direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4.10D10, C10.13C25, C20.48C24, D10.7C24, D20.40C23, C10⋊22- 1+4, Dic5.8C24, Dic10.37C23, C4○D4⋊18D10, (C2×C10).4C24, (Q8×D5)⋊14C22, C2.14(D5×C24), C4.63(C23×D5), C5⋊D4.1C23, (C2×D4).254D10, C5⋊2(C2×2- 1+4), C4○D20⋊26C22, (C2×Q8).212D10, D4.29(C22×D5), (C4×D5).19C23, (C5×D4).29C23, (C5×Q8).30C23, Q8.30(C22×D5), D4⋊2D5⋊13C22, (C2×C20).567C23, (C22×C4).292D10, C22.57(C23×D5), (C2×Dic10)⋊75C22, (C22×Dic10)⋊25C2, (D4×C10).279C22, (C2×D20).298C22, (Q8×C10).247C22, C23.215(C22×D5), (C22×C10).249C23, (C22×C20).303C22, (C2×Dic5).167C23, (C22×D5).260C23, (C22×Dic5).169C22, (C2×Q8×D5)⋊21C2, (C2×C4○D4)⋊14D5, (C10×C4○D4)⋊15C2, (C2×C4○D20)⋊38C2, (C2×D4⋊2D5)⋊30C2, (C5×C4○D4)⋊21C22, (C2×C4×D5).182C22, (C2×C4).253(C22×D5), (C2×C5⋊D4).152C22, SmallGroup(320,1620)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4.10D10
G = < a,b,c,d,e | a2=b4=c2=1, d10=e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=dbd-1=ebe-1=b-1, dcd-1=b2c, ce=ec, ede-1=d9 >
Subgroups: 2126 in 794 conjugacy classes, 447 normal (14 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, C23, D5, C10, C10, C10, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, C4○D4, Dic5, C20, D10, D10, C2×C10, C2×C10, C2×C10, C22×Q8, C2×C4○D4, C2×C4○D4, 2- 1+4, Dic10, C4×D5, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C5×Q8, C22×D5, C22×C10, C2×2- 1+4, C2×Dic10, C2×C4×D5, C2×D20, C4○D20, D4⋊2D5, Q8×D5, C22×Dic5, C2×C5⋊D4, C22×C20, D4×C10, Q8×C10, C5×C4○D4, C22×Dic10, C2×C4○D20, C2×D4⋊2D5, C2×Q8×D5, D4.10D10, C10×C4○D4, C2×D4.10D10
Quotients: C1, C2, C22, C23, D5, C24, D10, 2- 1+4, C25, C22×D5, C2×2- 1+4, C23×D5, D4.10D10, D5×C24, C2×D4.10D10
►On 160 points
Generators in S160
(1 69)(2 70)(3 71)(4 72)(5 73)(6 74)(7 75)(8 76)(9 77)(10 78)(11 79)(12 80)(13 61)(14 62)(15 63)(16 64)(17 65)(18 66)(19 67)(20 68)(21 149)(22 150)(23 151)(24 152)(25 153)(26 154)(27 155)(28 156)(29 157)(30 158)(31 159)(32 160)(33 141)(34 142)(35 143)(36 144)(37 145)(38 146)(39 147)(40 148)(41 99)(42 100)(43 81)(44 82)(45 83)(46 84)(47 85)(48 86)(49 87)(50 88)(51 89)(52 90)(53 91)(54 92)(55 93)(56 94)(57 95)(58 96)(59 97)(60 98)(101 134)(102 135)(103 136)(104 137)(105 138)(106 139)(107 140)(108 121)(109 122)(110 123)(111 124)(112 125)(113 126)(114 127)(115 128)(116 129)(117 130)(118 131)(119 132)(120 133)
(1 131 11 121)(2 122 12 132)(3 133 13 123)(4 124 14 134)(5 135 15 125)(6 126 16 136)(7 137 17 127)(8 128 18 138)(9 139 19 129)(10 130 20 140)(21 82 31 92)(22 93 32 83)(23 84 33 94)(24 95 34 85)(25 86 35 96)(26 97 36 87)(27 88 37 98)(28 99 38 89)(29 90 39 100)(30 81 40 91)(41 146 51 156)(42 157 52 147)(43 148 53 158)(44 159 54 149)(45 150 55 160)(46 141 56 151)(47 152 57 142)(48 143 58 153)(49 154 59 144)(50 145 60 155)(61 110 71 120)(62 101 72 111)(63 112 73 102)(64 103 74 113)(65 114 75 104)(66 105 76 115)(67 116 77 106)(68 107 78 117)(69 118 79 108)(70 109 80 119)
(1 154)(2 145)(3 156)(4 147)(5 158)(6 149)(7 160)(8 151)(9 142)(10 153)(11 144)(12 155)(13 146)(14 157)(15 148)(16 159)(17 150)(18 141)(19 152)(20 143)(21 74)(22 65)(23 76)(24 67)(25 78)(26 69)(27 80)(28 71)(29 62)(30 73)(31 64)(32 75)(33 66)(34 77)(35 68)(36 79)(37 70)(38 61)(39 72)(40 63)(41 123)(42 134)(43 125)(44 136)(45 127)(46 138)(47 129)(48 140)(49 131)(50 122)(51 133)(52 124)(53 135)(54 126)(55 137)(56 128)(57 139)(58 130)(59 121)(60 132)(81 112)(82 103)(83 114)(84 105)(85 116)(86 107)(87 118)(88 109)(89 120)(90 111)(91 102)(92 113)(93 104)(94 115)(95 106)(96 117)(97 108)(98 119)(99 110)(100 101)
(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 78 11 68)(2 67 12 77)(3 76 13 66)(4 65 14 75)(5 74 15 64)(6 63 16 73)(7 72 17 62)(8 61 18 71)(9 70 19 80)(10 79 20 69)(21 148 31 158)(22 157 32 147)(23 146 33 156)(24 155 34 145)(25 144 35 154)(26 153 36 143)(27 142 37 152)(28 151 38 141)(29 160 39 150)(30 149 40 159)(41 94 51 84)(42 83 52 93)(43 92 53 82)(44 81 54 91)(45 90 55 100)(46 99 56 89)(47 88 57 98)(48 97 58 87)(49 86 59 96)(50 95 60 85)(101 127 111 137)(102 136 112 126)(103 125 113 135)(104 134 114 124)(105 123 115 133)(106 132 116 122)(107 121 117 131)(108 130 118 140)(109 139 119 129)(110 128 120 138)
G:=sub<Sym(160)| (1,69)(2,70)(3,71)(4,72)(5,73)(6,74)(7,75)(8,76)(9,77)(10,78)(11,79)(12,80)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,149)(22,150)(23,151)(24,152)(25,153)(26,154)(27,155)(28,156)(29,157)(30,158)(31,159)(32,160)(33,141)(34,142)(35,143)(36,144)(37,145)(38,146)(39,147)(40,148)(41,99)(42,100)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,95)(58,96)(59,97)(60,98)(101,134)(102,135)(103,136)(104,137)(105,138)(106,139)(107,140)(108,121)(109,122)(110,123)(111,124)(112,125)(113,126)(114,127)(115,128)(116,129)(117,130)(118,131)(119,132)(120,133), (1,131,11,121)(2,122,12,132)(3,133,13,123)(4,124,14,134)(5,135,15,125)(6,126,16,136)(7,137,17,127)(8,128,18,138)(9,139,19,129)(10,130,20,140)(21,82,31,92)(22,93,32,83)(23,84,33,94)(24,95,34,85)(25,86,35,96)(26,97,36,87)(27,88,37,98)(28,99,38,89)(29,90,39,100)(30,81,40,91)(41,146,51,156)(42,157,52,147)(43,148,53,158)(44,159,54,149)(45,150,55,160)(46,141,56,151)(47,152,57,142)(48,143,58,153)(49,154,59,144)(50,145,60,155)(61,110,71,120)(62,101,72,111)(63,112,73,102)(64,103,74,113)(65,114,75,104)(66,105,76,115)(67,116,77,106)(68,107,78,117)(69,118,79,108)(70,109,80,119), (1,154)(2,145)(3,156)(4,147)(5,158)(6,149)(7,160)(8,151)(9,142)(10,153)(11,144)(12,155)(13,146)(14,157)(15,148)(16,159)(17,150)(18,141)(19,152)(20,143)(21,74)(22,65)(23,76)(24,67)(25,78)(26,69)(27,80)(28,71)(29,62)(30,73)(31,64)(32,75)(33,66)(34,77)(35,68)(36,79)(37,70)(38,61)(39,72)(40,63)(41,123)(42,134)(43,125)(44,136)(45,127)(46,138)(47,129)(48,140)(49,131)(50,122)(51,133)(52,124)(53,135)(54,126)(55,137)(56,128)(57,139)(58,130)(59,121)(60,132)(81,112)(82,103)(83,114)(84,105)(85,116)(86,107)(87,118)(88,109)(89,120)(90,111)(91,102)(92,113)(93,104)(94,115)(95,106)(96,117)(97,108)(98,119)(99,110)(100,101), (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), (1,78,11,68)(2,67,12,77)(3,76,13,66)(4,65,14,75)(5,74,15,64)(6,63,16,73)(7,72,17,62)(8,61,18,71)(9,70,19,80)(10,79,20,69)(21,148,31,158)(22,157,32,147)(23,146,33,156)(24,155,34,145)(25,144,35,154)(26,153,36,143)(27,142,37,152)(28,151,38,141)(29,160,39,150)(30,149,40,159)(41,94,51,84)(42,83,52,93)(43,92,53,82)(44,81,54,91)(45,90,55,100)(46,99,56,89)(47,88,57,98)(48,97,58,87)(49,86,59,96)(50,95,60,85)(101,127,111,137)(102,136,112,126)(103,125,113,135)(104,134,114,124)(105,123,115,133)(106,132,116,122)(107,121,117,131)(108,130,118,140)(109,139,119,129)(110,128,120,138)>;
G:=Group( (1,69)(2,70)(3,71)(4,72)(5,73)(6,74)(7,75)(8,76)(9,77)(10,78)(11,79)(12,80)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,149)(22,150)(23,151)(24,152)(25,153)(26,154)(27,155)(28,156)(29,157)(30,158)(31,159)(32,160)(33,141)(34,142)(35,143)(36,144)(37,145)(38,146)(39,147)(40,148)(41,99)(42,100)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,95)(58,96)(59,97)(60,98)(101,134)(102,135)(103,136)(104,137)(105,138)(106,139)(107,140)(108,121)(109,122)(110,123)(111,124)(112,125)(113,126)(114,127)(115,128)(116,129)(117,130)(118,131)(119,132)(120,133), (1,131,11,121)(2,122,12,132)(3,133,13,123)(4,124,14,134)(5,135,15,125)(6,126,16,136)(7,137,17,127)(8,128,18,138)(9,139,19,129)(10,130,20,140)(21,82,31,92)(22,93,32,83)(23,84,33,94)(24,95,34,85)(25,86,35,96)(26,97,36,87)(27,88,37,98)(28,99,38,89)(29,90,39,100)(30,81,40,91)(41,146,51,156)(42,157,52,147)(43,148,53,158)(44,159,54,149)(45,150,55,160)(46,141,56,151)(47,152,57,142)(48,143,58,153)(49,154,59,144)(50,145,60,155)(61,110,71,120)(62,101,72,111)(63,112,73,102)(64,103,74,113)(65,114,75,104)(66,105,76,115)(67,116,77,106)(68,107,78,117)(69,118,79,108)(70,109,80,119), (1,154)(2,145)(3,156)(4,147)(5,158)(6,149)(7,160)(8,151)(9,142)(10,153)(11,144)(12,155)(13,146)(14,157)(15,148)(16,159)(17,150)(18,141)(19,152)(20,143)(21,74)(22,65)(23,76)(24,67)(25,78)(26,69)(27,80)(28,71)(29,62)(30,73)(31,64)(32,75)(33,66)(34,77)(35,68)(36,79)(37,70)(38,61)(39,72)(40,63)(41,123)(42,134)(43,125)(44,136)(45,127)(46,138)(47,129)(48,140)(49,131)(50,122)(51,133)(52,124)(53,135)(54,126)(55,137)(56,128)(57,139)(58,130)(59,121)(60,132)(81,112)(82,103)(83,114)(84,105)(85,116)(86,107)(87,118)(88,109)(89,120)(90,111)(91,102)(92,113)(93,104)(94,115)(95,106)(96,117)(97,108)(98,119)(99,110)(100,101), (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), (1,78,11,68)(2,67,12,77)(3,76,13,66)(4,65,14,75)(5,74,15,64)(6,63,16,73)(7,72,17,62)(8,61,18,71)(9,70,19,80)(10,79,20,69)(21,148,31,158)(22,157,32,147)(23,146,33,156)(24,155,34,145)(25,144,35,154)(26,153,36,143)(27,142,37,152)(28,151,38,141)(29,160,39,150)(30,149,40,159)(41,94,51,84)(42,83,52,93)(43,92,53,82)(44,81,54,91)(45,90,55,100)(46,99,56,89)(47,88,57,98)(48,97,58,87)(49,86,59,96)(50,95,60,85)(101,127,111,137)(102,136,112,126)(103,125,113,135)(104,134,114,124)(105,123,115,133)(106,132,116,122)(107,121,117,131)(108,130,118,140)(109,139,119,129)(110,128,120,138) );
G=PermutationGroup([[(1,69),(2,70),(3,71),(4,72),(5,73),(6,74),(7,75),(8,76),(9,77),(10,78),(11,79),(12,80),(13,61),(14,62),(15,63),(16,64),(17,65),(18,66),(19,67),(20,68),(21,149),(22,150),(23,151),(24,152),(25,153),(26,154),(27,155),(28,156),(29,157),(30,158),(31,159),(32,160),(33,141),(34,142),(35,143),(36,144),(37,145),(38,146),(39,147),(40,148),(41,99),(42,100),(43,81),(44,82),(45,83),(46,84),(47,85),(48,86),(49,87),(50,88),(51,89),(52,90),(53,91),(54,92),(55,93),(56,94),(57,95),(58,96),(59,97),(60,98),(101,134),(102,135),(103,136),(104,137),(105,138),(106,139),(107,140),(108,121),(109,122),(110,123),(111,124),(112,125),(113,126),(114,127),(115,128),(116,129),(117,130),(118,131),(119,132),(120,133)], [(1,131,11,121),(2,122,12,132),(3,133,13,123),(4,124,14,134),(5,135,15,125),(6,126,16,136),(7,137,17,127),(8,128,18,138),(9,139,19,129),(10,130,20,140),(21,82,31,92),(22,93,32,83),(23,84,33,94),(24,95,34,85),(25,86,35,96),(26,97,36,87),(27,88,37,98),(28,99,38,89),(29,90,39,100),(30,81,40,91),(41,146,51,156),(42,157,52,147),(43,148,53,158),(44,159,54,149),(45,150,55,160),(46,141,56,151),(47,152,57,142),(48,143,58,153),(49,154,59,144),(50,145,60,155),(61,110,71,120),(62,101,72,111),(63,112,73,102),(64,103,74,113),(65,114,75,104),(66,105,76,115),(67,116,77,106),(68,107,78,117),(69,118,79,108),(70,109,80,119)], [(1,154),(2,145),(3,156),(4,147),(5,158),(6,149),(7,160),(8,151),(9,142),(10,153),(11,144),(12,155),(13,146),(14,157),(15,148),(16,159),(17,150),(18,141),(19,152),(20,143),(21,74),(22,65),(23,76),(24,67),(25,78),(26,69),(27,80),(28,71),(29,62),(30,73),(31,64),(32,75),(33,66),(34,77),(35,68),(36,79),(37,70),(38,61),(39,72),(40,63),(41,123),(42,134),(43,125),(44,136),(45,127),(46,138),(47,129),(48,140),(49,131),(50,122),(51,133),(52,124),(53,135),(54,126),(55,137),(56,128),(57,139),(58,130),(59,121),(60,132),(81,112),(82,103),(83,114),(84,105),(85,116),(86,107),(87,118),(88,109),(89,120),(90,111),(91,102),(92,113),(93,104),(94,115),(95,106),(96,117),(97,108),(98,119),(99,110),(100,101)], [(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)], [(1,78,11,68),(2,67,12,77),(3,76,13,66),(4,65,14,75),(5,74,15,64),(6,63,16,73),(7,72,17,62),(8,61,18,71),(9,70,19,80),(10,79,20,69),(21,148,31,158),(22,157,32,147),(23,146,33,156),(24,155,34,145),(25,144,35,154),(26,153,36,143),(27,142,37,152),(28,151,38,141),(29,160,39,150),(30,149,40,159),(41,94,51,84),(42,83,52,93),(43,92,53,82),(44,81,54,91),(45,90,55,100),(46,99,56,89),(47,88,57,98),(48,97,58,87),(49,86,59,96),(50,95,60,85),(101,127,111,137),(102,136,112,126),(103,125,113,135),(104,134,114,124),(105,123,115,133),(106,132,116,122),(107,121,117,131),(108,130,118,140),(109,139,119,129),(110,128,120,138)]])
74 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 2J | 2K | 2L | 2M | 4A | ··· | 4H | 4I | ··· | 4T | 5A | 5B | 10A | ··· | 10F | 10G | ··· | 10R | 20A | ··· | 20H | 20I | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
74 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | D10 | D10 | D10 | D10 | 2- 1+4 | D4.10D10 |
| kernel | C2×D4.10D10 | C22×Dic10 | C2×C4○D20 | C2×D4⋊2D5 | C2×Q8×D5 | D4.10D10 | C10×C4○D4 | C2×C4○D4 | C22×C4 | C2×D4 | C2×Q8 | C4○D4 | C10 | C2 |
| # reps | 1 | 3 | 3 | 6 | 2 | 16 | 1 | 2 | 6 | 6 | 2 | 16 | 2 | 8 |
Matrix representation of C2×D4.10D10 ►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 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 37 | 22 | 26 |
| 0 | 0 | 32 | 16 | 38 | 19 |
| 0 | 0 | 22 | 26 | 16 | 4 |
| 0 | 0 | 38 | 19 | 9 | 25 |
| 34 | 7 | 0 | 0 | 0 | 0 |
| 34 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 29 | 0 | 36 |
| 0 | 0 | 14 | 14 | 40 | 40 |
| 0 | 0 | 0 | 36 | 0 | 12 |
| 0 | 0 | 40 | 40 | 27 | 27 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 35 | 0 |
| 0 | 0 | 25 | 39 | 7 | 6 |
| 0 | 0 | 35 | 0 | 39 | 0 |
| 0 | 0 | 7 | 6 | 16 | 2 |
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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,40,0,0,0,0,0,0,40,0,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,25,32,22,38,0,0,37,16,26,19,0,0,22,38,16,9,0,0,26,19,4,25],[34,34,0,0,0,0,7,1,0,0,0,0,0,0,0,14,0,40,0,0,29,14,36,40,0,0,0,40,0,27,0,0,36,40,12,27],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,2,25,35,7,0,0,0,39,0,6,0,0,35,7,39,16,0,0,0,6,0,2] >;
C2×D4.10D10 in GAP, Magma, Sage, TeX
C_2\times D_4._{10}D_{10} % in TeX
G:=Group("C2xD4.10D10"); // GroupNames label
G:=SmallGroup(320,1620);
// by ID
G=gap.SmallGroup(320,1620);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,297,136,1684,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=1,d^10=e^2=b^2,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^-1=b^-1,d*c*d^-1=b^2*c,c*e=e*c,e*d*e^-1=d^9>;
// generators/relations