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G = C2×Dic5⋊4D4  order 320 = 26·5

Direct product of C2 and Dic5⋊4D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×Dic5⋊4D4, C24.53D10, C10⋊3(C4×D4), C23⋊4(C4×D5), Dic5⋊9(C2×D4), C22⋊C4⋊50D10, (C2×Dic5)⋊23D4, D10⋊3(C22×C4), (C2×C10).29C24, C10.29(C23×C4), (C23×Dic5)⋊3C2, Dic5⋊2(C22×C4), C22.124(D4×D5), C10.34(C22×D4), (C2×C20).570C23, (C4×Dic5)⋊73C22, (C22×C4).312D10, D10⋊C4⋊56C22, C22.18(C23×D5), C10.D4⋊57C22, (C23×C10).55C22, C23.319(C22×D5), C22.66(D4⋊2D5), (C22×C10).121C23, (C22×C20).351C22, (C2×Dic5).370C23, (C22×Dic5)⋊41C22, (C23×D5).106C22, (C22×D5).159C23, C5⋊3(C2×C4×D4), C2.2(C2×D4×D5), C22⋊2(C2×C4×D5), C5⋊D4⋊9(C2×C4), (C2×C5⋊D4)⋊13C4, (C2×C4×Dic5)⋊30C2, (D5×C22×C4)⋊16C2, (C2×C4×D5)⋊64C22, C2.10(D5×C22×C4), (C2×C10)⋊6(C22×C4), (C2×C22⋊C4)⋊19D5, C10.67(C2×C4○D4), C2.2(C2×D4⋊2D5), (C10×C22⋊C4)⋊25C2, (C22×C10)⋊16(C2×C4), (C2×Dic5)⋊25(C2×C4), (C2×C10).380(C2×D4), (C22×D5)⋊15(C2×C4), (C2×D10⋊C4)⋊30C2, (C22×C5⋊D4).8C2, (C2×C10.D4)⋊35C2, (C5×C22⋊C4)⋊60C22, (C2×C4).256(C22×D5), (C2×C5⋊D4).95C22, (C2×C10).167(C4○D4), SmallGroup(320,1157)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C10 — C2×Dic5⋊4D4
Chief series
C1 — C5 — C10 — C2×C10 — C22×D5 — C23×D5 — C22×C5⋊D4 — C2×Dic5⋊4D4
Lower central
C5 — C10 — C2×Dic5⋊4D4

Subgroups: 1358 in 426 conjugacy classes, 175 normal (31 characteristic)
C1, C2 [×3], C2 [×4], C2 [×8], C4 [×14], C22, C22 [×10], C22 [×28], C5, C2×C4 [×4], C2×C4 [×36], D4 [×16], C23, C23 [×6], C23 [×14], D5 [×4], C10 [×3], C10 [×4], C10 [×4], C42 [×4], C22⋊C4 [×4], C22⋊C4 [×4], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×19], C2×D4 [×12], C24, C24, Dic5 [×8], Dic5 [×2], C20 [×4], D10 [×4], D10 [×12], C2×C10, C2×C10 [×10], C2×C10 [×12], C2×C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C4×D4 [×8], C23×C4 [×2], C22×D4, C4×D5 [×8], C2×Dic5 [×14], C2×Dic5 [×10], C5⋊D4 [×16], C2×C20 [×4], C2×C20 [×4], C22×D5 [×6], C22×D5 [×4], C22×C10, C22×C10 [×6], C22×C10 [×4], C2×C4×D4, C4×Dic5 [×4], C10.D4 [×4], D10⋊C4 [×4], C5×C22⋊C4 [×4], C2×C4×D5 [×4], C2×C4×D5 [×4], C22×Dic5 [×3], C22×Dic5 [×4], C22×Dic5 [×4], C2×C5⋊D4 [×12], C22×C20 [×2], C23×D5, C23×C10, Dic5⋊4D4 [×8], C2×C4×Dic5, C2×C10.D4, C2×D10⋊C4, C10×C22⋊C4, D5×C22×C4, C23×Dic5, C22×C5⋊D4, C2×Dic5⋊4D4

Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], D4 [×4], C23 [×15], D5, C22×C4 [×14], C2×D4 [×6], C4○D4 [×2], C24, D10 [×7], C4×D4 [×4], C23×C4, C22×D4, C2×C4○D4, C4×D5 [×4], C22×D5 [×7], C2×C4×D4, C2×C4×D5 [×6], D4×D5 [×2], D4⋊2D5 [×2], C23×D5, Dic5⋊4D4 [×4], D5×C22×C4, C2×D4×D5, C2×D4⋊2D5, C2×Dic5⋊4D4

Generators and relations
 G = < a,b,c,d,e | a2=b10=d4=e2=1, c2=b5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, cd=dc, ce=ec, ede=d-1 >

Smallest permutation representation
►On 160 points
Generators in S160
(1 107)(2 108)(3 109)(4 110)(5 101)(6 102)(7 103)(8 104)(9 105)(10 106)(11 72)(12 73)(13 74)(14 75)(15 76)(16 77)(17 78)(18 79)(19 80)(20 71)(21 98)(22 99)(23 100)(24 91)(25 92)(26 93)(27 94)(28 95)(29 96)(30 97)(31 124)(32 125)(33 126)(34 127)(35 128)(36 129)(37 130)(38 121)(39 122)(40 123)(41 118)(42 119)(43 120)(44 111)(45 112)(46 113)(47 114)(48 115)(49 116)(50 117)(51 144)(52 145)(53 146)(54 147)(55 148)(56 149)(57 150)(58 141)(59 142)(60 143)(61 138)(62 139)(63 140)(64 131)(65 132)(66 133)(67 134)(68 135)(69 136)(70 137)(81 158)(82 159)(83 160)(84 151)(85 152)(86 153)(87 154)(88 155)(89 156)(90 157)

(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 42 6 47)(2 41 7 46)(3 50 8 45)(4 49 9 44)(5 48 10 43)(11 136 16 131)(12 135 17 140)(13 134 18 139)(14 133 19 138)(15 132 20 137)(21 35 26 40)(22 34 27 39)(23 33 28 38)(24 32 29 37)(25 31 30 36)(51 85 56 90)(52 84 57 89)(53 83 58 88)(54 82 59 87)(55 81 60 86)(61 75 66 80)(62 74 67 79)(63 73 68 78)(64 72 69 77)(65 71 70 76)(91 125 96 130)(92 124 97 129)(93 123 98 128)(94 122 99 127)(95 121 100 126)(101 115 106 120)(102 114 107 119)(103 113 108 118)(104 112 109 117)(105 111 110 116)(141 155 146 160)(142 154 147 159)(143 153 148 158)(144 152 149 157)(145 151 150 156)

(1 134 27 147)(2 133 28 146)(3 132 29 145)(4 131 30 144)(5 140 21 143)(6 139 22 142)(7 138 23 141)(8 137 24 150)(9 136 25 149)(10 135 26 148)(11 36 152 49)(12 35 153 48)(13 34 154 47)(14 33 155 46)(15 32 156 45)(16 31 157 44)(17 40 158 43)(18 39 159 42)(19 38 160 41)(20 37 151 50)(51 110 64 97)(52 109 65 96)(53 108 66 95)(54 107 67 94)(55 106 68 93)(56 105 69 92)(57 104 70 91)(58 103 61 100)(59 102 62 99)(60 101 63 98)(71 130 84 117)(72 129 85 116)(73 128 86 115)(74 127 87 114)(75 126 88 113)(76 125 89 112)(77 124 90 111)(78 123 81 120)(79 122 82 119)(80 121 83 118)

(1 54)(2 55)(3 56)(4 57)(5 58)(6 59)(7 60)(8 51)(9 52)(10 53)(11 125)(12 126)(13 127)(14 128)(15 129)(16 130)(17 121)(18 122)(19 123)(20 124)(21 61)(22 62)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 81)(42 82)(43 83)(44 84)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(91 131)(92 132)(93 133)(94 134)(95 135)(96 136)(97 137)(98 138)(99 139)(100 140)(101 141)(102 142)(103 143)(104 144)(105 145)(106 146)(107 147)(108 148)(109 149)(110 150)(111 151)(112 152)(113 153)(114 154)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)
 
G:=sub<Sym(160)| (1,107)(2,108)(3,109)(4,110)(5,101)(6,102)(7,103)(8,104)(9,105)(10,106)(11,72)(12,73)(13,74)(14,75)(15,76)(16,77)(17,78)(18,79)(19,80)(20,71)(21,98)(22,99)(23,100)(24,91)(25,92)(26,93)(27,94)(28,95)(29,96)(30,97)(31,124)(32,125)(33,126)(34,127)(35,128)(36,129)(37,130)(38,121)(39,122)(40,123)(41,118)(42,119)(43,120)(44,111)(45,112)(46,113)(47,114)(48,115)(49,116)(50,117)(51,144)(52,145)(53,146)(54,147)(55,148)(56,149)(57,150)(58,141)(59,142)(60,143)(61,138)(62,139)(63,140)(64,131)(65,132)(66,133)(67,134)(68,135)(69,136)(70,137)(81,158)(82,159)(83,160)(84,151)(85,152)(86,153)(87,154)(88,155)(89,156)(90,157), (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), (1,42,6,47)(2,41,7,46)(3,50,8,45)(4,49,9,44)(5,48,10,43)(11,136,16,131)(12,135,17,140)(13,134,18,139)(14,133,19,138)(15,132,20,137)(21,35,26,40)(22,34,27,39)(23,33,28,38)(24,32,29,37)(25,31,30,36)(51,85,56,90)(52,84,57,89)(53,83,58,88)(54,82,59,87)(55,81,60,86)(61,75,66,80)(62,74,67,79)(63,73,68,78)(64,72,69,77)(65,71,70,76)(91,125,96,130)(92,124,97,129)(93,123,98,128)(94,122,99,127)(95,121,100,126)(101,115,106,120)(102,114,107,119)(103,113,108,118)(104,112,109,117)(105,111,110,116)(141,155,146,160)(142,154,147,159)(143,153,148,158)(144,152,149,157)(145,151,150,156), (1,134,27,147)(2,133,28,146)(3,132,29,145)(4,131,30,144)(5,140,21,143)(6,139,22,142)(7,138,23,141)(8,137,24,150)(9,136,25,149)(10,135,26,148)(11,36,152,49)(12,35,153,48)(13,34,154,47)(14,33,155,46)(15,32,156,45)(16,31,157,44)(17,40,158,43)(18,39,159,42)(19,38,160,41)(20,37,151,50)(51,110,64,97)(52,109,65,96)(53,108,66,95)(54,107,67,94)(55,106,68,93)(56,105,69,92)(57,104,70,91)(58,103,61,100)(59,102,62,99)(60,101,63,98)(71,130,84,117)(72,129,85,116)(73,128,86,115)(74,127,87,114)(75,126,88,113)(76,125,89,112)(77,124,90,111)(78,123,81,120)(79,122,82,119)(80,121,83,118), (1,54)(2,55)(3,56)(4,57)(5,58)(6,59)(7,60)(8,51)(9,52)(10,53)(11,125)(12,126)(13,127)(14,128)(15,129)(16,130)(17,121)(18,122)(19,123)(20,124)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(99,139)(100,140)(101,141)(102,142)(103,143)(104,144)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160)>;
 
G:=Group( (1,107)(2,108)(3,109)(4,110)(5,101)(6,102)(7,103)(8,104)(9,105)(10,106)(11,72)(12,73)(13,74)(14,75)(15,76)(16,77)(17,78)(18,79)(19,80)(20,71)(21,98)(22,99)(23,100)(24,91)(25,92)(26,93)(27,94)(28,95)(29,96)(30,97)(31,124)(32,125)(33,126)(34,127)(35,128)(36,129)(37,130)(38,121)(39,122)(40,123)(41,118)(42,119)(43,120)(44,111)(45,112)(46,113)(47,114)(48,115)(49,116)(50,117)(51,144)(52,145)(53,146)(54,147)(55,148)(56,149)(57,150)(58,141)(59,142)(60,143)(61,138)(62,139)(63,140)(64,131)(65,132)(66,133)(67,134)(68,135)(69,136)(70,137)(81,158)(82,159)(83,160)(84,151)(85,152)(86,153)(87,154)(88,155)(89,156)(90,157), (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), (1,42,6,47)(2,41,7,46)(3,50,8,45)(4,49,9,44)(5,48,10,43)(11,136,16,131)(12,135,17,140)(13,134,18,139)(14,133,19,138)(15,132,20,137)(21,35,26,40)(22,34,27,39)(23,33,28,38)(24,32,29,37)(25,31,30,36)(51,85,56,90)(52,84,57,89)(53,83,58,88)(54,82,59,87)(55,81,60,86)(61,75,66,80)(62,74,67,79)(63,73,68,78)(64,72,69,77)(65,71,70,76)(91,125,96,130)(92,124,97,129)(93,123,98,128)(94,122,99,127)(95,121,100,126)(101,115,106,120)(102,114,107,119)(103,113,108,118)(104,112,109,117)(105,111,110,116)(141,155,146,160)(142,154,147,159)(143,153,148,158)(144,152,149,157)(145,151,150,156), (1,134,27,147)(2,133,28,146)(3,132,29,145)(4,131,30,144)(5,140,21,143)(6,139,22,142)(7,138,23,141)(8,137,24,150)(9,136,25,149)(10,135,26,148)(11,36,152,49)(12,35,153,48)(13,34,154,47)(14,33,155,46)(15,32,156,45)(16,31,157,44)(17,40,158,43)(18,39,159,42)(19,38,160,41)(20,37,151,50)(51,110,64,97)(52,109,65,96)(53,108,66,95)(54,107,67,94)(55,106,68,93)(56,105,69,92)(57,104,70,91)(58,103,61,100)(59,102,62,99)(60,101,63,98)(71,130,84,117)(72,129,85,116)(73,128,86,115)(74,127,87,114)(75,126,88,113)(76,125,89,112)(77,124,90,111)(78,123,81,120)(79,122,82,119)(80,121,83,118), (1,54)(2,55)(3,56)(4,57)(5,58)(6,59)(7,60)(8,51)(9,52)(10,53)(11,125)(12,126)(13,127)(14,128)(15,129)(16,130)(17,121)(18,122)(19,123)(20,124)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(99,139)(100,140)(101,141)(102,142)(103,143)(104,144)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160) );
 
G=PermutationGroup([(1,107),(2,108),(3,109),(4,110),(5,101),(6,102),(7,103),(8,104),(9,105),(10,106),(11,72),(12,73),(13,74),(14,75),(15,76),(16,77),(17,78),(18,79),(19,80),(20,71),(21,98),(22,99),(23,100),(24,91),(25,92),(26,93),(27,94),(28,95),(29,96),(30,97),(31,124),(32,125),(33,126),(34,127),(35,128),(36,129),(37,130),(38,121),(39,122),(40,123),(41,118),(42,119),(43,120),(44,111),(45,112),(46,113),(47,114),(48,115),(49,116),(50,117),(51,144),(52,145),(53,146),(54,147),(55,148),(56,149),(57,150),(58,141),(59,142),(60,143),(61,138),(62,139),(63,140),(64,131),(65,132),(66,133),(67,134),(68,135),(69,136),(70,137),(81,158),(82,159),(83,160),(84,151),(85,152),(86,153),(87,154),(88,155),(89,156),(90,157)], [(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)], [(1,42,6,47),(2,41,7,46),(3,50,8,45),(4,49,9,44),(5,48,10,43),(11,136,16,131),(12,135,17,140),(13,134,18,139),(14,133,19,138),(15,132,20,137),(21,35,26,40),(22,34,27,39),(23,33,28,38),(24,32,29,37),(25,31,30,36),(51,85,56,90),(52,84,57,89),(53,83,58,88),(54,82,59,87),(55,81,60,86),(61,75,66,80),(62,74,67,79),(63,73,68,78),(64,72,69,77),(65,71,70,76),(91,125,96,130),(92,124,97,129),(93,123,98,128),(94,122,99,127),(95,121,100,126),(101,115,106,120),(102,114,107,119),(103,113,108,118),(104,112,109,117),(105,111,110,116),(141,155,146,160),(142,154,147,159),(143,153,148,158),(144,152,149,157),(145,151,150,156)], [(1,134,27,147),(2,133,28,146),(3,132,29,145),(4,131,30,144),(5,140,21,143),(6,139,22,142),(7,138,23,141),(8,137,24,150),(9,136,25,149),(10,135,26,148),(11,36,152,49),(12,35,153,48),(13,34,154,47),(14,33,155,46),(15,32,156,45),(16,31,157,44),(17,40,158,43),(18,39,159,42),(19,38,160,41),(20,37,151,50),(51,110,64,97),(52,109,65,96),(53,108,66,95),(54,107,67,94),(55,106,68,93),(56,105,69,92),(57,104,70,91),(58,103,61,100),(59,102,62,99),(60,101,63,98),(71,130,84,117),(72,129,85,116),(73,128,86,115),(74,127,87,114),(75,126,88,113),(76,125,89,112),(77,124,90,111),(78,123,81,120),(79,122,82,119),(80,121,83,118)], [(1,54),(2,55),(3,56),(4,57),(5,58),(6,59),(7,60),(8,51),(9,52),(10,53),(11,125),(12,126),(13,127),(14,128),(15,129),(16,130),(17,121),(18,122),(19,123),(20,124),(21,61),(22,62),(23,63),(24,64),(25,65),(26,66),(27,67),(28,68),(29,69),(30,70),(31,71),(32,72),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(41,81),(42,82),(43,83),(44,84),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(91,131),(92,132),(93,133),(94,134),(95,135),(96,136),(97,137),(98,138),(99,139),(100,140),(101,141),(102,142),(103,143),(104,144),(105,145),(106,146),(107,147),(108,148),(109,149),(110,150),(111,151),(112,152),(113,153),(114,154),(115,155),(116,156),(117,157),(118,158),(119,159),(120,160)])
 

Matrix representation ►G ⊆ GL6(𝔽41)

4000000
0400000
001000
000100
000010
000001
,
7400000
8400000
0034100
0033100
000010
000001
,
3410000
3470000
00223200
00221900
000010
000001
,
7400000
7340000
0034100
0034700
00004039
000011
,
100000
010000
001000
000100
00004039
000001

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],[7,8,0,0,0,0,40,40,0,0,0,0,0,0,34,33,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[34,34,0,0,0,0,1,7,0,0,0,0,0,0,22,22,0,0,0,0,32,19,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[7,7,0,0,0,0,40,34,0,0,0,0,0,0,34,34,0,0,0,0,1,7,0,0,0,0,0,0,40,1,0,0,0,0,39,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,39,1] >;
 

80 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M2N2O4A···4H4I···4P4Q···4X5A5B10A···10N10O···10V20A···20P
order12···2222222224···44···44···45510···1010···1020···20
size11···12222101010102···25···510···10222···24···44···4

80 irreducible representations

dim1111111111222222244
type+++++++++++++++-
imageC1C2C2C2C2C2C2C2C2C4D4D5C4○D4D10D10D10C4×D5D4×D5D4⋊2D5
kernelC2×Dic5⋊4D4Dic5⋊4D4C2×C4×Dic5C2×C10.D4C2×D10⋊C4C10×C22⋊C4D5×C22×C4C23×Dic5C22×C5⋊D4C2×C5⋊D4C2×Dic5C2×C22⋊C4C2×C10C22⋊C4C22×C4C24C23C22C22
# reps181111111164248421644

In GAP, Magma, Sage, TeX 

C_2\times Dic_5\rtimes_4D_4
 
% in TeX
 
G:=Group("C2xDic5:4D4");
 
// GroupNames label
 
G:=SmallGroup(320,1157);
 
// by ID
 
G=gap.SmallGroup(320,1157);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,297,80,12550]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^10=d^4=e^2=1,c^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=d*b*d^-1=b^-1,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^-1>;
 
// generators/relations
 

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