direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D10⋊D4, C24.26D10, D10⋊1(C2×D4), Dic5⋊6(C2×D4), (C22×D5)⋊9D4, C10⋊1(C4⋊D4), C22⋊C4⋊39D10, (C2×Dic5)⋊19D4, (C22×D20)⋊6C2, (C2×D20)⋊44C22, (C2×C10).33C24, C10.36(C22×D4), C22.127(D4×D5), (C2×C20).573C23, (C22×C4).170D10, D10⋊C4⋊58C22, (C22×D5).6C23, C22.72(C23×D5), C23.80(C22×D5), C22.73(C4○D20), C10.D4⋊48C22, (C23×C10).59C22, (C22×C20).353C22, (C22×C10).125C23, (C2×Dic5).189C23, (C23×D5).108C22, (C22×Dic5).77C22, C5⋊1(C2×C4⋊D4), C2.10(C2×D4×D5), (C2×C4×D5)⋊66C22, (D5×C22×C4)⋊18C2, (C2×C22⋊C4)⋊12D5, C10.13(C2×C4○D4), C2.15(C2×C4○D20), (C22×C5⋊D4)⋊4C2, (C10×C22⋊C4)⋊17C2, (C2×C10).382(C2×D4), (C2×C5⋊D4)⋊35C22, (C2×D10⋊C4)⋊31C2, (C2×C10.D4)⋊22C2, (C5×C22⋊C4)⋊52C22, (C2×C4).134(C22×D5), (C2×C10).102(C4○D4), SmallGroup(320,1161)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D10⋊D4
G = < a,b,c,d,e | a2=b10=c2=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=dbd-1=ebe=b-1, dcd-1=b8c, ece=b3c, ede=d-1 >
Subgroups: 1742 in 426 conjugacy classes, 127 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, D5, C10, C10, C10, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, C24, Dic5, Dic5, C20, D10, D10, C2×C10, C2×C10, C2×C10, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, C4×D5, D20, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×D5, C22×C10, C22×C10, C22×C10, C2×C4⋊D4, C10.D4, D10⋊C4, C5×C22⋊C4, C2×C4×D5, C2×C4×D5, C2×D20, C2×D20, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, C23×D5, C23×C10, D10⋊D4, C2×C10.D4, C2×D10⋊C4, C10×C22⋊C4, D5×C22×C4, C22×D20, C22×C5⋊D4, C2×D10⋊D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C4⋊D4, C22×D4, C2×C4○D4, C22×D5, C2×C4⋊D4, C4○D20, D4×D5, C23×D5, D10⋊D4, C2×C4○D20, C2×D4×D5, C2×D10⋊D4
►On 160 points
Generators in S160
(1 110)(2 101)(3 102)(4 103)(5 104)(6 105)(7 106)(8 107)(9 108)(10 109)(11 85)(12 86)(13 87)(14 88)(15 89)(16 90)(17 81)(18 82)(19 83)(20 84)(21 91)(22 92)(23 93)(24 94)(25 95)(26 96)(27 97)(28 98)(29 99)(30 100)(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)
(1 151)(2 160)(3 159)(4 158)(5 157)(6 156)(7 155)(8 154)(9 153)(10 152)(11 26)(12 25)(13 24)(14 23)(15 22)(16 21)(17 30)(18 29)(19 28)(20 27)(31 137)(32 136)(33 135)(34 134)(35 133)(36 132)(37 131)(38 140)(39 139)(40 138)(41 143)(42 142)(43 141)(44 150)(45 149)(46 148)(47 147)(48 146)(49 145)(50 144)(51 117)(52 116)(53 115)(54 114)(55 113)(56 112)(57 111)(58 120)(59 119)(60 118)(61 123)(62 122)(63 121)(64 130)(65 129)(66 128)(67 127)(68 126)(69 125)(70 124)(71 110)(72 109)(73 108)(74 107)(75 106)(76 105)(77 104)(78 103)(79 102)(80 101)(81 100)(82 99)(83 98)(84 97)(85 96)(86 95)(87 94)(88 93)(89 92)(90 91)
(1 112 27 125)(2 111 28 124)(3 120 29 123)(4 119 30 122)(5 118 21 121)(6 117 22 130)(7 116 23 129)(8 115 24 128)(9 114 25 127)(10 113 26 126)(11 70 152 57)(12 69 153 56)(13 68 154 55)(14 67 155 54)(15 66 156 53)(16 65 157 52)(17 64 158 51)(18 63 159 60)(19 62 160 59)(20 61 151 58)(31 98 44 101)(32 97 45 110)(33 96 46 109)(34 95 47 108)(35 94 48 107)(36 93 49 106)(37 92 50 105)(38 91 41 104)(39 100 42 103)(40 99 43 102)(71 138 84 141)(72 137 85 150)(73 136 86 149)(74 135 87 148)(75 134 88 147)(76 133 89 146)(77 132 90 145)(78 131 81 144)(79 140 82 143)(80 139 83 142)
(1 92)(2 91)(3 100)(4 99)(5 98)(6 97)(7 96)(8 95)(9 94)(10 93)(11 72)(12 71)(13 80)(14 79)(15 78)(16 77)(17 76)(18 75)(19 74)(20 73)(21 101)(22 110)(23 109)(24 108)(25 107)(26 106)(27 105)(28 104)(29 103)(30 102)(31 118)(32 117)(33 116)(34 115)(35 114)(36 113)(37 112)(38 111)(39 120)(40 119)(41 124)(42 123)(43 122)(44 121)(45 130)(46 129)(47 128)(48 127)(49 126)(50 125)(51 133)(52 132)(53 131)(54 140)(55 139)(56 138)(57 137)(58 136)(59 135)(60 134)(61 149)(62 148)(63 147)(64 146)(65 145)(66 144)(67 143)(68 142)(69 141)(70 150)(81 156)(82 155)(83 154)(84 153)(85 152)(86 151)(87 160)(88 159)(89 158)(90 157)
G:=sub<Sym(160)| (1,110)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,109)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,81)(18,82)(19,83)(20,84)(21,91)(22,92)(23,93)(24,94)(25,95)(26,96)(27,97)(28,98)(29,99)(30,100)(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), (1,151)(2,160)(3,159)(4,158)(5,157)(6,156)(7,155)(8,154)(9,153)(10,152)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,30)(18,29)(19,28)(20,27)(31,137)(32,136)(33,135)(34,134)(35,133)(36,132)(37,131)(38,140)(39,139)(40,138)(41,143)(42,142)(43,141)(44,150)(45,149)(46,148)(47,147)(48,146)(49,145)(50,144)(51,117)(52,116)(53,115)(54,114)(55,113)(56,112)(57,111)(58,120)(59,119)(60,118)(61,123)(62,122)(63,121)(64,130)(65,129)(66,128)(67,127)(68,126)(69,125)(70,124)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91), (1,112,27,125)(2,111,28,124)(3,120,29,123)(4,119,30,122)(5,118,21,121)(6,117,22,130)(7,116,23,129)(8,115,24,128)(9,114,25,127)(10,113,26,126)(11,70,152,57)(12,69,153,56)(13,68,154,55)(14,67,155,54)(15,66,156,53)(16,65,157,52)(17,64,158,51)(18,63,159,60)(19,62,160,59)(20,61,151,58)(31,98,44,101)(32,97,45,110)(33,96,46,109)(34,95,47,108)(35,94,48,107)(36,93,49,106)(37,92,50,105)(38,91,41,104)(39,100,42,103)(40,99,43,102)(71,138,84,141)(72,137,85,150)(73,136,86,149)(74,135,87,148)(75,134,88,147)(76,133,89,146)(77,132,90,145)(78,131,81,144)(79,140,82,143)(80,139,83,142), (1,92)(2,91)(3,100)(4,99)(5,98)(6,97)(7,96)(8,95)(9,94)(10,93)(11,72)(12,71)(13,80)(14,79)(15,78)(16,77)(17,76)(18,75)(19,74)(20,73)(21,101)(22,110)(23,109)(24,108)(25,107)(26,106)(27,105)(28,104)(29,103)(30,102)(31,118)(32,117)(33,116)(34,115)(35,114)(36,113)(37,112)(38,111)(39,120)(40,119)(41,124)(42,123)(43,122)(44,121)(45,130)(46,129)(47,128)(48,127)(49,126)(50,125)(51,133)(52,132)(53,131)(54,140)(55,139)(56,138)(57,137)(58,136)(59,135)(60,134)(61,149)(62,148)(63,147)(64,146)(65,145)(66,144)(67,143)(68,142)(69,141)(70,150)(81,156)(82,155)(83,154)(84,153)(85,152)(86,151)(87,160)(88,159)(89,158)(90,157)>;
G:=Group( (1,110)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,109)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,81)(18,82)(19,83)(20,84)(21,91)(22,92)(23,93)(24,94)(25,95)(26,96)(27,97)(28,98)(29,99)(30,100)(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), (1,151)(2,160)(3,159)(4,158)(5,157)(6,156)(7,155)(8,154)(9,153)(10,152)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,30)(18,29)(19,28)(20,27)(31,137)(32,136)(33,135)(34,134)(35,133)(36,132)(37,131)(38,140)(39,139)(40,138)(41,143)(42,142)(43,141)(44,150)(45,149)(46,148)(47,147)(48,146)(49,145)(50,144)(51,117)(52,116)(53,115)(54,114)(55,113)(56,112)(57,111)(58,120)(59,119)(60,118)(61,123)(62,122)(63,121)(64,130)(65,129)(66,128)(67,127)(68,126)(69,125)(70,124)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91), (1,112,27,125)(2,111,28,124)(3,120,29,123)(4,119,30,122)(5,118,21,121)(6,117,22,130)(7,116,23,129)(8,115,24,128)(9,114,25,127)(10,113,26,126)(11,70,152,57)(12,69,153,56)(13,68,154,55)(14,67,155,54)(15,66,156,53)(16,65,157,52)(17,64,158,51)(18,63,159,60)(19,62,160,59)(20,61,151,58)(31,98,44,101)(32,97,45,110)(33,96,46,109)(34,95,47,108)(35,94,48,107)(36,93,49,106)(37,92,50,105)(38,91,41,104)(39,100,42,103)(40,99,43,102)(71,138,84,141)(72,137,85,150)(73,136,86,149)(74,135,87,148)(75,134,88,147)(76,133,89,146)(77,132,90,145)(78,131,81,144)(79,140,82,143)(80,139,83,142), (1,92)(2,91)(3,100)(4,99)(5,98)(6,97)(7,96)(8,95)(9,94)(10,93)(11,72)(12,71)(13,80)(14,79)(15,78)(16,77)(17,76)(18,75)(19,74)(20,73)(21,101)(22,110)(23,109)(24,108)(25,107)(26,106)(27,105)(28,104)(29,103)(30,102)(31,118)(32,117)(33,116)(34,115)(35,114)(36,113)(37,112)(38,111)(39,120)(40,119)(41,124)(42,123)(43,122)(44,121)(45,130)(46,129)(47,128)(48,127)(49,126)(50,125)(51,133)(52,132)(53,131)(54,140)(55,139)(56,138)(57,137)(58,136)(59,135)(60,134)(61,149)(62,148)(63,147)(64,146)(65,145)(66,144)(67,143)(68,142)(69,141)(70,150)(81,156)(82,155)(83,154)(84,153)(85,152)(86,151)(87,160)(88,159)(89,158)(90,157) );
G=PermutationGroup([[(1,110),(2,101),(3,102),(4,103),(5,104),(6,105),(7,106),(8,107),(9,108),(10,109),(11,85),(12,86),(13,87),(14,88),(15,89),(16,90),(17,81),(18,82),(19,83),(20,84),(21,91),(22,92),(23,93),(24,94),(25,95),(26,96),(27,97),(28,98),(29,99),(30,100),(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)], [(1,151),(2,160),(3,159),(4,158),(5,157),(6,156),(7,155),(8,154),(9,153),(10,152),(11,26),(12,25),(13,24),(14,23),(15,22),(16,21),(17,30),(18,29),(19,28),(20,27),(31,137),(32,136),(33,135),(34,134),(35,133),(36,132),(37,131),(38,140),(39,139),(40,138),(41,143),(42,142),(43,141),(44,150),(45,149),(46,148),(47,147),(48,146),(49,145),(50,144),(51,117),(52,116),(53,115),(54,114),(55,113),(56,112),(57,111),(58,120),(59,119),(60,118),(61,123),(62,122),(63,121),(64,130),(65,129),(66,128),(67,127),(68,126),(69,125),(70,124),(71,110),(72,109),(73,108),(74,107),(75,106),(76,105),(77,104),(78,103),(79,102),(80,101),(81,100),(82,99),(83,98),(84,97),(85,96),(86,95),(87,94),(88,93),(89,92),(90,91)], [(1,112,27,125),(2,111,28,124),(3,120,29,123),(4,119,30,122),(5,118,21,121),(6,117,22,130),(7,116,23,129),(8,115,24,128),(9,114,25,127),(10,113,26,126),(11,70,152,57),(12,69,153,56),(13,68,154,55),(14,67,155,54),(15,66,156,53),(16,65,157,52),(17,64,158,51),(18,63,159,60),(19,62,160,59),(20,61,151,58),(31,98,44,101),(32,97,45,110),(33,96,46,109),(34,95,47,108),(35,94,48,107),(36,93,49,106),(37,92,50,105),(38,91,41,104),(39,100,42,103),(40,99,43,102),(71,138,84,141),(72,137,85,150),(73,136,86,149),(74,135,87,148),(75,134,88,147),(76,133,89,146),(77,132,90,145),(78,131,81,144),(79,140,82,143),(80,139,83,142)], [(1,92),(2,91),(3,100),(4,99),(5,98),(6,97),(7,96),(8,95),(9,94),(10,93),(11,72),(12,71),(13,80),(14,79),(15,78),(16,77),(17,76),(18,75),(19,74),(20,73),(21,101),(22,110),(23,109),(24,108),(25,107),(26,106),(27,105),(28,104),(29,103),(30,102),(31,118),(32,117),(33,116),(34,115),(35,114),(36,113),(37,112),(38,111),(39,120),(40,119),(41,124),(42,123),(43,122),(44,121),(45,130),(46,129),(47,128),(48,127),(49,126),(50,125),(51,133),(52,132),(53,131),(54,140),(55,139),(56,138),(57,137),(58,136),(59,135),(60,134),(61,149),(62,148),(63,147),(64,146),(65,145),(66,144),(67,143),(68,142),(69,141),(70,150),(81,156),(82,155),(83,154),(84,153),(85,152),(86,151),(87,160),(88,159),(89,158),(90,157)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10V | 20A | ··· | 20P |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4○D20 | D4×D5 |
| kernel | C2×D10⋊D4 | D10⋊D4 | C2×C10.D4 | C2×D10⋊C4 | C10×C22⋊C4 | D5×C22×C4 | C22×D20 | C22×C5⋊D4 | C2×Dic5 | C22×D5 | C2×C22⋊C4 | C2×C10 | C22⋊C4 | C22×C4 | C24 | C22 | C22 |
| # reps | 1 | 8 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 2 | 4 | 8 | 4 | 2 | 16 | 8 |
Matrix representation of C2×D10⋊D4 ►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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 7 | 0 | 0 | 0 | 0 |
| 35 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 34 | 0 | 0 |
| 0 | 0 | 7 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 39 | 9 | 0 | 0 | 0 | 0 |
| 27 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 7 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 21 | 38 | 0 | 0 | 0 | 0 |
| 38 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 6 | 7 | 0 | 0 | 0 | 0 |
| 36 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 7 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,35,0,0,0,0,7,35,0,0,0,0,0,0,40,7,0,0,0,0,34,7,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[39,27,0,0,0,0,9,2,0,0,0,0,0,0,1,0,0,0,0,0,7,40,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[21,38,0,0,0,0,38,20,0,0,0,0,0,0,1,34,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[6,36,0,0,0,0,7,35,0,0,0,0,0,0,40,7,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1] >;
C2×D10⋊D4 in GAP, Magma, Sage, TeX
C_2\times D_{10}\rtimes D_4 % in TeX
G:=Group("C2xD10:D4"); // GroupNames label
G:=SmallGroup(320,1161);
// by ID
G=gap.SmallGroup(320,1161);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,100,1571,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^10=c^2=d^4=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=d*b*d^-1=e*b*e=b^-1,d*c*d^-1=b^8*c,e*c*e=b^3*c,e*d*e=d^-1>;
// generators/relations