direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4×D4⋊2D5, C42.227D10, D4⋊8(C4×D5), (D4×C20)⋊5C2, (C4×D4)⋊28D5, (D5×C42)⋊2C2, C20⋊15(C4○D4), C4⋊C4.313D10, (D4×Dic5)⋊43C2, (C4×Dic10)⋊23C2, Dic10⋊21(C2×C4), (C2×D4).240D10, (C2×C10).80C24, C20.66(C22×C4), C10.41(C23×C4), Dic5⋊11(C4○D4), Dic5⋊3Q8⋊45C2, Dic5⋊4D4⋊50C2, (C4×C20).143C22, (C2×C20).490C23, C22⋊C4.128D10, D10.16(C22×C4), (C22×C4).319D10, C22.30(C23×D5), (D4×C10).247C22, C4⋊Dic5.361C22, Dic5.54(C22×C4), C23.161(C22×D5), C23.11D10⋊31C2, (C22×C10).150C23, (C22×C20).362C22, (C2×Dic5).374C23, (C4×Dic5).333C22, (C22×D5).177C23, C23.D5.100C22, D10⋊C4.120C22, (C2×Dic10).294C22, C10.D4.133C22, (C22×Dic5).241C22, C5⋊4(C4×C4○D4), C4.31(C2×C4×D5), C5⋊D4⋊5(C2×C4), C2.3(D5×C4○D4), (C5×D4)⋊20(C2×C4), (C4×D5)⋊10(C2×C4), (C4×C5⋊D4)⋊37C2, C22.1(C2×C4×D5), (C2×C4×Dic5)⋊34C2, C4⋊C4⋊7D5⋊46C2, C2.22(D5×C22×C4), C2.5(C2×D4⋊2D5), (C2×Dic5)⋊26(C2×C4), C10.135(C2×C4○D4), (C2×C10).8(C22×C4), (C2×C4×D5).374C22, (C2×D4⋊2D5).19C2, (C5×C4⋊C4).316C22, (C2×C4).577(C22×D5), (C2×C5⋊D4).115C22, (C5×C22⋊C4).140C22, SmallGroup(320,1208)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4×D4⋊2D5
G = < a,b,c,d,e | a4=b4=c2=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ece=b2c, ede=d-1 >
Subgroups: 862 in 310 conjugacy classes, 157 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, D4, Q8, C23, C23, D5, C10, C10, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×C10, C2×C42, C42⋊C2, C4×D4, C4×D4, C4×Q8, C2×C4○D4, Dic10, C4×D5, C4×D5, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C4×C4○D4, C4×Dic5, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C4×C20, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, D4⋊2D5, C22×Dic5, C2×C5⋊D4, C22×C20, D4×C10, C4×Dic10, D5×C42, C23.11D10, Dic5⋊4D4, Dic5⋊3Q8, C4⋊C4⋊7D5, C2×C4×Dic5, C4×C5⋊D4, D4×Dic5, D4×C20, C2×D4⋊2D5, C4×D4⋊2D5
Quotients: C1, C2, C4, C22, C2×C4, C23, D5, C22×C4, C4○D4, C24, D10, C23×C4, C2×C4○D4, C4×D5, C22×D5, C4×C4○D4, C2×C4×D5, D4⋊2D5, C23×D5, D5×C22×C4, C2×D4⋊2D5, D5×C4○D4, C4×D4⋊2D5
►On 160 points
Generators in S160
(1 51 11 41)(2 52 12 42)(3 53 13 43)(4 54 14 44)(5 55 15 45)(6 56 16 46)(7 57 17 47)(8 58 18 48)(9 59 19 49)(10 60 20 50)(21 71 31 61)(22 72 32 62)(23 73 33 63)(24 74 34 64)(25 75 35 65)(26 76 36 66)(27 77 37 67)(28 78 38 68)(29 79 39 69)(30 80 40 70)(81 131 91 121)(82 132 92 122)(83 133 93 123)(84 134 94 124)(85 135 95 125)(86 136 96 126)(87 137 97 127)(88 138 98 128)(89 139 99 129)(90 140 100 130)(101 151 111 141)(102 152 112 142)(103 153 113 143)(104 154 114 144)(105 155 115 145)(106 156 116 146)(107 157 117 147)(108 158 118 148)(109 159 119 149)(110 160 120 150)
(1 116 16 101)(2 117 17 102)(3 118 18 103)(4 119 19 104)(5 120 20 105)(6 111 11 106)(7 112 12 107)(8 113 13 108)(9 114 14 109)(10 115 15 110)(21 96 36 81)(22 97 37 82)(23 98 38 83)(24 99 39 84)(25 100 40 85)(26 91 31 86)(27 92 32 87)(28 93 33 88)(29 94 34 89)(30 95 35 90)(41 156 56 141)(42 157 57 142)(43 158 58 143)(44 159 59 144)(45 160 60 145)(46 151 51 146)(47 152 52 147)(48 153 53 148)(49 154 54 149)(50 155 55 150)(61 136 76 121)(62 137 77 122)(63 138 78 123)(64 139 79 124)(65 140 80 125)(66 131 71 126)(67 132 72 127)(68 133 73 128)(69 134 74 129)(70 135 75 130)
(1 81)(2 82)(3 83)(4 84)(5 85)(6 86)(7 87)(8 88)(9 89)(10 90)(11 91)(12 92)(13 93)(14 94)(15 95)(16 96)(17 97)(18 98)(19 99)(20 100)(21 101)(22 102)(23 103)(24 104)(25 105)(26 106)(27 107)(28 108)(29 109)(30 110)(31 111)(32 112)(33 113)(34 114)(35 115)(36 116)(37 117)(38 118)(39 119)(40 120)(41 121)(42 122)(43 123)(44 124)(45 125)(46 126)(47 127)(48 128)(49 129)(50 130)(51 131)(52 132)(53 133)(54 134)(55 135)(56 136)(57 137)(58 138)(59 139)(60 140)(61 141)(62 142)(63 143)(64 144)(65 145)(66 146)(67 147)(68 148)(69 149)(70 150)(71 151)(72 152)(73 153)(74 154)(75 155)(76 156)(77 157)(78 158)(79 159)(80 160)
(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 20)(2 19)(3 18)(4 17)(5 16)(6 15)(7 14)(8 13)(9 12)(10 11)(21 25)(22 24)(26 30)(27 29)(31 35)(32 34)(36 40)(37 39)(41 60)(42 59)(43 58)(44 57)(45 56)(46 55)(47 54)(48 53)(49 52)(50 51)(61 65)(62 64)(66 70)(67 69)(71 75)(72 74)(76 80)(77 79)(81 85)(82 84)(86 90)(87 89)(91 95)(92 94)(96 100)(97 99)(101 120)(102 119)(103 118)(104 117)(105 116)(106 115)(107 114)(108 113)(109 112)(110 111)(121 125)(122 124)(126 130)(127 129)(131 135)(132 134)(136 140)(137 139)(141 160)(142 159)(143 158)(144 157)(145 156)(146 155)(147 154)(148 153)(149 152)(150 151)
G:=sub<Sym(160)| (1,51,11,41)(2,52,12,42)(3,53,13,43)(4,54,14,44)(5,55,15,45)(6,56,16,46)(7,57,17,47)(8,58,18,48)(9,59,19,49)(10,60,20,50)(21,71,31,61)(22,72,32,62)(23,73,33,63)(24,74,34,64)(25,75,35,65)(26,76,36,66)(27,77,37,67)(28,78,38,68)(29,79,39,69)(30,80,40,70)(81,131,91,121)(82,132,92,122)(83,133,93,123)(84,134,94,124)(85,135,95,125)(86,136,96,126)(87,137,97,127)(88,138,98,128)(89,139,99,129)(90,140,100,130)(101,151,111,141)(102,152,112,142)(103,153,113,143)(104,154,114,144)(105,155,115,145)(106,156,116,146)(107,157,117,147)(108,158,118,148)(109,159,119,149)(110,160,120,150), (1,116,16,101)(2,117,17,102)(3,118,18,103)(4,119,19,104)(5,120,20,105)(6,111,11,106)(7,112,12,107)(8,113,13,108)(9,114,14,109)(10,115,15,110)(21,96,36,81)(22,97,37,82)(23,98,38,83)(24,99,39,84)(25,100,40,85)(26,91,31,86)(27,92,32,87)(28,93,33,88)(29,94,34,89)(30,95,35,90)(41,156,56,141)(42,157,57,142)(43,158,58,143)(44,159,59,144)(45,160,60,145)(46,151,51,146)(47,152,52,147)(48,153,53,148)(49,154,54,149)(50,155,55,150)(61,136,76,121)(62,137,77,122)(63,138,78,123)(64,139,79,124)(65,140,80,125)(66,131,71,126)(67,132,72,127)(68,133,73,128)(69,134,74,129)(70,135,75,130), (1,81)(2,82)(3,83)(4,84)(5,85)(6,86)(7,87)(8,88)(9,89)(10,90)(11,91)(12,92)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,116)(37,117)(38,118)(39,119)(40,120)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,137)(58,138)(59,139)(60,140)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160), (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), (1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,25)(22,24)(26,30)(27,29)(31,35)(32,34)(36,40)(37,39)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(61,65)(62,64)(66,70)(67,69)(71,75)(72,74)(76,80)(77,79)(81,85)(82,84)(86,90)(87,89)(91,95)(92,94)(96,100)(97,99)(101,120)(102,119)(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,112)(110,111)(121,125)(122,124)(126,130)(127,129)(131,135)(132,134)(136,140)(137,139)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)>;
G:=Group( (1,51,11,41)(2,52,12,42)(3,53,13,43)(4,54,14,44)(5,55,15,45)(6,56,16,46)(7,57,17,47)(8,58,18,48)(9,59,19,49)(10,60,20,50)(21,71,31,61)(22,72,32,62)(23,73,33,63)(24,74,34,64)(25,75,35,65)(26,76,36,66)(27,77,37,67)(28,78,38,68)(29,79,39,69)(30,80,40,70)(81,131,91,121)(82,132,92,122)(83,133,93,123)(84,134,94,124)(85,135,95,125)(86,136,96,126)(87,137,97,127)(88,138,98,128)(89,139,99,129)(90,140,100,130)(101,151,111,141)(102,152,112,142)(103,153,113,143)(104,154,114,144)(105,155,115,145)(106,156,116,146)(107,157,117,147)(108,158,118,148)(109,159,119,149)(110,160,120,150), (1,116,16,101)(2,117,17,102)(3,118,18,103)(4,119,19,104)(5,120,20,105)(6,111,11,106)(7,112,12,107)(8,113,13,108)(9,114,14,109)(10,115,15,110)(21,96,36,81)(22,97,37,82)(23,98,38,83)(24,99,39,84)(25,100,40,85)(26,91,31,86)(27,92,32,87)(28,93,33,88)(29,94,34,89)(30,95,35,90)(41,156,56,141)(42,157,57,142)(43,158,58,143)(44,159,59,144)(45,160,60,145)(46,151,51,146)(47,152,52,147)(48,153,53,148)(49,154,54,149)(50,155,55,150)(61,136,76,121)(62,137,77,122)(63,138,78,123)(64,139,79,124)(65,140,80,125)(66,131,71,126)(67,132,72,127)(68,133,73,128)(69,134,74,129)(70,135,75,130), (1,81)(2,82)(3,83)(4,84)(5,85)(6,86)(7,87)(8,88)(9,89)(10,90)(11,91)(12,92)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,116)(37,117)(38,118)(39,119)(40,120)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,137)(58,138)(59,139)(60,140)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160), (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), (1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,25)(22,24)(26,30)(27,29)(31,35)(32,34)(36,40)(37,39)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(61,65)(62,64)(66,70)(67,69)(71,75)(72,74)(76,80)(77,79)(81,85)(82,84)(86,90)(87,89)(91,95)(92,94)(96,100)(97,99)(101,120)(102,119)(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,112)(110,111)(121,125)(122,124)(126,130)(127,129)(131,135)(132,134)(136,140)(137,139)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151) );
G=PermutationGroup([[(1,51,11,41),(2,52,12,42),(3,53,13,43),(4,54,14,44),(5,55,15,45),(6,56,16,46),(7,57,17,47),(8,58,18,48),(9,59,19,49),(10,60,20,50),(21,71,31,61),(22,72,32,62),(23,73,33,63),(24,74,34,64),(25,75,35,65),(26,76,36,66),(27,77,37,67),(28,78,38,68),(29,79,39,69),(30,80,40,70),(81,131,91,121),(82,132,92,122),(83,133,93,123),(84,134,94,124),(85,135,95,125),(86,136,96,126),(87,137,97,127),(88,138,98,128),(89,139,99,129),(90,140,100,130),(101,151,111,141),(102,152,112,142),(103,153,113,143),(104,154,114,144),(105,155,115,145),(106,156,116,146),(107,157,117,147),(108,158,118,148),(109,159,119,149),(110,160,120,150)], [(1,116,16,101),(2,117,17,102),(3,118,18,103),(4,119,19,104),(5,120,20,105),(6,111,11,106),(7,112,12,107),(8,113,13,108),(9,114,14,109),(10,115,15,110),(21,96,36,81),(22,97,37,82),(23,98,38,83),(24,99,39,84),(25,100,40,85),(26,91,31,86),(27,92,32,87),(28,93,33,88),(29,94,34,89),(30,95,35,90),(41,156,56,141),(42,157,57,142),(43,158,58,143),(44,159,59,144),(45,160,60,145),(46,151,51,146),(47,152,52,147),(48,153,53,148),(49,154,54,149),(50,155,55,150),(61,136,76,121),(62,137,77,122),(63,138,78,123),(64,139,79,124),(65,140,80,125),(66,131,71,126),(67,132,72,127),(68,133,73,128),(69,134,74,129),(70,135,75,130)], [(1,81),(2,82),(3,83),(4,84),(5,85),(6,86),(7,87),(8,88),(9,89),(10,90),(11,91),(12,92),(13,93),(14,94),(15,95),(16,96),(17,97),(18,98),(19,99),(20,100),(21,101),(22,102),(23,103),(24,104),(25,105),(26,106),(27,107),(28,108),(29,109),(30,110),(31,111),(32,112),(33,113),(34,114),(35,115),(36,116),(37,117),(38,118),(39,119),(40,120),(41,121),(42,122),(43,123),(44,124),(45,125),(46,126),(47,127),(48,128),(49,129),(50,130),(51,131),(52,132),(53,133),(54,134),(55,135),(56,136),(57,137),(58,138),(59,139),(60,140),(61,141),(62,142),(63,143),(64,144),(65,145),(66,146),(67,147),(68,148),(69,149),(70,150),(71,151),(72,152),(73,153),(74,154),(75,155),(76,156),(77,157),(78,158),(79,159),(80,160)], [(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)], [(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,25),(22,24),(26,30),(27,29),(31,35),(32,34),(36,40),(37,39),(41,60),(42,59),(43,58),(44,57),(45,56),(46,55),(47,54),(48,53),(49,52),(50,51),(61,65),(62,64),(66,70),(67,69),(71,75),(72,74),(76,80),(77,79),(81,85),(82,84),(86,90),(87,89),(91,95),(92,94),(96,100),(97,99),(101,120),(102,119),(103,118),(104,117),(105,116),(106,115),(107,114),(108,113),(109,112),(110,111),(121,125),(122,124),(126,130),(127,129),(131,135),(132,134),(136,140),(137,139),(141,160),(142,159),(143,158),(144,157),(145,156),(146,155),(147,154),(148,153),(149,152),(150,151)]])
80 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 4M | ··· | 4T | 4U | ··· | 4AD | 5A | 5B | 10A | ··· | 10F | 10G | ··· | 10N | 20A | ··· | 20H | 20I | ··· | 20X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 10 | 10 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 5 | ··· | 5 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D5 | C4○D4 | C4○D4 | D10 | D10 | D10 | D10 | D10 | C4×D5 | D4⋊2D5 | D5×C4○D4 |
| kernel | C4×D4⋊2D5 | C4×Dic10 | D5×C42 | C23.11D10 | Dic5⋊4D4 | Dic5⋊3Q8 | C4⋊C4⋊7D5 | C2×C4×Dic5 | C4×C5⋊D4 | D4×Dic5 | D4×C20 | C2×D4⋊2D5 | D4⋊2D5 | C4×D4 | Dic5 | C20 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | D4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 16 | 2 | 4 | 4 | 2 | 4 | 2 | 4 | 2 | 16 | 4 | 4 |
Matrix representation of C4×D4⋊2D5 ►in GL4(𝔽41) generated by
| 9 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 |
| 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 9 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 32 | 36 |
| 0 | 0 | 0 | 9 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 9 | 5 |
| 0 | 0 | 25 | 32 |
| 0 | 40 | 0 | 0 |
| 1 | 34 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 34 | 7 | 0 | 0 |
| 40 | 7 | 0 | 0 |
| 0 | 0 | 40 | 4 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(41))| [9,0,0,0,0,9,0,0,0,0,9,0,0,0,0,9],[1,0,0,0,0,1,0,0,0,0,32,0,0,0,36,9],[1,0,0,0,0,1,0,0,0,0,9,25,0,0,5,32],[0,1,0,0,40,34,0,0,0,0,1,0,0,0,0,1],[34,40,0,0,7,7,0,0,0,0,40,0,0,0,4,1] >;
C4×D4⋊2D5 in GAP, Magma, Sage, TeX
C_4\times D_4\rtimes_2D_5
% in TeX
G:=Group("C4xD4:2D5"); // GroupNames label
G:=SmallGroup(320,1208);
// by ID
G=gap.SmallGroup(320,1208);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,100,794,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=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^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^2*c,e*d*e=d^-1>;
// generators/relations