direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×SD16⋊3D5, C20.8C24, SD16⋊12D10, C40.44C23, D20.4C23, Dic10.4C23, C4.45(D4×D5), C10⋊3(C4○D8), (C4×D5).68D4, C20.83(C2×D4), C4.8(C23×D5), D4⋊D5⋊11C22, (C2×SD16)⋊16D5, D10.22(C2×D4), (C2×C8).265D10, (C8×D5)⋊18C22, (C5×D4).6C23, C5⋊Q16⋊7C22, D4.6(C22×D5), C8.41(C22×D5), (C10×SD16)⋊11C2, (C2×D4).184D10, (C5×Q8).2C23, Q8.2(C22×D5), D4⋊2D5⋊7C22, C40⋊C2⋊18C22, C5⋊2C8.21C23, (C2×Q8).151D10, Q8⋊2D5⋊6C22, (C4×D5).62C23, (C22×D5).93D4, C22.141(D4×D5), (C2×C20).525C23, (C2×C40).166C22, Dic5.124(C2×D4), (C2×Dic5).284D4, (C5×SD16)⋊13C22, C10.109(C22×D4), (C2×D20).184C22, (D4×C10).166C22, (Q8×C10).148C22, (C2×Dic10).203C22, C5⋊3(C2×C4○D8), (D5×C2×C8)⋊10C2, C2.82(C2×D4×D5), (C2×D4⋊D5)⋊28C2, (C2×C40⋊C2)⋊32C2, (C2×C5⋊Q16)⋊26C2, (C2×D4⋊2D5)⋊25C2, (C2×Q8⋊2D5)⋊15C2, (C2×C10).398(C2×D4), (C2×C4×D5).328C22, (C2×C4).614(C22×D5), (C2×C5⋊2C8).292C22, SmallGroup(320,1433)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×SD16⋊3D5
G = < a,b,c,d,e | a2=b8=c2=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b3, bd=db, be=eb, cd=dc, ece=b4c, ede=d-1 >
Subgroups: 990 in 266 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, D8, 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, C22×C8, C2×D8, C2×SD16, C2×SD16, C2×Q16, C4○D8, C2×C4○D4, C5⋊2C8, C40, Dic10, Dic10, C4×D5, C4×D5, D20, D20, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C5×D4, C5×Q8, C5×Q8, C22×D5, C22×D5, C22×C10, C2×C4○D8, C8×D5, C40⋊C2, C2×C5⋊2C8, D4⋊D5, C5⋊Q16, C2×C40, C5×SD16, C2×Dic10, C2×C4×D5, C2×C4×D5, C2×D20, C2×D20, D4⋊2D5, D4⋊2D5, Q8⋊2D5, Q8⋊2D5, C22×Dic5, C2×C5⋊D4, D4×C10, Q8×C10, D5×C2×C8, C2×C40⋊C2, SD16⋊3D5, C2×D4⋊D5, C2×C5⋊Q16, C10×SD16, C2×D4⋊2D5, C2×Q8⋊2D5, C2×SD16⋊3D5
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C4○D8, C22×D4, C22×D5, C2×C4○D8, D4×D5, C23×D5, SD16⋊3D5, C2×D4×D5, C2×SD16⋊3D5
►On 160 points
Generators in S160
(1 96)(2 89)(3 90)(4 91)(5 92)(6 93)(7 94)(8 95)(9 109)(10 110)(11 111)(12 112)(13 105)(14 106)(15 107)(16 108)(17 157)(18 158)(19 159)(20 160)(21 153)(22 154)(23 155)(24 156)(25 147)(26 148)(27 149)(28 150)(29 151)(30 152)(31 145)(32 146)(33 144)(34 137)(35 138)(36 139)(37 140)(38 141)(39 142)(40 143)(41 88)(42 81)(43 82)(44 83)(45 84)(46 85)(47 86)(48 87)(49 101)(50 102)(51 103)(52 104)(53 97)(54 98)(55 99)(56 100)(57 122)(58 123)(59 124)(60 125)(61 126)(62 127)(63 128)(64 121)(65 115)(66 116)(67 117)(68 118)(69 119)(70 120)(71 113)(72 114)(73 133)(74 134)(75 135)(76 136)(77 129)(78 130)(79 131)(80 132)
(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 66)(2 69)(3 72)(4 67)(5 70)(6 65)(7 68)(8 71)(9 31)(10 26)(11 29)(12 32)(13 27)(14 30)(15 25)(16 28)(17 139)(18 142)(19 137)(20 140)(21 143)(22 138)(23 141)(24 144)(33 156)(34 159)(35 154)(36 157)(37 160)(38 155)(39 158)(40 153)(41 60)(42 63)(43 58)(44 61)(45 64)(46 59)(47 62)(48 57)(49 77)(50 80)(51 75)(52 78)(53 73)(54 76)(55 79)(56 74)(81 128)(82 123)(83 126)(84 121)(85 124)(86 127)(87 122)(88 125)(89 119)(90 114)(91 117)(92 120)(93 115)(94 118)(95 113)(96 116)(97 133)(98 136)(99 131)(100 134)(101 129)(102 132)(103 135)(104 130)(105 149)(106 152)(107 147)(108 150)(109 145)(110 148)(111 151)(112 146)
(1 106 35 127 135)(2 107 36 128 136)(3 108 37 121 129)(4 109 38 122 130)(5 110 39 123 131)(6 111 40 124 132)(7 112 33 125 133)(8 105 34 126 134)(9 141 57 78 91)(10 142 58 79 92)(11 143 59 80 93)(12 144 60 73 94)(13 137 61 74 95)(14 138 62 75 96)(15 139 63 76 89)(16 140 64 77 90)(17 42 54 119 25)(18 43 55 120 26)(19 44 56 113 27)(20 45 49 114 28)(21 46 50 115 29)(22 47 51 116 30)(23 48 52 117 31)(24 41 53 118 32)(65 151 153 85 102)(66 152 154 86 103)(67 145 155 87 104)(68 146 156 88 97)(69 147 157 81 98)(70 148 158 82 99)(71 149 159 83 100)(72 150 160 84 101)
(1 102)(2 103)(3 104)(4 97)(5 98)(6 99)(7 100)(8 101)(9 41)(10 42)(11 43)(12 44)(13 45)(14 46)(15 47)(16 48)(17 142)(18 143)(19 144)(20 137)(21 138)(22 139)(23 140)(24 141)(25 58)(26 59)(27 60)(28 61)(29 62)(30 63)(31 64)(32 57)(33 159)(34 160)(35 153)(36 154)(37 155)(38 156)(39 157)(40 158)(49 95)(50 96)(51 89)(52 90)(53 91)(54 92)(55 93)(56 94)(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)(81 110)(82 111)(83 112)(84 105)(85 106)(86 107)(87 108)(88 109)(121 145)(122 146)(123 147)(124 148)(125 149)(126 150)(127 151)(128 152)
G:=sub<Sym(160)| (1,96)(2,89)(3,90)(4,91)(5,92)(6,93)(7,94)(8,95)(9,109)(10,110)(11,111)(12,112)(13,105)(14,106)(15,107)(16,108)(17,157)(18,158)(19,159)(20,160)(21,153)(22,154)(23,155)(24,156)(25,147)(26,148)(27,149)(28,150)(29,151)(30,152)(31,145)(32,146)(33,144)(34,137)(35,138)(36,139)(37,140)(38,141)(39,142)(40,143)(41,88)(42,81)(43,82)(44,83)(45,84)(46,85)(47,86)(48,87)(49,101)(50,102)(51,103)(52,104)(53,97)(54,98)(55,99)(56,100)(57,122)(58,123)(59,124)(60,125)(61,126)(62,127)(63,128)(64,121)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,113)(72,114)(73,133)(74,134)(75,135)(76,136)(77,129)(78,130)(79,131)(80,132), (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), (1,66)(2,69)(3,72)(4,67)(5,70)(6,65)(7,68)(8,71)(9,31)(10,26)(11,29)(12,32)(13,27)(14,30)(15,25)(16,28)(17,139)(18,142)(19,137)(20,140)(21,143)(22,138)(23,141)(24,144)(33,156)(34,159)(35,154)(36,157)(37,160)(38,155)(39,158)(40,153)(41,60)(42,63)(43,58)(44,61)(45,64)(46,59)(47,62)(48,57)(49,77)(50,80)(51,75)(52,78)(53,73)(54,76)(55,79)(56,74)(81,128)(82,123)(83,126)(84,121)(85,124)(86,127)(87,122)(88,125)(89,119)(90,114)(91,117)(92,120)(93,115)(94,118)(95,113)(96,116)(97,133)(98,136)(99,131)(100,134)(101,129)(102,132)(103,135)(104,130)(105,149)(106,152)(107,147)(108,150)(109,145)(110,148)(111,151)(112,146), (1,106,35,127,135)(2,107,36,128,136)(3,108,37,121,129)(4,109,38,122,130)(5,110,39,123,131)(6,111,40,124,132)(7,112,33,125,133)(8,105,34,126,134)(9,141,57,78,91)(10,142,58,79,92)(11,143,59,80,93)(12,144,60,73,94)(13,137,61,74,95)(14,138,62,75,96)(15,139,63,76,89)(16,140,64,77,90)(17,42,54,119,25)(18,43,55,120,26)(19,44,56,113,27)(20,45,49,114,28)(21,46,50,115,29)(22,47,51,116,30)(23,48,52,117,31)(24,41,53,118,32)(65,151,153,85,102)(66,152,154,86,103)(67,145,155,87,104)(68,146,156,88,97)(69,147,157,81,98)(70,148,158,82,99)(71,149,159,83,100)(72,150,160,84,101), (1,102)(2,103)(3,104)(4,97)(5,98)(6,99)(7,100)(8,101)(9,41)(10,42)(11,43)(12,44)(13,45)(14,46)(15,47)(16,48)(17,142)(18,143)(19,144)(20,137)(21,138)(22,139)(23,140)(24,141)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,57)(33,159)(34,160)(35,153)(36,154)(37,155)(38,156)(39,157)(40,158)(49,95)(50,96)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(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)(81,110)(82,111)(83,112)(84,105)(85,106)(86,107)(87,108)(88,109)(121,145)(122,146)(123,147)(124,148)(125,149)(126,150)(127,151)(128,152)>;
G:=Group( (1,96)(2,89)(3,90)(4,91)(5,92)(6,93)(7,94)(8,95)(9,109)(10,110)(11,111)(12,112)(13,105)(14,106)(15,107)(16,108)(17,157)(18,158)(19,159)(20,160)(21,153)(22,154)(23,155)(24,156)(25,147)(26,148)(27,149)(28,150)(29,151)(30,152)(31,145)(32,146)(33,144)(34,137)(35,138)(36,139)(37,140)(38,141)(39,142)(40,143)(41,88)(42,81)(43,82)(44,83)(45,84)(46,85)(47,86)(48,87)(49,101)(50,102)(51,103)(52,104)(53,97)(54,98)(55,99)(56,100)(57,122)(58,123)(59,124)(60,125)(61,126)(62,127)(63,128)(64,121)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,113)(72,114)(73,133)(74,134)(75,135)(76,136)(77,129)(78,130)(79,131)(80,132), (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), (1,66)(2,69)(3,72)(4,67)(5,70)(6,65)(7,68)(8,71)(9,31)(10,26)(11,29)(12,32)(13,27)(14,30)(15,25)(16,28)(17,139)(18,142)(19,137)(20,140)(21,143)(22,138)(23,141)(24,144)(33,156)(34,159)(35,154)(36,157)(37,160)(38,155)(39,158)(40,153)(41,60)(42,63)(43,58)(44,61)(45,64)(46,59)(47,62)(48,57)(49,77)(50,80)(51,75)(52,78)(53,73)(54,76)(55,79)(56,74)(81,128)(82,123)(83,126)(84,121)(85,124)(86,127)(87,122)(88,125)(89,119)(90,114)(91,117)(92,120)(93,115)(94,118)(95,113)(96,116)(97,133)(98,136)(99,131)(100,134)(101,129)(102,132)(103,135)(104,130)(105,149)(106,152)(107,147)(108,150)(109,145)(110,148)(111,151)(112,146), (1,106,35,127,135)(2,107,36,128,136)(3,108,37,121,129)(4,109,38,122,130)(5,110,39,123,131)(6,111,40,124,132)(7,112,33,125,133)(8,105,34,126,134)(9,141,57,78,91)(10,142,58,79,92)(11,143,59,80,93)(12,144,60,73,94)(13,137,61,74,95)(14,138,62,75,96)(15,139,63,76,89)(16,140,64,77,90)(17,42,54,119,25)(18,43,55,120,26)(19,44,56,113,27)(20,45,49,114,28)(21,46,50,115,29)(22,47,51,116,30)(23,48,52,117,31)(24,41,53,118,32)(65,151,153,85,102)(66,152,154,86,103)(67,145,155,87,104)(68,146,156,88,97)(69,147,157,81,98)(70,148,158,82,99)(71,149,159,83,100)(72,150,160,84,101), (1,102)(2,103)(3,104)(4,97)(5,98)(6,99)(7,100)(8,101)(9,41)(10,42)(11,43)(12,44)(13,45)(14,46)(15,47)(16,48)(17,142)(18,143)(19,144)(20,137)(21,138)(22,139)(23,140)(24,141)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,57)(33,159)(34,160)(35,153)(36,154)(37,155)(38,156)(39,157)(40,158)(49,95)(50,96)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(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)(81,110)(82,111)(83,112)(84,105)(85,106)(86,107)(87,108)(88,109)(121,145)(122,146)(123,147)(124,148)(125,149)(126,150)(127,151)(128,152) );
G=PermutationGroup([[(1,96),(2,89),(3,90),(4,91),(5,92),(6,93),(7,94),(8,95),(9,109),(10,110),(11,111),(12,112),(13,105),(14,106),(15,107),(16,108),(17,157),(18,158),(19,159),(20,160),(21,153),(22,154),(23,155),(24,156),(25,147),(26,148),(27,149),(28,150),(29,151),(30,152),(31,145),(32,146),(33,144),(34,137),(35,138),(36,139),(37,140),(38,141),(39,142),(40,143),(41,88),(42,81),(43,82),(44,83),(45,84),(46,85),(47,86),(48,87),(49,101),(50,102),(51,103),(52,104),(53,97),(54,98),(55,99),(56,100),(57,122),(58,123),(59,124),(60,125),(61,126),(62,127),(63,128),(64,121),(65,115),(66,116),(67,117),(68,118),(69,119),(70,120),(71,113),(72,114),(73,133),(74,134),(75,135),(76,136),(77,129),(78,130),(79,131),(80,132)], [(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)], [(1,66),(2,69),(3,72),(4,67),(5,70),(6,65),(7,68),(8,71),(9,31),(10,26),(11,29),(12,32),(13,27),(14,30),(15,25),(16,28),(17,139),(18,142),(19,137),(20,140),(21,143),(22,138),(23,141),(24,144),(33,156),(34,159),(35,154),(36,157),(37,160),(38,155),(39,158),(40,153),(41,60),(42,63),(43,58),(44,61),(45,64),(46,59),(47,62),(48,57),(49,77),(50,80),(51,75),(52,78),(53,73),(54,76),(55,79),(56,74),(81,128),(82,123),(83,126),(84,121),(85,124),(86,127),(87,122),(88,125),(89,119),(90,114),(91,117),(92,120),(93,115),(94,118),(95,113),(96,116),(97,133),(98,136),(99,131),(100,134),(101,129),(102,132),(103,135),(104,130),(105,149),(106,152),(107,147),(108,150),(109,145),(110,148),(111,151),(112,146)], [(1,106,35,127,135),(2,107,36,128,136),(3,108,37,121,129),(4,109,38,122,130),(5,110,39,123,131),(6,111,40,124,132),(7,112,33,125,133),(8,105,34,126,134),(9,141,57,78,91),(10,142,58,79,92),(11,143,59,80,93),(12,144,60,73,94),(13,137,61,74,95),(14,138,62,75,96),(15,139,63,76,89),(16,140,64,77,90),(17,42,54,119,25),(18,43,55,120,26),(19,44,56,113,27),(20,45,49,114,28),(21,46,50,115,29),(22,47,51,116,30),(23,48,52,117,31),(24,41,53,118,32),(65,151,153,85,102),(66,152,154,86,103),(67,145,155,87,104),(68,146,156,88,97),(69,147,157,81,98),(70,148,158,82,99),(71,149,159,83,100),(72,150,160,84,101)], [(1,102),(2,103),(3,104),(4,97),(5,98),(6,99),(7,100),(8,101),(9,41),(10,42),(11,43),(12,44),(13,45),(14,46),(15,47),(16,48),(17,142),(18,143),(19,144),(20,137),(21,138),(22,139),(23,140),(24,141),(25,58),(26,59),(27,60),(28,61),(29,62),(30,63),(31,64),(32,57),(33,159),(34,160),(35,153),(36,154),(37,155),(38,156),(39,157),(40,158),(49,95),(50,96),(51,89),(52,90),(53,91),(54,92),(55,93),(56,94),(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),(81,110),(82,111),(83,112),(84,105),(85,106),(86,107),(87,108),(88,109),(121,145),(122,146),(123,147),(124,148),(125,149),(126,150),(127,151),(128,152)]])
56 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 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 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 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 | 20 | 20 | 2 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 20 | 20 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | D10 | D10 | D10 | D10 | C4○D8 | D4×D5 | D4×D5 | SD16⋊3D5 |
| kernel | C2×SD16⋊3D5 | D5×C2×C8 | C2×C40⋊C2 | SD16⋊3D5 | C2×D4⋊D5 | C2×C5⋊Q16 | C10×SD16 | C2×D4⋊2D5 | C2×Q8⋊2D5 | 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 | 8 | 2 | 2 | 8 |
Matrix representation of C2×SD16⋊3D5 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 0 | 0 |
| 0 | 15 | 11 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 |
| 0 | 29 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 0 | 1 | 34 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 9 | 23 | 0 | 0 |
| 0 | 9 | 32 | 0 | 0 |
| 0 | 0 | 0 | 7 | 40 |
| 0 | 0 | 0 | 7 | 34 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,15,0,0,0,11,11,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,29,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,40,34],[40,0,0,0,0,0,9,9,0,0,0,23,32,0,0,0,0,0,7,7,0,0,0,40,34] >;
C2×SD16⋊3D5 in GAP, Magma, Sage, TeX
C_2\times {\rm SD}_{16}\rtimes_3D_5 % in TeX
G:=Group("C2xSD16:3D5"); // GroupNames label
G:=SmallGroup(320,1433);
// by ID
G=gap.SmallGroup(320,1433);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,1123,185,136,438,235,102,12550]);
// 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,b*e=e*b,c*d=d*c,e*c*e=b^4*c,e*d*e=d^-1>;
// generators/relations