direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×SD16⋊D5, SD16⋊9D10, C20.7C24, C40.35C23, Dic20⋊17C22, Dic10.3C23, C4.44(D4×D5), (C2×SD16)⋊5D5, (C4×D5).16D4, C20.82(C2×D4), (Q8×D5)⋊6C22, C4.7(C23×D5), (C10×SD16)⋊6C2, D10.85(C2×D4), (C2×C8).103D10, C8⋊D5⋊9C22, C5⋊2C8.2C23, C5⋊Q16⋊6C22, D4.5(C22×D5), (C5×D4).5C23, (C4×D5).4C23, C8.11(C22×D5), (C2×Dic20)⋊26C2, (C2×D4).183D10, Q8.1(C22×D5), (C5×Q8).1C23, C10⋊2(C8.C22), D4.D5⋊10C22, (C2×Q8).150D10, Dic5.96(C2×D4), (C5×SD16)⋊9C22, C22.140(D4×D5), (C2×C20).524C23, (C2×C40).117C22, (C2×Dic5).249D4, D4⋊2D5.8C22, (C22×D5).136D4, C10.108(C22×D4), (D4×C10).165C22, (Q8×C10).147C22, (C2×Dic10).202C22, (C2×Q8×D5)⋊15C2, C2.81(C2×D4×D5), C5⋊2(C2×C8.C22), (C2×C8⋊D5)⋊5C2, (C2×D4.D5)⋊28C2, (C2×C5⋊Q16)⋊25C2, (C2×C10).397(C2×D4), (C2×C4×D5).166C22, (C2×D4⋊2D5).12C2, (C2×C4).613(C22×D5), (C2×C5⋊2C8).180C22, SmallGroup(320,1432)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×SD16⋊D5
G = < a,b,c,d,e | a2=b8=c2=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b3, bd=db, ebe=b5, cd=dc, ece=b4c, ede=d-1 >
Subgroups: 894 in 258 conjugacy classes, 103 normal (33 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C5, C8, C8, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, D5, C10, C10, C10, C2×C8, C2×C8, M4(2), SD16, SD16, Q16, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×M4(2), C2×SD16, C2×SD16, C2×Q16, C8.C22, C22×Q8, C2×C4○D4, C5⋊2C8, C40, Dic10, Dic10, C4×D5, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C5×D4, C5×Q8, C5×Q8, C22×D5, C22×C10, C2×C8.C22, C8⋊D5, Dic20, C2×C5⋊2C8, D4.D5, C5⋊Q16, C2×C40, C5×SD16, C2×Dic10, C2×Dic10, C2×C4×D5, C2×C4×D5, D4⋊2D5, D4⋊2D5, Q8×D5, Q8×D5, C22×Dic5, C2×C5⋊D4, D4×C10, Q8×C10, C2×C8⋊D5, C2×Dic20, SD16⋊D5, C2×D4.D5, C2×C5⋊Q16, C10×SD16, C2×D4⋊2D5, C2×Q8×D5, C2×SD16⋊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, SD16⋊D5, C2×D4×D5, C2×SD16⋊D5
►On 160 points
Generators in S160
(1 87)(2 88)(3 81)(4 82)(5 83)(6 84)(7 85)(8 86)(9 124)(10 125)(11 126)(12 127)(13 128)(14 121)(15 122)(16 123)(17 157)(18 158)(19 159)(20 160)(21 153)(22 154)(23 155)(24 156)(25 139)(26 140)(27 141)(28 142)(29 143)(30 144)(31 137)(32 138)(33 97)(34 98)(35 99)(36 100)(37 101)(38 102)(39 103)(40 104)(41 148)(42 149)(43 150)(44 151)(45 152)(46 145)(47 146)(48 147)(49 91)(50 92)(51 93)(52 94)(53 95)(54 96)(55 89)(56 90)(57 110)(58 111)(59 112)(60 105)(61 106)(62 107)(63 108)(64 109)(65 135)(66 136)(67 129)(68 130)(69 131)(70 132)(71 133)(72 134)(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 62)(2 57)(3 60)(4 63)(5 58)(6 61)(7 64)(8 59)(9 47)(10 42)(11 45)(12 48)(13 43)(14 46)(15 41)(16 44)(17 140)(18 143)(19 138)(20 141)(21 144)(22 139)(23 142)(24 137)(25 154)(26 157)(27 160)(28 155)(29 158)(30 153)(31 156)(32 159)(33 78)(34 73)(35 76)(36 79)(37 74)(38 77)(39 80)(40 75)(49 72)(50 67)(51 70)(52 65)(53 68)(54 71)(55 66)(56 69)(81 105)(82 108)(83 111)(84 106)(85 109)(86 112)(87 107)(88 110)(89 136)(90 131)(91 134)(92 129)(93 132)(94 135)(95 130)(96 133)(97 118)(98 113)(99 116)(100 119)(101 114)(102 117)(103 120)(104 115)(121 145)(122 148)(123 151)(124 146)(125 149)(126 152)(127 147)(128 150)
(1 127 32 119 133)(2 128 25 120 134)(3 121 26 113 135)(4 122 27 114 136)(5 123 28 115 129)(6 124 29 116 130)(7 125 30 117 131)(8 126 31 118 132)(9 143 76 68 84)(10 144 77 69 85)(11 137 78 70 86)(12 138 79 71 87)(13 139 80 72 88)(14 140 73 65 81)(15 141 74 66 82)(16 142 75 67 83)(17 34 52 105 46)(18 35 53 106 47)(19 36 54 107 48)(20 37 55 108 41)(21 38 56 109 42)(22 39 49 110 43)(23 40 50 111 44)(24 33 51 112 45)(57 150 154 103 91)(58 151 155 104 92)(59 152 156 97 93)(60 145 157 98 94)(61 146 158 99 95)(62 147 159 100 96)(63 148 160 101 89)(64 149 153 102 90)
(1 133)(2 130)(3 135)(4 132)(5 129)(6 134)(7 131)(8 136)(9 80)(10 77)(11 74)(12 79)(13 76)(14 73)(15 78)(16 75)(17 21)(19 23)(25 29)(27 31)(33 45)(34 42)(35 47)(36 44)(37 41)(38 46)(39 43)(40 48)(49 110)(50 107)(51 112)(52 109)(53 106)(54 111)(55 108)(56 105)(57 91)(58 96)(59 93)(60 90)(61 95)(62 92)(63 89)(64 94)(65 81)(66 86)(67 83)(68 88)(69 85)(70 82)(71 87)(72 84)(97 152)(98 149)(99 146)(100 151)(101 148)(102 145)(103 150)(104 147)(113 121)(114 126)(115 123)(116 128)(117 125)(118 122)(119 127)(120 124)(137 141)(139 143)(153 157)(155 159)
G:=sub<Sym(160)| (1,87)(2,88)(3,81)(4,82)(5,83)(6,84)(7,85)(8,86)(9,124)(10,125)(11,126)(12,127)(13,128)(14,121)(15,122)(16,123)(17,157)(18,158)(19,159)(20,160)(21,153)(22,154)(23,155)(24,156)(25,139)(26,140)(27,141)(28,142)(29,143)(30,144)(31,137)(32,138)(33,97)(34,98)(35,99)(36,100)(37,101)(38,102)(39,103)(40,104)(41,148)(42,149)(43,150)(44,151)(45,152)(46,145)(47,146)(48,147)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,89)(56,90)(57,110)(58,111)(59,112)(60,105)(61,106)(62,107)(63,108)(64,109)(65,135)(66,136)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(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), (1,62)(2,57)(3,60)(4,63)(5,58)(6,61)(7,64)(8,59)(9,47)(10,42)(11,45)(12,48)(13,43)(14,46)(15,41)(16,44)(17,140)(18,143)(19,138)(20,141)(21,144)(22,139)(23,142)(24,137)(25,154)(26,157)(27,160)(28,155)(29,158)(30,153)(31,156)(32,159)(33,78)(34,73)(35,76)(36,79)(37,74)(38,77)(39,80)(40,75)(49,72)(50,67)(51,70)(52,65)(53,68)(54,71)(55,66)(56,69)(81,105)(82,108)(83,111)(84,106)(85,109)(86,112)(87,107)(88,110)(89,136)(90,131)(91,134)(92,129)(93,132)(94,135)(95,130)(96,133)(97,118)(98,113)(99,116)(100,119)(101,114)(102,117)(103,120)(104,115)(121,145)(122,148)(123,151)(124,146)(125,149)(126,152)(127,147)(128,150), (1,127,32,119,133)(2,128,25,120,134)(3,121,26,113,135)(4,122,27,114,136)(5,123,28,115,129)(6,124,29,116,130)(7,125,30,117,131)(8,126,31,118,132)(9,143,76,68,84)(10,144,77,69,85)(11,137,78,70,86)(12,138,79,71,87)(13,139,80,72,88)(14,140,73,65,81)(15,141,74,66,82)(16,142,75,67,83)(17,34,52,105,46)(18,35,53,106,47)(19,36,54,107,48)(20,37,55,108,41)(21,38,56,109,42)(22,39,49,110,43)(23,40,50,111,44)(24,33,51,112,45)(57,150,154,103,91)(58,151,155,104,92)(59,152,156,97,93)(60,145,157,98,94)(61,146,158,99,95)(62,147,159,100,96)(63,148,160,101,89)(64,149,153,102,90), (1,133)(2,130)(3,135)(4,132)(5,129)(6,134)(7,131)(8,136)(9,80)(10,77)(11,74)(12,79)(13,76)(14,73)(15,78)(16,75)(17,21)(19,23)(25,29)(27,31)(33,45)(34,42)(35,47)(36,44)(37,41)(38,46)(39,43)(40,48)(49,110)(50,107)(51,112)(52,109)(53,106)(54,111)(55,108)(56,105)(57,91)(58,96)(59,93)(60,90)(61,95)(62,92)(63,89)(64,94)(65,81)(66,86)(67,83)(68,88)(69,85)(70,82)(71,87)(72,84)(97,152)(98,149)(99,146)(100,151)(101,148)(102,145)(103,150)(104,147)(113,121)(114,126)(115,123)(116,128)(117,125)(118,122)(119,127)(120,124)(137,141)(139,143)(153,157)(155,159)>;
G:=Group( (1,87)(2,88)(3,81)(4,82)(5,83)(6,84)(7,85)(8,86)(9,124)(10,125)(11,126)(12,127)(13,128)(14,121)(15,122)(16,123)(17,157)(18,158)(19,159)(20,160)(21,153)(22,154)(23,155)(24,156)(25,139)(26,140)(27,141)(28,142)(29,143)(30,144)(31,137)(32,138)(33,97)(34,98)(35,99)(36,100)(37,101)(38,102)(39,103)(40,104)(41,148)(42,149)(43,150)(44,151)(45,152)(46,145)(47,146)(48,147)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,89)(56,90)(57,110)(58,111)(59,112)(60,105)(61,106)(62,107)(63,108)(64,109)(65,135)(66,136)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(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), (1,62)(2,57)(3,60)(4,63)(5,58)(6,61)(7,64)(8,59)(9,47)(10,42)(11,45)(12,48)(13,43)(14,46)(15,41)(16,44)(17,140)(18,143)(19,138)(20,141)(21,144)(22,139)(23,142)(24,137)(25,154)(26,157)(27,160)(28,155)(29,158)(30,153)(31,156)(32,159)(33,78)(34,73)(35,76)(36,79)(37,74)(38,77)(39,80)(40,75)(49,72)(50,67)(51,70)(52,65)(53,68)(54,71)(55,66)(56,69)(81,105)(82,108)(83,111)(84,106)(85,109)(86,112)(87,107)(88,110)(89,136)(90,131)(91,134)(92,129)(93,132)(94,135)(95,130)(96,133)(97,118)(98,113)(99,116)(100,119)(101,114)(102,117)(103,120)(104,115)(121,145)(122,148)(123,151)(124,146)(125,149)(126,152)(127,147)(128,150), (1,127,32,119,133)(2,128,25,120,134)(3,121,26,113,135)(4,122,27,114,136)(5,123,28,115,129)(6,124,29,116,130)(7,125,30,117,131)(8,126,31,118,132)(9,143,76,68,84)(10,144,77,69,85)(11,137,78,70,86)(12,138,79,71,87)(13,139,80,72,88)(14,140,73,65,81)(15,141,74,66,82)(16,142,75,67,83)(17,34,52,105,46)(18,35,53,106,47)(19,36,54,107,48)(20,37,55,108,41)(21,38,56,109,42)(22,39,49,110,43)(23,40,50,111,44)(24,33,51,112,45)(57,150,154,103,91)(58,151,155,104,92)(59,152,156,97,93)(60,145,157,98,94)(61,146,158,99,95)(62,147,159,100,96)(63,148,160,101,89)(64,149,153,102,90), (1,133)(2,130)(3,135)(4,132)(5,129)(6,134)(7,131)(8,136)(9,80)(10,77)(11,74)(12,79)(13,76)(14,73)(15,78)(16,75)(17,21)(19,23)(25,29)(27,31)(33,45)(34,42)(35,47)(36,44)(37,41)(38,46)(39,43)(40,48)(49,110)(50,107)(51,112)(52,109)(53,106)(54,111)(55,108)(56,105)(57,91)(58,96)(59,93)(60,90)(61,95)(62,92)(63,89)(64,94)(65,81)(66,86)(67,83)(68,88)(69,85)(70,82)(71,87)(72,84)(97,152)(98,149)(99,146)(100,151)(101,148)(102,145)(103,150)(104,147)(113,121)(114,126)(115,123)(116,128)(117,125)(118,122)(119,127)(120,124)(137,141)(139,143)(153,157)(155,159) );
G=PermutationGroup([[(1,87),(2,88),(3,81),(4,82),(5,83),(6,84),(7,85),(8,86),(9,124),(10,125),(11,126),(12,127),(13,128),(14,121),(15,122),(16,123),(17,157),(18,158),(19,159),(20,160),(21,153),(22,154),(23,155),(24,156),(25,139),(26,140),(27,141),(28,142),(29,143),(30,144),(31,137),(32,138),(33,97),(34,98),(35,99),(36,100),(37,101),(38,102),(39,103),(40,104),(41,148),(42,149),(43,150),(44,151),(45,152),(46,145),(47,146),(48,147),(49,91),(50,92),(51,93),(52,94),(53,95),(54,96),(55,89),(56,90),(57,110),(58,111),(59,112),(60,105),(61,106),(62,107),(63,108),(64,109),(65,135),(66,136),(67,129),(68,130),(69,131),(70,132),(71,133),(72,134),(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)], [(1,62),(2,57),(3,60),(4,63),(5,58),(6,61),(7,64),(8,59),(9,47),(10,42),(11,45),(12,48),(13,43),(14,46),(15,41),(16,44),(17,140),(18,143),(19,138),(20,141),(21,144),(22,139),(23,142),(24,137),(25,154),(26,157),(27,160),(28,155),(29,158),(30,153),(31,156),(32,159),(33,78),(34,73),(35,76),(36,79),(37,74),(38,77),(39,80),(40,75),(49,72),(50,67),(51,70),(52,65),(53,68),(54,71),(55,66),(56,69),(81,105),(82,108),(83,111),(84,106),(85,109),(86,112),(87,107),(88,110),(89,136),(90,131),(91,134),(92,129),(93,132),(94,135),(95,130),(96,133),(97,118),(98,113),(99,116),(100,119),(101,114),(102,117),(103,120),(104,115),(121,145),(122,148),(123,151),(124,146),(125,149),(126,152),(127,147),(128,150)], [(1,127,32,119,133),(2,128,25,120,134),(3,121,26,113,135),(4,122,27,114,136),(5,123,28,115,129),(6,124,29,116,130),(7,125,30,117,131),(8,126,31,118,132),(9,143,76,68,84),(10,144,77,69,85),(11,137,78,70,86),(12,138,79,71,87),(13,139,80,72,88),(14,140,73,65,81),(15,141,74,66,82),(16,142,75,67,83),(17,34,52,105,46),(18,35,53,106,47),(19,36,54,107,48),(20,37,55,108,41),(21,38,56,109,42),(22,39,49,110,43),(23,40,50,111,44),(24,33,51,112,45),(57,150,154,103,91),(58,151,155,104,92),(59,152,156,97,93),(60,145,157,98,94),(61,146,158,99,95),(62,147,159,100,96),(63,148,160,101,89),(64,149,153,102,90)], [(1,133),(2,130),(3,135),(4,132),(5,129),(6,134),(7,131),(8,136),(9,80),(10,77),(11,74),(12,79),(13,76),(14,73),(15,78),(16,75),(17,21),(19,23),(25,29),(27,31),(33,45),(34,42),(35,47),(36,44),(37,41),(38,46),(39,43),(40,48),(49,110),(50,107),(51,112),(52,109),(53,106),(54,111),(55,108),(56,105),(57,91),(58,96),(59,93),(60,90),(61,95),(62,92),(63,89),(64,94),(65,81),(66,86),(67,83),(68,88),(69,85),(70,82),(71,87),(72,84),(97,152),(98,149),(99,146),(100,151),(101,148),(102,145),(103,150),(104,147),(113,121),(114,126),(115,123),(116,128),(117,125),(118,122),(119,127),(120,124),(137,141),(139,143),(153,157),(155,159)]])
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 | 10G | 10H | 10I | 10J | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 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 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 10 | 10 | 2 | 2 | 4 | 4 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | ··· | 2 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 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 | D10 | C8.C22 | D4×D5 | D4×D5 | SD16⋊D5 |
| kernel | C2×SD16⋊D5 | C2×C8⋊D5 | C2×Dic20 | SD16⋊D5 | C2×D4.D5 | C2×C5⋊Q16 | C10×SD16 | C2×D4⋊2D5 | C2×Q8×D5 | C4×D5 | C2×Dic5 | C22×D5 | C2×SD16 | C2×C8 | SD16 | C2×D4 | C2×Q8 | C10 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 8 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 2 | 8 |
Matrix representation of C2×SD16⋊D5 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 11 | 30 | 0 | 0 | 0 | 0 |
| 26 | 30 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 25 | 34 | 16 |
| 0 | 0 | 16 | 34 | 25 | 7 |
| 0 | 0 | 24 | 33 | 0 | 0 |
| 0 | 0 | 8 | 17 | 0 | 0 |
| 40 | 4 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 29 | 39 | 28 |
| 0 | 0 | 12 | 5 | 13 | 2 |
| 0 | 0 | 35 | 2 | 5 | 12 |
| 0 | 0 | 39 | 6 | 29 | 36 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 40 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 40 | 0 | 0 |
| 0 | 0 | 35 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 40 |
| 0 | 0 | 0 | 0 | 35 | 35 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[11,26,0,0,0,0,30,30,0,0,0,0,0,0,7,16,24,8,0,0,25,34,33,17,0,0,34,25,0,0,0,0,16,7,0,0],[40,0,0,0,0,0,4,1,0,0,0,0,0,0,36,12,35,39,0,0,29,5,2,6,0,0,39,13,5,29,0,0,28,2,12,36],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,6,1,0,0,0,0,40,0,0,0,0,0,0,0,6,1,0,0,0,0,40,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,6,35,0,0,0,0,40,35,0,0,0,0,0,0,6,35,0,0,0,0,40,35] >;
C2×SD16⋊D5 in GAP, Magma, Sage, TeX
C_2\times {\rm SD}_{16}\rtimes D_5 % in TeX
G:=Group("C2xSD16:D5"); // GroupNames label
G:=SmallGroup(320,1432);
// by ID
G=gap.SmallGroup(320,1432);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,1123,185,438,235,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^8=c^2=d^5=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^3,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