direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q16⋊D5, Q16⋊8D10, C20.11C24, C40.41C23, D20.6C23, Dic10.7C23, C4.47(D4×D5), (C2×Q16)⋊11D5, (C4×D5).17D4, C20.86(C2×D4), Q8⋊D5⋊9C22, (Q8×D5)⋊7C22, (C10×Q16)⋊11C2, D10.86(C2×D4), (C2×C8).104D10, C5⋊2C8.4C23, C5⋊Q16⋊9C22, (C4×D5).6C23, C4.11(C23×D5), C8.13(C22×D5), (C5×Q8).5C23, Q8.5(C22×D5), C8⋊D5⋊14C22, C40⋊C2⋊15C22, C10⋊3(C8.C22), (C2×Q8).153D10, Dic5.97(C2×D4), (C5×Q16)⋊12C22, C22.143(D4×D5), (C2×C40).152C22, (C2×C20).528C23, (C2×Dic5).250D4, (C22×D5).137D4, C10.112(C22×D4), Q8⋊2D5.8C22, (C2×D20).185C22, (Q8×C10).150C22, (C2×Dic10).205C22, (C2×Q8×D5)⋊16C2, C2.85(C2×D4×D5), C5⋊3(C2×C8.C22), (C2×C8⋊D5)⋊9C2, (C2×Q8⋊D5)⋊27C2, (C2×C40⋊C2)⋊25C2, (C2×C5⋊Q16)⋊28C2, (C2×C10).401(C2×D4), (C2×Q8⋊2D5).8C2, (C2×C4×D5).167C22, (C2×C4).616(C22×D5), (C2×C5⋊2C8).181C22, SmallGroup(320,1436)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Q16⋊D5
G = < a,b,c,d,e | a2=b8=d5=e2=1, c2=b4, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, ebe=b5, cd=dc, ece=b4c, ede=d-1 >
Subgroups: 958 in 258 conjugacy classes, 103 normal (33 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C5, C8, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, D5, C10, C10, C2×C8, C2×C8, M4(2), SD16, Q16, Q16, C22×C4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×M4(2), C2×SD16, C2×Q16, C2×Q16, C8.C22, C22×Q8, C2×C4○D4, C5⋊2C8, C40, Dic10, Dic10, C4×D5, C4×D5, D20, D20, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×Q8, C5×Q8, C22×D5, C22×D5, C2×C8.C22, C8⋊D5, C40⋊C2, C2×C5⋊2C8, Q8⋊D5, C5⋊Q16, C2×C40, C5×Q16, C2×Dic10, C2×Dic10, C2×C4×D5, C2×C4×D5, C2×D20, C2×D20, Q8×D5, Q8×D5, Q8⋊2D5, Q8⋊2D5, Q8×C10, C2×C8⋊D5, C2×C40⋊C2, Q16⋊D5, C2×Q8⋊D5, C2×C5⋊Q16, C10×Q16, C2×Q8×D5, C2×Q8⋊2D5, C2×Q16⋊D5
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C8.C22, C22×D4, C22×D5, C2×C8.C22, D4×D5, C23×D5, Q16⋊D5, C2×D4×D5, C2×Q16⋊D5
►On 160 points
Generators in S160
(1 83)(2 84)(3 85)(4 86)(5 87)(6 88)(7 81)(8 82)(9 112)(10 105)(11 106)(12 107)(13 108)(14 109)(15 110)(16 111)(17 157)(18 158)(19 159)(20 160)(21 153)(22 154)(23 155)(24 156)(25 152)(26 145)(27 146)(28 147)(29 148)(30 149)(31 150)(32 151)(33 138)(34 139)(35 140)(36 141)(37 142)(38 143)(39 144)(40 137)(41 103)(42 104)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 91)(50 92)(51 93)(52 94)(53 95)(54 96)(55 89)(56 90)(57 132)(58 133)(59 134)(60 135)(61 136)(62 129)(63 130)(64 131)(65 128)(66 121)(67 122)(68 123)(69 124)(70 125)(71 126)(72 127)(73 113)(74 114)(75 115)(76 116)(77 117)(78 118)(79 119)(80 120)
(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 77 5 73)(2 76 6 80)(3 75 7 79)(4 74 8 78)(9 31 13 27)(10 30 14 26)(11 29 15 25)(12 28 16 32)(17 140 21 144)(18 139 22 143)(19 138 23 142)(20 137 24 141)(33 155 37 159)(34 154 38 158)(35 153 39 157)(36 160 40 156)(41 67 45 71)(42 66 46 70)(43 65 47 69)(44 72 48 68)(49 59 53 63)(50 58 54 62)(51 57 55 61)(52 64 56 60)(81 119 85 115)(82 118 86 114)(83 117 87 113)(84 116 88 120)(89 136 93 132)(90 135 94 131)(91 134 95 130)(92 133 96 129)(97 128 101 124)(98 127 102 123)(99 126 103 122)(100 125 104 121)(105 149 109 145)(106 148 110 152)(107 147 111 151)(108 146 112 150)
(1 107 33 125 133)(2 108 34 126 134)(3 109 35 127 135)(4 110 36 128 136)(5 111 37 121 129)(6 112 38 122 130)(7 105 39 123 131)(8 106 40 124 132)(9 143 67 63 88)(10 144 68 64 81)(11 137 69 57 82)(12 138 70 58 83)(13 139 71 59 84)(14 140 72 60 85)(15 141 65 61 86)(16 142 66 62 87)(17 44 56 119 30)(18 45 49 120 31)(19 46 50 113 32)(20 47 51 114 25)(21 48 52 115 26)(22 41 53 116 27)(23 42 54 117 28)(24 43 55 118 29)(73 151 159 100 92)(74 152 160 101 93)(75 145 153 102 94)(76 146 154 103 95)(77 147 155 104 96)(78 148 156 97 89)(79 149 157 98 90)(80 150 158 99 91)
(1 92)(2 89)(3 94)(4 91)(5 96)(6 93)(7 90)(8 95)(9 47)(10 44)(11 41)(12 46)(13 43)(14 48)(15 45)(16 42)(17 144)(18 141)(19 138)(20 143)(21 140)(22 137)(23 142)(24 139)(25 67)(26 72)(27 69)(28 66)(29 71)(30 68)(31 65)(32 70)(33 159)(34 156)(35 153)(36 158)(37 155)(38 160)(39 157)(40 154)(49 86)(50 83)(51 88)(52 85)(53 82)(54 87)(55 84)(56 81)(57 116)(58 113)(59 118)(60 115)(61 120)(62 117)(63 114)(64 119)(73 133)(74 130)(75 135)(76 132)(77 129)(78 134)(79 131)(80 136)(97 108)(98 105)(99 110)(100 107)(101 112)(102 109)(103 106)(104 111)(121 147)(122 152)(123 149)(124 146)(125 151)(126 148)(127 145)(128 150)
G:=sub<Sym(160)| (1,83)(2,84)(3,85)(4,86)(5,87)(6,88)(7,81)(8,82)(9,112)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,157)(18,158)(19,159)(20,160)(21,153)(22,154)(23,155)(24,156)(25,152)(26,145)(27,146)(28,147)(29,148)(30,149)(31,150)(32,151)(33,138)(34,139)(35,140)(36,141)(37,142)(38,143)(39,144)(40,137)(41,103)(42,104)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,89)(56,90)(57,132)(58,133)(59,134)(60,135)(61,136)(62,129)(63,130)(64,131)(65,128)(66,121)(67,122)(68,123)(69,124)(70,125)(71,126)(72,127)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120), (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), (1,77,5,73)(2,76,6,80)(3,75,7,79)(4,74,8,78)(9,31,13,27)(10,30,14,26)(11,29,15,25)(12,28,16,32)(17,140,21,144)(18,139,22,143)(19,138,23,142)(20,137,24,141)(33,155,37,159)(34,154,38,158)(35,153,39,157)(36,160,40,156)(41,67,45,71)(42,66,46,70)(43,65,47,69)(44,72,48,68)(49,59,53,63)(50,58,54,62)(51,57,55,61)(52,64,56,60)(81,119,85,115)(82,118,86,114)(83,117,87,113)(84,116,88,120)(89,136,93,132)(90,135,94,131)(91,134,95,130)(92,133,96,129)(97,128,101,124)(98,127,102,123)(99,126,103,122)(100,125,104,121)(105,149,109,145)(106,148,110,152)(107,147,111,151)(108,146,112,150), (1,107,33,125,133)(2,108,34,126,134)(3,109,35,127,135)(4,110,36,128,136)(5,111,37,121,129)(6,112,38,122,130)(7,105,39,123,131)(8,106,40,124,132)(9,143,67,63,88)(10,144,68,64,81)(11,137,69,57,82)(12,138,70,58,83)(13,139,71,59,84)(14,140,72,60,85)(15,141,65,61,86)(16,142,66,62,87)(17,44,56,119,30)(18,45,49,120,31)(19,46,50,113,32)(20,47,51,114,25)(21,48,52,115,26)(22,41,53,116,27)(23,42,54,117,28)(24,43,55,118,29)(73,151,159,100,92)(74,152,160,101,93)(75,145,153,102,94)(76,146,154,103,95)(77,147,155,104,96)(78,148,156,97,89)(79,149,157,98,90)(80,150,158,99,91), (1,92)(2,89)(3,94)(4,91)(5,96)(6,93)(7,90)(8,95)(9,47)(10,44)(11,41)(12,46)(13,43)(14,48)(15,45)(16,42)(17,144)(18,141)(19,138)(20,143)(21,140)(22,137)(23,142)(24,139)(25,67)(26,72)(27,69)(28,66)(29,71)(30,68)(31,65)(32,70)(33,159)(34,156)(35,153)(36,158)(37,155)(38,160)(39,157)(40,154)(49,86)(50,83)(51,88)(52,85)(53,82)(54,87)(55,84)(56,81)(57,116)(58,113)(59,118)(60,115)(61,120)(62,117)(63,114)(64,119)(73,133)(74,130)(75,135)(76,132)(77,129)(78,134)(79,131)(80,136)(97,108)(98,105)(99,110)(100,107)(101,112)(102,109)(103,106)(104,111)(121,147)(122,152)(123,149)(124,146)(125,151)(126,148)(127,145)(128,150)>;
G:=Group( (1,83)(2,84)(3,85)(4,86)(5,87)(6,88)(7,81)(8,82)(9,112)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,157)(18,158)(19,159)(20,160)(21,153)(22,154)(23,155)(24,156)(25,152)(26,145)(27,146)(28,147)(29,148)(30,149)(31,150)(32,151)(33,138)(34,139)(35,140)(36,141)(37,142)(38,143)(39,144)(40,137)(41,103)(42,104)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,89)(56,90)(57,132)(58,133)(59,134)(60,135)(61,136)(62,129)(63,130)(64,131)(65,128)(66,121)(67,122)(68,123)(69,124)(70,125)(71,126)(72,127)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120), (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), (1,77,5,73)(2,76,6,80)(3,75,7,79)(4,74,8,78)(9,31,13,27)(10,30,14,26)(11,29,15,25)(12,28,16,32)(17,140,21,144)(18,139,22,143)(19,138,23,142)(20,137,24,141)(33,155,37,159)(34,154,38,158)(35,153,39,157)(36,160,40,156)(41,67,45,71)(42,66,46,70)(43,65,47,69)(44,72,48,68)(49,59,53,63)(50,58,54,62)(51,57,55,61)(52,64,56,60)(81,119,85,115)(82,118,86,114)(83,117,87,113)(84,116,88,120)(89,136,93,132)(90,135,94,131)(91,134,95,130)(92,133,96,129)(97,128,101,124)(98,127,102,123)(99,126,103,122)(100,125,104,121)(105,149,109,145)(106,148,110,152)(107,147,111,151)(108,146,112,150), (1,107,33,125,133)(2,108,34,126,134)(3,109,35,127,135)(4,110,36,128,136)(5,111,37,121,129)(6,112,38,122,130)(7,105,39,123,131)(8,106,40,124,132)(9,143,67,63,88)(10,144,68,64,81)(11,137,69,57,82)(12,138,70,58,83)(13,139,71,59,84)(14,140,72,60,85)(15,141,65,61,86)(16,142,66,62,87)(17,44,56,119,30)(18,45,49,120,31)(19,46,50,113,32)(20,47,51,114,25)(21,48,52,115,26)(22,41,53,116,27)(23,42,54,117,28)(24,43,55,118,29)(73,151,159,100,92)(74,152,160,101,93)(75,145,153,102,94)(76,146,154,103,95)(77,147,155,104,96)(78,148,156,97,89)(79,149,157,98,90)(80,150,158,99,91), (1,92)(2,89)(3,94)(4,91)(5,96)(6,93)(7,90)(8,95)(9,47)(10,44)(11,41)(12,46)(13,43)(14,48)(15,45)(16,42)(17,144)(18,141)(19,138)(20,143)(21,140)(22,137)(23,142)(24,139)(25,67)(26,72)(27,69)(28,66)(29,71)(30,68)(31,65)(32,70)(33,159)(34,156)(35,153)(36,158)(37,155)(38,160)(39,157)(40,154)(49,86)(50,83)(51,88)(52,85)(53,82)(54,87)(55,84)(56,81)(57,116)(58,113)(59,118)(60,115)(61,120)(62,117)(63,114)(64,119)(73,133)(74,130)(75,135)(76,132)(77,129)(78,134)(79,131)(80,136)(97,108)(98,105)(99,110)(100,107)(101,112)(102,109)(103,106)(104,111)(121,147)(122,152)(123,149)(124,146)(125,151)(126,148)(127,145)(128,150) );
G=PermutationGroup([[(1,83),(2,84),(3,85),(4,86),(5,87),(6,88),(7,81),(8,82),(9,112),(10,105),(11,106),(12,107),(13,108),(14,109),(15,110),(16,111),(17,157),(18,158),(19,159),(20,160),(21,153),(22,154),(23,155),(24,156),(25,152),(26,145),(27,146),(28,147),(29,148),(30,149),(31,150),(32,151),(33,138),(34,139),(35,140),(36,141),(37,142),(38,143),(39,144),(40,137),(41,103),(42,104),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,91),(50,92),(51,93),(52,94),(53,95),(54,96),(55,89),(56,90),(57,132),(58,133),(59,134),(60,135),(61,136),(62,129),(63,130),(64,131),(65,128),(66,121),(67,122),(68,123),(69,124),(70,125),(71,126),(72,127),(73,113),(74,114),(75,115),(76,116),(77,117),(78,118),(79,119),(80,120)], [(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)], [(1,77,5,73),(2,76,6,80),(3,75,7,79),(4,74,8,78),(9,31,13,27),(10,30,14,26),(11,29,15,25),(12,28,16,32),(17,140,21,144),(18,139,22,143),(19,138,23,142),(20,137,24,141),(33,155,37,159),(34,154,38,158),(35,153,39,157),(36,160,40,156),(41,67,45,71),(42,66,46,70),(43,65,47,69),(44,72,48,68),(49,59,53,63),(50,58,54,62),(51,57,55,61),(52,64,56,60),(81,119,85,115),(82,118,86,114),(83,117,87,113),(84,116,88,120),(89,136,93,132),(90,135,94,131),(91,134,95,130),(92,133,96,129),(97,128,101,124),(98,127,102,123),(99,126,103,122),(100,125,104,121),(105,149,109,145),(106,148,110,152),(107,147,111,151),(108,146,112,150)], [(1,107,33,125,133),(2,108,34,126,134),(3,109,35,127,135),(4,110,36,128,136),(5,111,37,121,129),(6,112,38,122,130),(7,105,39,123,131),(8,106,40,124,132),(9,143,67,63,88),(10,144,68,64,81),(11,137,69,57,82),(12,138,70,58,83),(13,139,71,59,84),(14,140,72,60,85),(15,141,65,61,86),(16,142,66,62,87),(17,44,56,119,30),(18,45,49,120,31),(19,46,50,113,32),(20,47,51,114,25),(21,48,52,115,26),(22,41,53,116,27),(23,42,54,117,28),(24,43,55,118,29),(73,151,159,100,92),(74,152,160,101,93),(75,145,153,102,94),(76,146,154,103,95),(77,147,155,104,96),(78,148,156,97,89),(79,149,157,98,90),(80,150,158,99,91)], [(1,92),(2,89),(3,94),(4,91),(5,96),(6,93),(7,90),(8,95),(9,47),(10,44),(11,41),(12,46),(13,43),(14,48),(15,45),(16,42),(17,144),(18,141),(19,138),(20,143),(21,140),(22,137),(23,142),(24,139),(25,67),(26,72),(27,69),(28,66),(29,71),(30,68),(31,65),(32,70),(33,159),(34,156),(35,153),(36,158),(37,155),(38,160),(39,157),(40,154),(49,86),(50,83),(51,88),(52,85),(53,82),(54,87),(55,84),(56,81),(57,116),(58,113),(59,118),(60,115),(61,120),(62,117),(63,114),(64,119),(73,133),(74,130),(75,135),(76,132),(77,129),(78,134),(79,131),(80,136),(97,108),(98,105),(99,110),(100,107),(101,112),(102,109),(103,106),(104,111),(121,147),(122,152),(123,149),(124,146),(125,151),(126,148),(127,145),(128,150)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 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 | 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 | 10 | 10 | 20 | 20 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | 10 | 20 | 20 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | D10 | D10 | D10 | C8.C22 | D4×D5 | D4×D5 | Q16⋊D5 |
| kernel | C2×Q16⋊D5 | C2×C8⋊D5 | C2×C40⋊C2 | Q16⋊D5 | C2×Q8⋊D5 | C2×C5⋊Q16 | C10×Q16 | C2×Q8×D5 | C2×Q8⋊2D5 | C4×D5 | C2×Dic5 | C22×D5 | C2×Q16 | C2×C8 | Q16 | C2×Q8 | C10 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 8 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 8 | 4 | 2 | 2 | 2 | 8 |
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 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 39 | 17 | 2 | 24 |
| 0 | 0 | 24 | 2 | 17 | 39 |
| 0 | 0 | 40 | 29 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 40 | 22 | 0 |
| 0 | 0 | 1 | 13 | 0 | 22 |
| 0 | 0 | 17 | 40 | 35 | 1 |
| 0 | 0 | 1 | 24 | 40 | 28 |
| 40 | 40 | 0 | 0 | 0 | 0 |
| 36 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 40 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 7 | 0 | 0 | 0 | 0 |
| 6 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 39 | 35 | 10 | 19 |
| 0 | 0 | 8 | 2 | 31 | 31 |
| 0 | 0 | 36 | 11 | 8 | 13 |
| 0 | 0 | 5 | 5 | 39 | 33 |
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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,39,24,40,12,0,0,17,2,29,1,0,0,2,17,0,0,0,0,24,39,0,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,6,1,17,1,0,0,40,13,40,24,0,0,22,0,35,40,0,0,0,22,1,28],[40,36,0,0,0,0,40,35,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,34,1,0,0,0,0,40,0],[0,6,0,0,0,0,7,0,0,0,0,0,0,0,39,8,36,5,0,0,35,2,11,5,0,0,10,31,8,39,0,0,19,31,13,33] >;
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(320,1436);
// by ID
G=gap.SmallGroup(320,1436);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,1123,185,136,438,235,102,12550]);
// 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,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=b^5,c*d=d*c,e*c*e=b^4*c,e*d*e=d^-1>;
// generators/relations