(C2xQ16):D5 - GroupNames

G = (C₂×Q₁₆)⋊D₅ order 320 = 2⁶·5

2^nd semidirect product of C₂×Q₁₆ and D₅ acting via D₅/C₅=C₂

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C₂×Q₁₆)⋊₂D₅, (C₅×Q₈).₈D₄, (Q₈×Dic₅)⋊₇C₂, (C₂×C₈).₃₇D₁₀, (C₁₀×Q₁₆)⋊₁₂C₂, C₂₀.₁₈₅(C₂×D₄), (C₂×Q₈).₆₁D₁₀, Q₈.₃(C₅⋊D₄), C₅⋊₇(Q₈.D₄), C₁₀.₇₉(C₄○D₈), Q₈⋊Dic₅⋊₃₂C₂, C₂₀.₈Q₈⋊₂₉C₂, (C₂×Dic₅).₈₃D₄, C₂².₂₇₆(D₄×D₅), D₂₀⋊₅C₄.₁₂C₂, C₂₀.₁₀₆(C₄○D₄), C₄.₁₄(D₄⋊₂D₅), (C₂×C₂₀).₄₅₉C₂³, (C₂×C₄₀).₂₅₁C₂², C₂₀.₂₃D₄.₇C₂, (Q₈×C₁₀).₈₈C₂², C₂.₁₆(Q₈.D₁₀), C₁₀.₁₂₀(C₄⋊D₄), C₂.₂₇(Q₁₆⋊D₅), (C₂×D₂₀).₁₂₈C₂², C₁₀.₇₇(C₈.C₂²), C₄⋊Dic₅.₁₈₂C₂², (C₄×Dic₅).₆₁C₂², C₂.₂₉(Dic₅⋊D₄), C₄.₄₇(C₂×C₅⋊D₄), (C₂×Q₈⋊D₅).₈C₂, (C₂×C₁₀).₃₇₀(C₂×D₄), (C₂×C₄).₅₄₇(C₂²×D₅), (C₂×C₅⋊₂C₈).₁₆₄C₂², SmallGroup(320,812)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂×C₂₀ — (C₂×Q₁₆)⋊D₅

Chief series

C₁ — C₅ — C₁₀ — C₂₀ — C₂×C₂₀ — C₄×Dic₅ — Q₈×Dic₅ — (C₂×Q₁₆)⋊D₅

Lower central

C₅ — C₁₀ — C₂×C₂₀ — (C₂×Q₁₆)⋊D₅

Upper central

C₁ — C₂² — C₂×C₄ — C₂×Q₁₆

Generators and relations for (C₂×Q₁₆)⋊D₅
G = < a,b,c,d,e | a²=b⁸=d⁵=e²=1, c²=b⁴, ab=ba, ece=ac=ca, ad=da, ae=ea, cbc^-1=b^-1, bd=db, ebe=ab^-1, cd=dc, ede=d^-1 >

Subgroups: 454 in 112 conjugacy classes, 41 normal (37 characteristic)
C₁, C₂, C₂, C₄, C₄, C₂², C₂², C₅, C₈, C₂×C₄, C₂×C₄, D₄, Q₈, Q₈, C₂³, D₅, C₁₀, C₄², C₂²⋊C₄, C₄⋊C₄, C₂×C₈, C₂×C₈, SD₁₆, Q₁₆, C₂×D₄, C₂×Q₈, Dic₅, C₂₀, C₂₀, D₁₀, C₂×C₁₀, D₄⋊C₄, Q₈⋊C₄, C₄⋊C₈, C₄×Q₈, C₄.₄D₄, C₂×SD₁₆, C₂×Q₁₆, C₅⋊₂C₈, C₄₀, D₂₀, C₂×Dic₅, C₂×Dic₅, C₂×C₂₀, C₂×C₂₀, C₅×Q₈, C₅×Q₈, C₂²×D₅, Q₈.D₄, C₂×C₅⋊₂C₈, C₄×Dic₅, C₄×Dic₅, C₄⋊Dic₅, C₄⋊Dic₅, D₁₀⋊C₄, Q₈⋊D₅, C₂×C₄₀, C₅×Q₁₆, C₂×D₂₀, Q₈×C₁₀, C₂₀.₈Q₈, D₂₀⋊₅C₄, Q₈⋊Dic₅, C₂×Q₈⋊D₅, Q₈×Dic₅, C₂₀.₂₃D₄, C₁₀×Q₁₆, (C₂×Q₁₆)⋊D₅
Quotients: C₁, C₂, C₂², D₄, C₂³, D₅, C₂×D₄, C₄○D₄, D₁₀, C₄⋊D₄, C₄○D₈, C₈.C₂², C₅⋊D₄, C₂²×D₅, Q₈.D₄, D₄×D₅, D₄⋊₂D₅, C₂×C₅⋊D₄, Q₁₆⋊D₅, Q₈.D₁₀, Dic₅⋊D₄, (C₂×Q₁₆)⋊D₅

Smallest permutation representation of (C₂×Q₁₆)⋊D₅
►On 160 points

Generators in S₁₆₀

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

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

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

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

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

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

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

47 conjugacy classes

class	1	2A	2B	2C	2D	4A	4B	4C	4D	4E	4F	4G	4H	4I	4J	5A	5B	8A	8B	8C	8D	10A	···	10F	20A	20B	20C	20D	20E	···	20L	40A	···	40H
order	1	2	2	2	2	4	4	4	4	4	4	4	4	4	4	5	5	8	8	8	8	10	···	10	20	20	20	20	20	···	20	40	···	40
size	1	1	1	1	40	2	2	4	4	8	10	10	20	20	20	2	2	4	4	20	20	2	···	2	4	4	4	4	8	···	8	4	···	4

47 irreducible representations

dim	1	1	1	1	1	1	1	1	2	2	2	2	2	2	2	2	4	4	4	4	4
type	+	+	+	+	+	+	+	+	+	+	+		+	+			-	-	+		+
image	C₁	C₂	C₂	C₂	C₂	C₂	C₂	C₂	D₄	D₄	D₅	C₄○D₄	D₁₀	D₁₀	C₄○D₈	C₅⋊D₄	C₈.C₂²	D₄⋊₂D₅	D₄×D₅	Q₁₆⋊D₅	Q₈.D₁₀
kernel	(C₂×Q₁₆)⋊D₅	C₂₀.₈Q₈	D₂₀⋊₅C₄	Q₈⋊Dic₅	C₂×Q₈⋊D₅	Q₈×Dic₅	C₂₀.₂₃D₄	C₁₀×Q₁₆	C₂×Dic₅	C₅×Q₈	C₂×Q₁₆	C₂₀	C₂×C₈	C₂×Q₈	C₁₀	Q₈	C₁₀	C₄	C₂²	C₂	C₂
# reps	1	1	1	1	1	1	1	1	2	2	2	2	2	4	4	8	1	2	2	4	4

Matrix representation of (C₂×Q₁₆)⋊D₅ ►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

9	0	0	0	0	0
9	32	0	0	0	0
0	0	40	0	0	0
0	0	0	40	0	0
0	0	0	0	0	15
0	0	0	0	30	24

40	2	0	0	0	0
0	1	0	0	0	0
0	0	40	0	0	0
0	0	0	40	0	0
0	0	0	0	32	0
0	0	0	0	2	9

1	0	0	0	0	0
0	1	0	0	0	0
0	0	40	1	0	0
0	0	33	7	0	0
0	0	0	0	1	0
0	0	0	0	0	1

1	0	0	0	0	0
1	40	0	0	0	0
0	0	40	0	0	0
0	0	33	1	0	0
0	0	0	0	1	0
0	0	0	0	18	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],[9,9,0,0,0,0,0,32,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,30,0,0,0,0,15,24],[40,0,0,0,0,0,2,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,32,2,0,0,0,0,0,9],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,33,0,0,0,0,1,7,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,40,0,0,0,0,0,0,40,33,0,0,0,0,0,1,0,0,0,0,0,0,1,18,0,0,0,0,0,40] >;

(C₂×Q₁₆)⋊D₅ in GAP, Magma, Sage, TeX

(C_2\times Q_{16})\rtimes D_5

% in TeX

G:=Group("(C2xQ16):D5");

// GroupNames label

G:=SmallGroup(320,812);

// by ID

G=gap.SmallGroup(320,812);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,1094,135,184,570,297,136,12550]);

// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^8=d^5=e^2=1,c^2=b^4,a*b=b*a,e*c*e=a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,e*b*e=a*b^-1,c*d=d*c,e*d*e=d^-1>;

// generators/relations

G = (C2×Q16)⋊D5 order 320 = 26·5

2nd semidirect product of C2×Q16 and D5 acting via D5/C5=C2

G = (C₂×Q₁₆)⋊D₅ order 320 = 2⁶·5

2^nd semidirect product of C₂×Q₁₆ and D₅ acting via D₅/C₅=C₂