C2xDic5.14D4 - GroupNames

G = C₂×Dic₅.₁₄D₄ order 320 = 2⁶·5

Direct product of C₂ and Dic₅.₁₄D₄

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

Aliases: C₂×Dic₅.₁₄D₄, C₂³⋊₃Dic₁₀, C₂⁴.₅₁D₁₀, (C₂²×C₁₀)⋊₄Q₈, C₁₀⋊₁(C₂²⋊Q₈), C₁₀.₅(C₂²×Q₈), (C₂×C₁₀).₂₅C₂⁴, C₄⋊Dic₅⋊₄₉C₂², C₂²⋊C₄.₈₄D₁₀, Dic₅.₈₁(C₂×D₄), C₂²⋊₂(C₂×Dic₁₀), C₁₀.₃₂(C₂²×D₄), C₂².₁₂₂(D₄×D₅), (C₂×C₂₀).₁₂₅C₂³, (C₂×Dic₅).₂₄₅D₄, (C₂²×Dic₁₀)⋊₅C₂, (C₂²×C₄).₁₆₇D₁₀, (C₂³×Dic₅).₈C₂, C₂.₇(C₂²×Dic₁₀), C₂².₆₇(C₂³×D₅), (C₂×Dic₁₀)⋊₄₇C₂², C₁₀.D₄⋊₄₆C₂², (C₂²×C₂₀).₇₀C₂², (C₂³×C₁₀).₅₁C₂², C₂³.₃₁₈(C₂²×D₅), C₂³.D₅.₈₃C₂², C₂².₆₄(D₄⋊₂D₅), (C₂²×C₁₀).₁₁₇C₂³, (C₂×Dic₅).₁₈₅C₂³, (C₂²×Dic₅).₂₂₅C₂², C₂.₇(C₂×D₄×D₅), C₅⋊₁(C₂×C₂²⋊Q₈), (C₂×C₁₀)⋊₄(C₂×Q₈), (C₂×C₄⋊Dic₅)⋊₁₇C₂, C₁₀.₆₆(C₂×C₄○D₄), C₂.₇(C₂×D₄⋊₂D₅), (C₂×C₁₀).₃₇₈(C₂×D₄), (C₂×C₂²⋊C₄).₁₆D₅, (C₂×C₁₀.D₄)⋊₂₁C₂, (C₁₀×C₂²⋊C₄).₁₇C₂, (C₂×C₄).₁₃₂(C₂²×D₅), (C₂×C₂³.D₅).₂₀C₂, (C₂×C₁₀).₁₆₆(C₄○D₄), (C₅×C₂²⋊C₄).₉₆C₂², SmallGroup(320,1153)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂×C₁₀ — C₂×Dic₅.₁₄D₄

Chief series

C₁ — C₅ — C₁₀ — C₂×C₁₀ — C₂×Dic₅ — C₂²×Dic₅ — C₂³×Dic₅ — C₂×Dic₅.₁₄D₄

Lower central

C₅ — C₂×C₁₀ — C₂×Dic₅.₁₄D₄

Upper central

C₁ — C₂³ — C₂×C₂²⋊C₄

Generators and relations for C₂×Dic₅.₁₄D₄
G = < a,b,c,d,e | a²=b¹⁰=d⁴=e²=1, c²=b⁵, ab=ba, ac=ca, ad=da, ae=ea, cbc^-1=b^-1, bd=db, be=eb, dcd^-1=b⁵c, ce=ec, ede=b⁵d^-1 >

Subgroups: 974 in 322 conjugacy classes, 135 normal (31 characteristic)
C₁, C₂, C₂, C₂, C₄, C₂², C₂², C₂², C₅, C₂×C₄, C₂×C₄, Q₈, C₂³, C₂³, C₂³, C₁₀, C₁₀, C₁₀, C₂²⋊C₄, C₂²⋊C₄, C₄⋊C₄, C₂²×C₄, C₂²×C₄, C₂×Q₈, C₂⁴, Dic₅, Dic₅, C₂₀, C₂×C₁₀, C₂×C₁₀, C₂×C₁₀, C₂×C₂²⋊C₄, C₂×C₂²⋊C₄, C₂×C₄⋊C₄, C₂²⋊Q₈, C₂³×C₄, C₂²×Q₈, Dic₁₀, C₂×Dic₅, C₂×Dic₅, C₂×C₂₀, C₂×C₂₀, C₂²×C₁₀, C₂²×C₁₀, C₂²×C₁₀, C₂×C₂²⋊Q₈, C₁₀.D₄, C₄⋊Dic₅, C₂³.D₅, C₅×C₂²⋊C₄, C₂×Dic₁₀, C₂×Dic₁₀, C₂²×Dic₅, C₂²×Dic₅, C₂²×Dic₅, C₂²×C₂₀, C₂³×C₁₀, Dic₅.₁₄D₄, C₂×C₁₀.D₄, C₂×C₄⋊Dic₅, C₂×C₂³.D₅, C₁₀×C₂²⋊C₄, C₂²×Dic₁₀, C₂³×Dic₅, C₂×Dic₅.₁₄D₄
Quotients: C₁, C₂, C₂², D₄, Q₈, C₂³, D₅, C₂×D₄, C₂×Q₈, C₄○D₄, C₂⁴, D₁₀, C₂²⋊Q₈, C₂²×D₄, C₂²×Q₈, C₂×C₄○D₄, Dic₁₀, C₂²×D₅, C₂×C₂²⋊Q₈, C₂×Dic₁₀, D₄×D₅, D₄⋊₂D₅, C₂³×D₅, Dic₅.₁₄D₄, C₂²×Dic₁₀, C₂×D₄×D₅, C₂×D₄⋊₂D₅, C₂×Dic₅.₁₄D₄

Smallest permutation representation of C₂×Dic₅.₁₄D₄
►On 160 points

Generators in S₁₆₀

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

(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)

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

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

(11 154)(12 155)(13 156)(14 157)(15 158)(16 159)(17 160)(18 151)(19 152)(20 153)(31 42)(32 43)(33 44)(34 45)(35 46)(36 47)(37 48)(38 49)(39 50)(40 41)(71 85)(72 86)(73 87)(74 88)(75 89)(76 90)(77 81)(78 82)(79 83)(80 84)(111 125)(112 126)(113 127)(114 128)(115 129)(116 130)(117 121)(118 122)(119 123)(120 124)

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

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

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

68 conjugacy classes

class	1	2A	···	2G	2H	2I	2J	2K	4A	4B	4C	4D	4E	···	4L	4M	4N	4O	4P	5A	5B	10A	···	10N	10O	···	10V	20A	···	20P
order	1	2	···	2	2	2	2	2	4	4	4	4	4	···	4	4	4	4	4	5	5	10	···	10	10	···	10	20	···	20
size	1	1	···	1	2	2	2	2	4	4	4	4	10	···	10	20	20	20	20	2	2	2	···	2	4	···	4	4	···	4

68 irreducible representations

dim	1	1	1	1	1	1	1	1	2	2	2	2	2	2	2	2	4	4
type	+	+	+	+	+	+	+	+	+	-	+		+	+	+	-	+	-
image	C₁	C₂	C₂	C₂	C₂	C₂	C₂	C₂	D₄	Q₈	D₅	C₄○D₄	D₁₀	D₁₀	D₁₀	Dic₁₀	D₄×D₅	D₄⋊₂D₅
kernel	C₂×Dic₅.₁₄D₄	Dic₅.₁₄D₄	C₂×C₁₀.D₄	C₂×C₄⋊Dic₅	C₂×C₂³.D₅	C₁₀×C₂²⋊C₄	C₂²×Dic₁₀	C₂³×Dic₅	C₂×Dic₅	C₂²×C₁₀	C₂×C₂²⋊C₄	C₂×C₁₀	C₂²⋊C₄	C₂²×C₄	C₂⁴	C₂³	C₂²	C₂²
# reps	1	8	2	1	1	1	1	1	4	4	2	4	8	4	2	16	4	4

Matrix representation of C₂×Dic₅.₁₄D₄ ►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	40	0
0	0	0	0	0	40

34	40	0	0	0	0
1	0	0	0	0	0
0	0	1	1	0	0
0	0	5	6	0	0
0	0	0	0	40	0
0	0	0	0	0	40

2	35	0	0	0	0
21	39	0	0	0	0
0	0	20	3	0	0
0	0	3	21	0	0
0	0	0	0	32	0
0	0	0	0	0	9

40	0	0	0	0	0
0	40	0	0	0	0
0	0	39	9	0	0
0	0	4	2	0	0
0	0	0	0	0	40
0	0	0	0	40	0

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	1	0
0	0	0	0	0	40

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[34,1,0,0,0,0,40,0,0,0,0,0,0,0,1,5,0,0,0,0,1,6,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[2,21,0,0,0,0,35,39,0,0,0,0,0,0,20,3,0,0,0,0,3,21,0,0,0,0,0,0,32,0,0,0,0,0,0,9],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,39,4,0,0,0,0,9,2,0,0,0,0,0,0,0,40,0,0,0,0,40,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40] >;

C₂×Dic₅.₁₄D₄ in GAP, Magma, Sage, TeX

C_2\times {\rm Dic}_5._{14}D_4

% in TeX

G:=Group("C2xDic5.14D4");

// GroupNames label

G:=SmallGroup(320,1153);

// by ID

G=gap.SmallGroup(320,1153);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,675,297,80,12550]);

// 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=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=b^5*c,c*e=e*c,e*d*e=b^5*d^-1>;

// generators/relations

G = C2×Dic5.14D4 order 320 = 26·5

Direct product of C2 and Dic5.14D4

G = C₂×Dic₅.₁₄D₄ order 320 = 2⁶·5

Direct product of C₂ and Dic₅.₁₄D₄