metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.56D10, C4⋊D4.4D5, (C2×D4).36D10, (C2×C20).261D4, C10.95(C4○D8), C10.D8⋊35C2, C20.55D4⋊9C2, D4⋊Dic5⋊14C2, C20.Q8⋊34C2, (C22×C10).81D4, C20.182(C4○D4), C4.92(D4⋊2D5), C10.89(C8⋊C22), (C2×C20).354C23, (D4×C10).52C22, (C22×C4).118D10, C23.22(C5⋊D4), C5⋊7(C23.19D4), C4⋊Dic5.336C22, C2.10(D4.D10), C2.14(D4.8D10), C23.21D10⋊15C2, (C22×C20).158C22, C10.79(C22.D4), C2.13(C23.18D10), (C5×C4⋊D4).3C2, (C2×C10).485(C2×D4), (C2×C4).170(C5⋊D4), (C5×C4⋊C4).103C22, (C2×C4).454(C22×D5), C22.160(C2×C5⋊D4), (C2×C5⋊2C8).107C22, SmallGroup(320,662)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×D4).D10
G = < a,b,c,d,e | a2=b4=c2=1, d10=b2, e2=a, ab=ba, ac=ca, ad=da, ae=ea, cbc=ebe-1=b-1, bd=db, dcd-1=ab2c, ece-1=b-1c, ede-1=d9 >
Subgroups: 334 in 106 conjugacy classes, 39 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, D4, C23, C23, C10, C10, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C2×D4, C2×D4, Dic5, C20, C20, C2×C10, C2×C10, C22⋊C8, D4⋊C4, C4.Q8, C2.D8, C42⋊C2, C4⋊D4, C5⋊2C8, C2×Dic5, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C23.19D4, C2×C5⋊2C8, C4×Dic5, C4⋊Dic5, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C22×C20, D4×C10, D4×C10, C10.D8, C20.Q8, C20.55D4, D4⋊Dic5, C23.21D10, C5×C4⋊D4, (C2×D4).D10
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, D10, C22.D4, C4○D8, C8⋊C22, C5⋊D4, C22×D5, C23.19D4, D4⋊2D5, C2×C5⋊D4, D4.D10, C23.18D10, D4.8D10, (C2×D4).D10
►On 160 points
Generators in S160
(1 130)(2 131)(3 132)(4 133)(5 134)(6 135)(7 136)(8 137)(9 138)(10 139)(11 140)(12 121)(13 122)(14 123)(15 124)(16 125)(17 126)(18 127)(19 128)(20 129)(21 92)(22 93)(23 94)(24 95)(25 96)(26 97)(27 98)(28 99)(29 100)(30 81)(31 82)(32 83)(33 84)(34 85)(35 86)(36 87)(37 88)(38 89)(39 90)(40 91)(41 149)(42 150)(43 151)(44 152)(45 153)(46 154)(47 155)(48 156)(49 157)(50 158)(51 159)(52 160)(53 141)(54 142)(55 143)(56 144)(57 145)(58 146)(59 147)(60 148)(61 120)(62 101)(63 102)(64 103)(65 104)(66 105)(67 106)(68 107)(69 108)(70 109)(71 110)(72 111)(73 112)(74 113)(75 114)(76 115)(77 116)(78 117)(79 118)(80 119)
(1 106 11 116)(2 107 12 117)(3 108 13 118)(4 109 14 119)(5 110 15 120)(6 111 16 101)(7 112 17 102)(8 113 18 103)(9 114 19 104)(10 115 20 105)(21 42 31 52)(22 43 32 53)(23 44 33 54)(24 45 34 55)(25 46 35 56)(26 47 36 57)(27 48 37 58)(28 49 38 59)(29 50 39 60)(30 51 40 41)(61 134 71 124)(62 135 72 125)(63 136 73 126)(64 137 74 127)(65 138 75 128)(66 139 76 129)(67 140 77 130)(68 121 78 131)(69 122 79 132)(70 123 80 133)(81 159 91 149)(82 160 92 150)(83 141 93 151)(84 142 94 152)(85 143 95 153)(86 144 96 154)(87 145 97 155)(88 146 98 156)(89 147 99 157)(90 148 100 158)
(2 121)(4 123)(6 125)(8 127)(10 129)(12 131)(14 133)(16 135)(18 137)(20 139)(21 150)(22 53)(23 152)(24 55)(25 154)(26 57)(27 156)(28 59)(29 158)(30 41)(31 160)(32 43)(33 142)(34 45)(35 144)(36 47)(37 146)(38 49)(39 148)(40 51)(42 92)(44 94)(46 96)(48 98)(50 100)(52 82)(54 84)(56 86)(58 88)(60 90)(61 71)(62 101)(63 73)(64 103)(65 75)(66 105)(67 77)(68 107)(69 79)(70 109)(72 111)(74 113)(76 115)(78 117)(80 119)(81 149)(83 151)(85 153)(87 155)(89 157)(91 159)(93 141)(95 143)(97 145)(99 147)(102 112)(104 114)(106 116)(108 118)(110 120)
(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 83 130 32)(2 92 131 21)(3 81 132 30)(4 90 133 39)(5 99 134 28)(6 88 135 37)(7 97 136 26)(8 86 137 35)(9 95 138 24)(10 84 139 33)(11 93 140 22)(12 82 121 31)(13 91 122 40)(14 100 123 29)(15 89 124 38)(16 98 125 27)(17 87 126 36)(18 96 127 25)(19 85 128 34)(20 94 129 23)(41 108 149 69)(42 117 150 78)(43 106 151 67)(44 115 152 76)(45 104 153 65)(46 113 154 74)(47 102 155 63)(48 111 156 72)(49 120 157 61)(50 109 158 70)(51 118 159 79)(52 107 160 68)(53 116 141 77)(54 105 142 66)(55 114 143 75)(56 103 144 64)(57 112 145 73)(58 101 146 62)(59 110 147 71)(60 119 148 80)
G:=sub<Sym(160)| (1,130)(2,131)(3,132)(4,133)(5,134)(6,135)(7,136)(8,137)(9,138)(10,139)(11,140)(12,121)(13,122)(14,123)(15,124)(16,125)(17,126)(18,127)(19,128)(20,129)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,100)(30,81)(31,82)(32,83)(33,84)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,149)(42,150)(43,151)(44,152)(45,153)(46,154)(47,155)(48,156)(49,157)(50,158)(51,159)(52,160)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,148)(61,120)(62,101)(63,102)(64,103)(65,104)(66,105)(67,106)(68,107)(69,108)(70,109)(71,110)(72,111)(73,112)(74,113)(75,114)(76,115)(77,116)(78,117)(79,118)(80,119), (1,106,11,116)(2,107,12,117)(3,108,13,118)(4,109,14,119)(5,110,15,120)(6,111,16,101)(7,112,17,102)(8,113,18,103)(9,114,19,104)(10,115,20,105)(21,42,31,52)(22,43,32,53)(23,44,33,54)(24,45,34,55)(25,46,35,56)(26,47,36,57)(27,48,37,58)(28,49,38,59)(29,50,39,60)(30,51,40,41)(61,134,71,124)(62,135,72,125)(63,136,73,126)(64,137,74,127)(65,138,75,128)(66,139,76,129)(67,140,77,130)(68,121,78,131)(69,122,79,132)(70,123,80,133)(81,159,91,149)(82,160,92,150)(83,141,93,151)(84,142,94,152)(85,143,95,153)(86,144,96,154)(87,145,97,155)(88,146,98,156)(89,147,99,157)(90,148,100,158), (2,121)(4,123)(6,125)(8,127)(10,129)(12,131)(14,133)(16,135)(18,137)(20,139)(21,150)(22,53)(23,152)(24,55)(25,154)(26,57)(27,156)(28,59)(29,158)(30,41)(31,160)(32,43)(33,142)(34,45)(35,144)(36,47)(37,146)(38,49)(39,148)(40,51)(42,92)(44,94)(46,96)(48,98)(50,100)(52,82)(54,84)(56,86)(58,88)(60,90)(61,71)(62,101)(63,73)(64,103)(65,75)(66,105)(67,77)(68,107)(69,79)(70,109)(72,111)(74,113)(76,115)(78,117)(80,119)(81,149)(83,151)(85,153)(87,155)(89,157)(91,159)(93,141)(95,143)(97,145)(99,147)(102,112)(104,114)(106,116)(108,118)(110,120), (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), (1,83,130,32)(2,92,131,21)(3,81,132,30)(4,90,133,39)(5,99,134,28)(6,88,135,37)(7,97,136,26)(8,86,137,35)(9,95,138,24)(10,84,139,33)(11,93,140,22)(12,82,121,31)(13,91,122,40)(14,100,123,29)(15,89,124,38)(16,98,125,27)(17,87,126,36)(18,96,127,25)(19,85,128,34)(20,94,129,23)(41,108,149,69)(42,117,150,78)(43,106,151,67)(44,115,152,76)(45,104,153,65)(46,113,154,74)(47,102,155,63)(48,111,156,72)(49,120,157,61)(50,109,158,70)(51,118,159,79)(52,107,160,68)(53,116,141,77)(54,105,142,66)(55,114,143,75)(56,103,144,64)(57,112,145,73)(58,101,146,62)(59,110,147,71)(60,119,148,80)>;
G:=Group( (1,130)(2,131)(3,132)(4,133)(5,134)(6,135)(7,136)(8,137)(9,138)(10,139)(11,140)(12,121)(13,122)(14,123)(15,124)(16,125)(17,126)(18,127)(19,128)(20,129)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,100)(30,81)(31,82)(32,83)(33,84)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,149)(42,150)(43,151)(44,152)(45,153)(46,154)(47,155)(48,156)(49,157)(50,158)(51,159)(52,160)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,148)(61,120)(62,101)(63,102)(64,103)(65,104)(66,105)(67,106)(68,107)(69,108)(70,109)(71,110)(72,111)(73,112)(74,113)(75,114)(76,115)(77,116)(78,117)(79,118)(80,119), (1,106,11,116)(2,107,12,117)(3,108,13,118)(4,109,14,119)(5,110,15,120)(6,111,16,101)(7,112,17,102)(8,113,18,103)(9,114,19,104)(10,115,20,105)(21,42,31,52)(22,43,32,53)(23,44,33,54)(24,45,34,55)(25,46,35,56)(26,47,36,57)(27,48,37,58)(28,49,38,59)(29,50,39,60)(30,51,40,41)(61,134,71,124)(62,135,72,125)(63,136,73,126)(64,137,74,127)(65,138,75,128)(66,139,76,129)(67,140,77,130)(68,121,78,131)(69,122,79,132)(70,123,80,133)(81,159,91,149)(82,160,92,150)(83,141,93,151)(84,142,94,152)(85,143,95,153)(86,144,96,154)(87,145,97,155)(88,146,98,156)(89,147,99,157)(90,148,100,158), (2,121)(4,123)(6,125)(8,127)(10,129)(12,131)(14,133)(16,135)(18,137)(20,139)(21,150)(22,53)(23,152)(24,55)(25,154)(26,57)(27,156)(28,59)(29,158)(30,41)(31,160)(32,43)(33,142)(34,45)(35,144)(36,47)(37,146)(38,49)(39,148)(40,51)(42,92)(44,94)(46,96)(48,98)(50,100)(52,82)(54,84)(56,86)(58,88)(60,90)(61,71)(62,101)(63,73)(64,103)(65,75)(66,105)(67,77)(68,107)(69,79)(70,109)(72,111)(74,113)(76,115)(78,117)(80,119)(81,149)(83,151)(85,153)(87,155)(89,157)(91,159)(93,141)(95,143)(97,145)(99,147)(102,112)(104,114)(106,116)(108,118)(110,120), (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), (1,83,130,32)(2,92,131,21)(3,81,132,30)(4,90,133,39)(5,99,134,28)(6,88,135,37)(7,97,136,26)(8,86,137,35)(9,95,138,24)(10,84,139,33)(11,93,140,22)(12,82,121,31)(13,91,122,40)(14,100,123,29)(15,89,124,38)(16,98,125,27)(17,87,126,36)(18,96,127,25)(19,85,128,34)(20,94,129,23)(41,108,149,69)(42,117,150,78)(43,106,151,67)(44,115,152,76)(45,104,153,65)(46,113,154,74)(47,102,155,63)(48,111,156,72)(49,120,157,61)(50,109,158,70)(51,118,159,79)(52,107,160,68)(53,116,141,77)(54,105,142,66)(55,114,143,75)(56,103,144,64)(57,112,145,73)(58,101,146,62)(59,110,147,71)(60,119,148,80) );
G=PermutationGroup([[(1,130),(2,131),(3,132),(4,133),(5,134),(6,135),(7,136),(8,137),(9,138),(10,139),(11,140),(12,121),(13,122),(14,123),(15,124),(16,125),(17,126),(18,127),(19,128),(20,129),(21,92),(22,93),(23,94),(24,95),(25,96),(26,97),(27,98),(28,99),(29,100),(30,81),(31,82),(32,83),(33,84),(34,85),(35,86),(36,87),(37,88),(38,89),(39,90),(40,91),(41,149),(42,150),(43,151),(44,152),(45,153),(46,154),(47,155),(48,156),(49,157),(50,158),(51,159),(52,160),(53,141),(54,142),(55,143),(56,144),(57,145),(58,146),(59,147),(60,148),(61,120),(62,101),(63,102),(64,103),(65,104),(66,105),(67,106),(68,107),(69,108),(70,109),(71,110),(72,111),(73,112),(74,113),(75,114),(76,115),(77,116),(78,117),(79,118),(80,119)], [(1,106,11,116),(2,107,12,117),(3,108,13,118),(4,109,14,119),(5,110,15,120),(6,111,16,101),(7,112,17,102),(8,113,18,103),(9,114,19,104),(10,115,20,105),(21,42,31,52),(22,43,32,53),(23,44,33,54),(24,45,34,55),(25,46,35,56),(26,47,36,57),(27,48,37,58),(28,49,38,59),(29,50,39,60),(30,51,40,41),(61,134,71,124),(62,135,72,125),(63,136,73,126),(64,137,74,127),(65,138,75,128),(66,139,76,129),(67,140,77,130),(68,121,78,131),(69,122,79,132),(70,123,80,133),(81,159,91,149),(82,160,92,150),(83,141,93,151),(84,142,94,152),(85,143,95,153),(86,144,96,154),(87,145,97,155),(88,146,98,156),(89,147,99,157),(90,148,100,158)], [(2,121),(4,123),(6,125),(8,127),(10,129),(12,131),(14,133),(16,135),(18,137),(20,139),(21,150),(22,53),(23,152),(24,55),(25,154),(26,57),(27,156),(28,59),(29,158),(30,41),(31,160),(32,43),(33,142),(34,45),(35,144),(36,47),(37,146),(38,49),(39,148),(40,51),(42,92),(44,94),(46,96),(48,98),(50,100),(52,82),(54,84),(56,86),(58,88),(60,90),(61,71),(62,101),(63,73),(64,103),(65,75),(66,105),(67,77),(68,107),(69,79),(70,109),(72,111),(74,113),(76,115),(78,117),(80,119),(81,149),(83,151),(85,153),(87,155),(89,157),(91,159),(93,141),(95,143),(97,145),(99,147),(102,112),(104,114),(106,116),(108,118),(110,120)], [(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)], [(1,83,130,32),(2,92,131,21),(3,81,132,30),(4,90,133,39),(5,99,134,28),(6,88,135,37),(7,97,136,26),(8,86,137,35),(9,95,138,24),(10,84,139,33),(11,93,140,22),(12,82,121,31),(13,91,122,40),(14,100,123,29),(15,89,124,38),(16,98,125,27),(17,87,126,36),(18,96,127,25),(19,85,128,34),(20,94,129,23),(41,108,149,69),(42,117,150,78),(43,106,151,67),(44,115,152,76),(45,104,153,65),(46,113,154,74),(47,102,155,63),(48,111,156,72),(49,120,157,61),(50,109,158,70),(51,118,159,79),(52,107,160,68),(53,116,141,77),(54,105,142,66),(55,114,143,75),(56,103,144,64),(57,112,145,73),(58,101,146,62),(59,110,147,71),(60,119,148,80)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 10M | 10N | 20A | ··· | 20H | 20I | 20J | 20K | 20L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 8 | 2 | 2 | 2 | 2 | 8 | 20 | 20 | 20 | 20 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | 8 | 8 | 8 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4○D8 | C5⋊D4 | C5⋊D4 | C8⋊C22 | D4⋊2D5 | D4.D10 | D4.8D10 |
| kernel | (C2×D4).D10 | C10.D8 | C20.Q8 | C20.55D4 | D4⋊Dic5 | C23.21D10 | C5×C4⋊D4 | C2×C20 | C22×C10 | C4⋊D4 | C20 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C2×C4 | C23 | C10 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 2 | 4 | 4 | 4 | 1 | 4 | 4 | 4 |
Matrix representation of (C2×D4).D10 ►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 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 22 | 0 | 0 | 0 | 0 |
| 26 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 26 | 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 | 26 | 40 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 35 | 0 | 0 |
| 0 | 0 | 15 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 22 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 2 | 0 | 0 | 0 | 0 |
| 20 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 38 | 0 | 0 |
| 0 | 0 | 8 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 7 |
| 0 | 0 | 0 | 0 | 0 | 9 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,26,0,0,0,0,22,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,26,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,26,0,0,0,0,0,40],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,20,15,0,0,0,0,35,14,0,0,0,0,0,0,1,0,0,0,0,0,22,40],[0,20,0,0,0,0,2,0,0,0,0,0,0,0,36,8,0,0,0,0,38,5,0,0,0,0,0,0,32,0,0,0,0,0,7,9] >;
(C2×D4).D10 in GAP, Magma, Sage, TeX
(C_2\times D_4).D_{10} % in TeX
G:=Group("(C2xD4).D10"); // GroupNames label
G:=SmallGroup(320,662);
// by ID
G=gap.SmallGroup(320,662);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,254,219,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=1,d^10=b^2,e^2=a,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=a*b^2*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^9>;
// generators/relations