,120,100,110)(121,156,131,146)(122,157,132,147)(123,158,133,148)(124,159,134,149)(125,160,135,150)(126,151,136,141)(127,152,137,142)(128,153,138,143)(129,154,139,144)(130,155,140,145)>;
G:=Group( (1,89)(2,90)(3,86)(4,87)(5,88)(6,81)(7,82)(8,83)(9,84)(10,85)(11,96)(12,97)(13,98)(14,99)(15,100)(16,91)(17,92)(18,93)(19,94)(20,95)(21,106)(22,107)(23,108)(24,109)(25,110)(26,101)(27,102)(28,103)(29,104)(30,105)(31,116)(32,117)(33,118)(34,119)(35,120)(36,111)(37,112)(38,113)(39,114)(40,115)(41,126)(42,127)(43,128)(44,129)(45,130)(46,121)(47,122)(48,123)(49,124)(50,125)(51,136)(52,137)(53,138)(54,139)(55,140)(56,131)(57,132)(58,133)(59,134)(60,135)(61,146)(62,147)(63,148)(64,149)(65,150)(66,141)(67,142)(68,143)(69,144)(70,145)(71,156)(72,157)(73,158)(74,159)(75,160)(76,151)(77,152)(78,153)(79,154)(80,155), (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), (1,5)(2,4)(7,10)(8,9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(67,70)(68,69)(72,75)(73,74)(77,80)(78,79)(82,85)(83,84)(87,90)(88,89)(92,95)(93,94)(97,100)(98,99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159), (1,139,9,134)(2,140,10,135)(3,136,6,131)(4,137,7,132)(5,138,8,133)(11,126,16,121)(12,127,17,122)(13,128,18,123)(14,129,19,124)(15,130,20,125)(21,156,26,151)(22,157,27,152)(23,158,28,153)(24,159,29,154)(25,160,30,155)(31,146,36,141)(32,147,37,142)(33,148,38,143)(34,149,39,144)(35,150,40,145)(41,91,46,96)(42,92,47,97)(43,93,48,98)(44,94,49,99)(45,95,50,100)(51,81,56,86)(52,82,57,87)(53,83,58,88)(54,84,59,89)(55,85,60,90)(61,111,66,116)(62,112,67,117)(63,113,68,118)(64,114,69,119)(65,115,70,120)(71,101,76,106)(72,102,77,107)(73,103,78,108)(74,104,79,109)(75,105,80,110), (1,34,14,24)(2,35,15,25)(3,31,11,21)(4,32,12,22)(5,33,13,23)(6,36,16,26)(7,37,17,27)(8,38,18,28)(9,39,19,29)(10,40,20,30)(41,76,51,66)(42,77,52,67)(43,78,53,68)(44,79,54,69)(45,80,55,70)(46,71,56,61)(47,72,57,62)(48,73,58,63)(49,74,59,64)(50,75,60,65)(81,111,91,101)(82,112,92,102)(83,113,93,103)(84,114,94,104)(85,115,95,105)(86,116,96,106)(87,117,97,107)(88,118,98,108)(89,119,99,109)(90,120,100,110)(121,156,131,146)(122,157,132,147)(123,158,133,148)(124,159,134,149)(125,160,135,150)(126,151,136,141)(127,152,137,142)(128,153,138,143)(129,154,139,144)(130,155,140,145) );
G=PermutationGroup([[(1,89),(2,90),(3,86),(4,87),(5,88),(6,81),(7,82),(8,83),(9,84),(10,85),(11,96),(12,97),(13,98),(14,99),(15,100),(16,91),(17,92),(18,93),(19,94),(20,95),(21,106),(22,107),(23,108),(24,109),(25,110),(26,101),(27,102),(28,103),(29,104),(30,105),(31,116),(32,117),(33,118),(34,119),(35,120),(36,111),(37,112),(38,113),(39,114),(40,115),(41,126),(42,127),(43,128),(44,129),(45,130),(46,121),(47,122),(48,123),(49,124),(50,125),(51,136),(52,137),(53,138),(54,139),(55,140),(56,131),(57,132),(58,133),(59,134),(60,135),(61,146),(62,147),(63,148),(64,149),(65,150),(66,141),(67,142),(68,143),(69,144),(70,145),(71,156),(72,157),(73,158),(74,159),(75,160),(76,151),(77,152),(78,153),(79,154),(80,155)], [(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)], [(1,5),(2,4),(7,10),(8,9),(12,15),(13,14),(17,20),(18,19),(22,25),(23,24),(27,30),(28,29),(32,35),(33,34),(37,40),(38,39),(42,45),(43,44),(47,50),(48,49),(52,55),(53,54),(57,60),(58,59),(62,65),(63,64),(67,70),(68,69),(72,75),(73,74),(77,80),(78,79),(82,85),(83,84),(87,90),(88,89),(92,95),(93,94),(97,100),(98,99),(102,105),(103,104),(107,110),(108,109),(112,115),(113,114),(117,120),(118,119),(122,125),(123,124),(127,130),(128,129),(132,135),(133,134),(137,140),(138,139),(142,145),(143,144),(147,150),(148,149),(152,155),(153,154),(157,160),(158,159)], [(1,139,9,134),(2,140,10,135),(3,136,6,131),(4,137,7,132),(5,138,8,133),(11,126,16,121),(12,127,17,122),(13,128,18,123),(14,129,19,124),(15,130,20,125),(21,156,26,151),(22,157,27,152),(23,158,28,153),(24,159,29,154),(25,160,30,155),(31,146,36,141),(32,147,37,142),(33,148,38,143),(34,149,39,144),(35,150,40,145),(41,91,46,96),(42,92,47,97),(43,93,48,98),(44,94,49,99),(45,95,50,100),(51,81,56,86),(52,82,57,87),(53,83,58,88),(54,84,59,89),(55,85,60,90),(61,111,66,116),(62,112,67,117),(63,113,68,118),(64,114,69,119),(65,115,70,120),(71,101,76,106),(72,102,77,107),(73,103,78,108),(74,104,79,109),(75,105,80,110)], [(1,34,14,24),(2,35,15,25),(3,31,11,21),(4,32,12,22),(5,33,13,23),(6,36,16,26),(7,37,17,27),(8,38,18,28),(9,39,19,29),(10,40,20,30),(41,76,51,66),(42,77,52,67),(43,78,53,68),(44,79,54,69),(45,80,55,70),(46,71,56,61),(47,72,57,62),(48,73,58,63),(49,74,59,64),(50,75,60,65),(81,111,91,101),(82,112,92,102),(83,113,93,103),(84,114,94,104),(85,115,95,105),(86,116,96,106),(87,117,97,107),(88,118,98,108),(89,119,99,109),(90,120,100,110),(121,156,131,146),(122,157,132,147),(123,158,133,148),(124,159,134,149),(125,160,135,150),(126,151,136,141),(127,152,137,142),(128,153,138,143),(129,154,139,144),(130,155,140,145)]])
80 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 4A | ··· | 4L | 4M | ··· | 4X | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 5 | ··· | 5 | 2 | ··· | 2 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | D5 | D10 | D10 | C4×D5 | D4×D5 | Q8×D5 |
| kernel | C2×D5×C4⋊C4 | D5×C4⋊C4 | C2×C10.D4 | C2×C4⋊Dic5 | C10×C4⋊C4 | D5×C22×C4 | C2×C4×D5 | C22×D5 | C22×D5 | C2×C4⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 8 | 2 | 1 | 1 | 3 | 16 | 4 | 4 | 2 | 8 | 6 | 16 | 4 | 4 |
Matrix representation of C2×D5×C4⋊C4 ►in GL6(𝔽41)
| 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 1 | 0 | 0 |
| 0 | 0 | 33 | 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 | 40 | 40 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 23 | 27 |
| 0 | 0 | 0 | 0 | 32 | 18 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 37 |
| 0 | 0 | 0 | 0 | 0 | 40 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,40,0,0,0,0,1,34,0,0,0,0,0,0,7,33,0,0,0,0,1,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,40,0,0,0,0,0,40,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,23,32,0,0,0,0,27,18],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,1,0,0,0,0,0,37,40] >;
C2×D5×C4⋊C4 in GAP, Magma, Sage, TeX
C_2\times D_5\times C_4\rtimes C_4
% in TeX
G:=Group("C2xD5xC4:C4"); // GroupNames label
G:=SmallGroup(320,1173);
// by ID
G=gap.SmallGroup(320,1173);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,297,80,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^5=c^2=d^4=e^4=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations