metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×Dic5)⋊3D4, (C2×C4).19D20, (C2×C20).30D4, C10.5C22≀C2, C10.6(C4⋊D4), C2.8(C4⋊D20), (C22×D5).15D4, (C22×D20).2C2, (C22×C4).71D10, C22.156(D4×D5), C22.81(C2×D20), C2.9(D10⋊D4), C2.8(C22⋊D20), C10.2(C4.4D4), C2.6(C4.D20), C2.C42⋊11D5, C5⋊1(C23.10D4), (C23×D5).4C22, C22.89(C4○D20), (C22×C20).16C22, C23.360(C22×D5), C2.9(D10.13D4), (C22×C10).297C23, C22.45(Q8⋊2D5), C10.40(C22.D4), (C22×Dic5).19C22, (C2×D10⋊C4)⋊1C2, (C2×C10).205(C2×D4), (C2×C10).59(C4○D4), (C2×C10.D4)⋊19C2, (C5×C2.C42)⋊9C2, SmallGroup(320,299)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×Dic5)⋊3D4
G = < a,b,c,d,e | a2=b10=d4=e2=1, c2=b5, ab=ba, ece=ac=ca, ad=da, ae=ea, cbc-1=ebe=b-1, bd=db, dcd-1=b5c, ede=d-1 >
Subgroups: 1174 in 238 conjugacy classes, 61 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, D5, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C24, Dic5, C20, D10, C2×C10, C2×C10, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C22×D4, D20, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, C22×D5, C22×C10, C23.10D4, C10.D4, D10⋊C4, C2×D20, C22×Dic5, C22×C20, C22×C20, C23×D5, C5×C2.C42, C2×C10.D4, C2×D10⋊C4, C22×D20, (C2×Dic5)⋊3D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, D10, C22≀C2, C4⋊D4, C22.D4, C4.4D4, D20, C22×D5, C23.10D4, C2×D20, C4○D20, D4×D5, Q8⋊2D5, C4.D20, C22⋊D20, D10⋊D4, D10.13D4, C4⋊D20, (C2×Dic5)⋊3D4
►On 160 points
Generators in S160
(1 17)(2 18)(3 19)(4 20)(5 11)(6 12)(7 13)(8 14)(9 15)(10 16)(21 58)(22 59)(23 60)(24 51)(25 52)(26 53)(27 54)(28 55)(29 56)(30 57)(31 130)(32 121)(33 122)(34 123)(35 124)(36 125)(37 126)(38 127)(39 128)(40 129)(41 96)(42 97)(43 98)(44 99)(45 100)(46 91)(47 92)(48 93)(49 94)(50 95)(61 76)(62 77)(63 78)(64 79)(65 80)(66 71)(67 72)(68 73)(69 74)(70 75)(81 136)(82 137)(83 138)(84 139)(85 140)(86 131)(87 132)(88 133)(89 134)(90 135)(101 116)(102 117)(103 118)(104 119)(105 120)(106 111)(107 112)(108 113)(109 114)(110 115)(141 156)(142 157)(143 158)(144 159)(145 160)(146 151)(147 152)(148 153)(149 154)(150 155)
(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)
(1 132 6 137)(2 131 7 136)(3 140 8 135)(4 139 9 134)(5 138 10 133)(11 83 16 88)(12 82 17 87)(13 81 18 86)(14 90 19 85)(15 89 20 84)(21 111 26 116)(22 120 27 115)(23 119 28 114)(24 118 29 113)(25 117 30 112)(31 78 36 73)(32 77 37 72)(33 76 38 71)(34 75 39 80)(35 74 40 79)(41 147 46 142)(42 146 47 141)(43 145 48 150)(44 144 49 149)(45 143 50 148)(51 103 56 108)(52 102 57 107)(53 101 58 106)(54 110 59 105)(55 109 60 104)(61 127 66 122)(62 126 67 121)(63 125 68 130)(64 124 69 129)(65 123 70 128)(91 157 96 152)(92 156 97 151)(93 155 98 160)(94 154 99 159)(95 153 100 158)
(1 146 53 33)(2 147 54 34)(3 148 55 35)(4 149 56 36)(5 150 57 37)(6 141 58 38)(7 142 59 39)(8 143 60 40)(9 144 51 31)(10 145 52 32)(11 155 30 126)(12 156 21 127)(13 157 22 128)(14 158 23 129)(15 159 24 130)(16 160 25 121)(17 151 26 122)(18 152 27 123)(19 153 28 124)(20 154 29 125)(41 110 80 131)(42 101 71 132)(43 102 72 133)(44 103 73 134)(45 104 74 135)(46 105 75 136)(47 106 76 137)(48 107 77 138)(49 108 78 139)(50 109 79 140)(61 82 92 111)(62 83 93 112)(63 84 94 113)(64 85 95 114)(65 86 96 115)(66 87 97 116)(67 88 98 117)(68 89 99 118)(69 90 100 119)(70 81 91 120)
(2 10)(3 9)(4 8)(5 7)(11 13)(14 20)(15 19)(16 18)(22 30)(23 29)(24 28)(25 27)(31 148)(32 147)(33 146)(34 145)(35 144)(36 143)(37 142)(38 141)(39 150)(40 149)(41 67)(42 66)(43 65)(44 64)(45 63)(46 62)(47 61)(48 70)(49 69)(50 68)(51 55)(52 54)(56 60)(57 59)(71 97)(72 96)(73 95)(74 94)(75 93)(76 92)(77 91)(78 100)(79 99)(80 98)(81 138)(82 137)(83 136)(84 135)(85 134)(86 133)(87 132)(88 131)(89 140)(90 139)(101 116)(102 115)(103 114)(104 113)(105 112)(106 111)(107 120)(108 119)(109 118)(110 117)(121 152)(122 151)(123 160)(124 159)(125 158)(126 157)(127 156)(128 155)(129 154)(130 153)
G:=sub<Sym(160)| (1,17)(2,18)(3,19)(4,20)(5,11)(6,12)(7,13)(8,14)(9,15)(10,16)(21,58)(22,59)(23,60)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(30,57)(31,130)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,127)(39,128)(40,129)(41,96)(42,97)(43,98)(44,99)(45,100)(46,91)(47,92)(48,93)(49,94)(50,95)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(81,136)(82,137)(83,138)(84,139)(85,140)(86,131)(87,132)(88,133)(89,134)(90,135)(101,116)(102,117)(103,118)(104,119)(105,120)(106,111)(107,112)(108,113)(109,114)(110,115)(141,156)(142,157)(143,158)(144,159)(145,160)(146,151)(147,152)(148,153)(149,154)(150,155), (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), (1,132,6,137)(2,131,7,136)(3,140,8,135)(4,139,9,134)(5,138,10,133)(11,83,16,88)(12,82,17,87)(13,81,18,86)(14,90,19,85)(15,89,20,84)(21,111,26,116)(22,120,27,115)(23,119,28,114)(24,118,29,113)(25,117,30,112)(31,78,36,73)(32,77,37,72)(33,76,38,71)(34,75,39,80)(35,74,40,79)(41,147,46,142)(42,146,47,141)(43,145,48,150)(44,144,49,149)(45,143,50,148)(51,103,56,108)(52,102,57,107)(53,101,58,106)(54,110,59,105)(55,109,60,104)(61,127,66,122)(62,126,67,121)(63,125,68,130)(64,124,69,129)(65,123,70,128)(91,157,96,152)(92,156,97,151)(93,155,98,160)(94,154,99,159)(95,153,100,158), (1,146,53,33)(2,147,54,34)(3,148,55,35)(4,149,56,36)(5,150,57,37)(6,141,58,38)(7,142,59,39)(8,143,60,40)(9,144,51,31)(10,145,52,32)(11,155,30,126)(12,156,21,127)(13,157,22,128)(14,158,23,129)(15,159,24,130)(16,160,25,121)(17,151,26,122)(18,152,27,123)(19,153,28,124)(20,154,29,125)(41,110,80,131)(42,101,71,132)(43,102,72,133)(44,103,73,134)(45,104,74,135)(46,105,75,136)(47,106,76,137)(48,107,77,138)(49,108,78,139)(50,109,79,140)(61,82,92,111)(62,83,93,112)(63,84,94,113)(64,85,95,114)(65,86,96,115)(66,87,97,116)(67,88,98,117)(68,89,99,118)(69,90,100,119)(70,81,91,120), (2,10)(3,9)(4,8)(5,7)(11,13)(14,20)(15,19)(16,18)(22,30)(23,29)(24,28)(25,27)(31,148)(32,147)(33,146)(34,145)(35,144)(36,143)(37,142)(38,141)(39,150)(40,149)(41,67)(42,66)(43,65)(44,64)(45,63)(46,62)(47,61)(48,70)(49,69)(50,68)(51,55)(52,54)(56,60)(57,59)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)(78,100)(79,99)(80,98)(81,138)(82,137)(83,136)(84,135)(85,134)(86,133)(87,132)(88,131)(89,140)(90,139)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,120)(108,119)(109,118)(110,117)(121,152)(122,151)(123,160)(124,159)(125,158)(126,157)(127,156)(128,155)(129,154)(130,153)>;
G:=Group( (1,17)(2,18)(3,19)(4,20)(5,11)(6,12)(7,13)(8,14)(9,15)(10,16)(21,58)(22,59)(23,60)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(30,57)(31,130)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,127)(39,128)(40,129)(41,96)(42,97)(43,98)(44,99)(45,100)(46,91)(47,92)(48,93)(49,94)(50,95)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(81,136)(82,137)(83,138)(84,139)(85,140)(86,131)(87,132)(88,133)(89,134)(90,135)(101,116)(102,117)(103,118)(104,119)(105,120)(106,111)(107,112)(108,113)(109,114)(110,115)(141,156)(142,157)(143,158)(144,159)(145,160)(146,151)(147,152)(148,153)(149,154)(150,155), (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), (1,132,6,137)(2,131,7,136)(3,140,8,135)(4,139,9,134)(5,138,10,133)(11,83,16,88)(12,82,17,87)(13,81,18,86)(14,90,19,85)(15,89,20,84)(21,111,26,116)(22,120,27,115)(23,119,28,114)(24,118,29,113)(25,117,30,112)(31,78,36,73)(32,77,37,72)(33,76,38,71)(34,75,39,80)(35,74,40,79)(41,147,46,142)(42,146,47,141)(43,145,48,150)(44,144,49,149)(45,143,50,148)(51,103,56,108)(52,102,57,107)(53,101,58,106)(54,110,59,105)(55,109,60,104)(61,127,66,122)(62,126,67,121)(63,125,68,130)(64,124,69,129)(65,123,70,128)(91,157,96,152)(92,156,97,151)(93,155,98,160)(94,154,99,159)(95,153,100,158), (1,146,53,33)(2,147,54,34)(3,148,55,35)(4,149,56,36)(5,150,57,37)(6,141,58,38)(7,142,59,39)(8,143,60,40)(9,144,51,31)(10,145,52,32)(11,155,30,126)(12,156,21,127)(13,157,22,128)(14,158,23,129)(15,159,24,130)(16,160,25,121)(17,151,26,122)(18,152,27,123)(19,153,28,124)(20,154,29,125)(41,110,80,131)(42,101,71,132)(43,102,72,133)(44,103,73,134)(45,104,74,135)(46,105,75,136)(47,106,76,137)(48,107,77,138)(49,108,78,139)(50,109,79,140)(61,82,92,111)(62,83,93,112)(63,84,94,113)(64,85,95,114)(65,86,96,115)(66,87,97,116)(67,88,98,117)(68,89,99,118)(69,90,100,119)(70,81,91,120), (2,10)(3,9)(4,8)(5,7)(11,13)(14,20)(15,19)(16,18)(22,30)(23,29)(24,28)(25,27)(31,148)(32,147)(33,146)(34,145)(35,144)(36,143)(37,142)(38,141)(39,150)(40,149)(41,67)(42,66)(43,65)(44,64)(45,63)(46,62)(47,61)(48,70)(49,69)(50,68)(51,55)(52,54)(56,60)(57,59)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)(78,100)(79,99)(80,98)(81,138)(82,137)(83,136)(84,135)(85,134)(86,133)(87,132)(88,131)(89,140)(90,139)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,120)(108,119)(109,118)(110,117)(121,152)(122,151)(123,160)(124,159)(125,158)(126,157)(127,156)(128,155)(129,154)(130,153) );
G=PermutationGroup([[(1,17),(2,18),(3,19),(4,20),(5,11),(6,12),(7,13),(8,14),(9,15),(10,16),(21,58),(22,59),(23,60),(24,51),(25,52),(26,53),(27,54),(28,55),(29,56),(30,57),(31,130),(32,121),(33,122),(34,123),(35,124),(36,125),(37,126),(38,127),(39,128),(40,129),(41,96),(42,97),(43,98),(44,99),(45,100),(46,91),(47,92),(48,93),(49,94),(50,95),(61,76),(62,77),(63,78),(64,79),(65,80),(66,71),(67,72),(68,73),(69,74),(70,75),(81,136),(82,137),(83,138),(84,139),(85,140),(86,131),(87,132),(88,133),(89,134),(90,135),(101,116),(102,117),(103,118),(104,119),(105,120),(106,111),(107,112),(108,113),(109,114),(110,115),(141,156),(142,157),(143,158),(144,159),(145,160),(146,151),(147,152),(148,153),(149,154),(150,155)], [(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)], [(1,132,6,137),(2,131,7,136),(3,140,8,135),(4,139,9,134),(5,138,10,133),(11,83,16,88),(12,82,17,87),(13,81,18,86),(14,90,19,85),(15,89,20,84),(21,111,26,116),(22,120,27,115),(23,119,28,114),(24,118,29,113),(25,117,30,112),(31,78,36,73),(32,77,37,72),(33,76,38,71),(34,75,39,80),(35,74,40,79),(41,147,46,142),(42,146,47,141),(43,145,48,150),(44,144,49,149),(45,143,50,148),(51,103,56,108),(52,102,57,107),(53,101,58,106),(54,110,59,105),(55,109,60,104),(61,127,66,122),(62,126,67,121),(63,125,68,130),(64,124,69,129),(65,123,70,128),(91,157,96,152),(92,156,97,151),(93,155,98,160),(94,154,99,159),(95,153,100,158)], [(1,146,53,33),(2,147,54,34),(3,148,55,35),(4,149,56,36),(5,150,57,37),(6,141,58,38),(7,142,59,39),(8,143,60,40),(9,144,51,31),(10,145,52,32),(11,155,30,126),(12,156,21,127),(13,157,22,128),(14,158,23,129),(15,159,24,130),(16,160,25,121),(17,151,26,122),(18,152,27,123),(19,153,28,124),(20,154,29,125),(41,110,80,131),(42,101,71,132),(43,102,72,133),(44,103,73,134),(45,104,74,135),(46,105,75,136),(47,106,76,137),(48,107,77,138),(49,108,78,139),(50,109,79,140),(61,82,92,111),(62,83,93,112),(63,84,94,113),(64,85,95,114),(65,86,96,115),(66,87,97,116),(67,88,98,117),(68,89,99,118),(69,90,100,119),(70,81,91,120)], [(2,10),(3,9),(4,8),(5,7),(11,13),(14,20),(15,19),(16,18),(22,30),(23,29),(24,28),(25,27),(31,148),(32,147),(33,146),(34,145),(35,144),(36,143),(37,142),(38,141),(39,150),(40,149),(41,67),(42,66),(43,65),(44,64),(45,63),(46,62),(47,61),(48,70),(49,69),(50,68),(51,55),(52,54),(56,60),(57,59),(71,97),(72,96),(73,95),(74,94),(75,93),(76,92),(77,91),(78,100),(79,99),(80,98),(81,138),(82,137),(83,136),(84,135),(85,134),(86,133),(87,132),(88,131),(89,140),(90,139),(101,116),(102,115),(103,114),(104,113),(105,112),(106,111),(107,120),(108,119),(109,118),(110,117),(121,152),(122,151),(123,160),(124,159),(125,158),(126,157),(127,156),(128,155),(129,154),(130,153)]])
62 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 20 | 20 | 20 | 20 | 4 | ··· | 4 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | C4○D4 | D10 | D20 | C4○D20 | D4×D5 | Q8⋊2D5 |
| kernel | (C2×Dic5)⋊3D4 | C5×C2.C42 | C2×C10.D4 | C2×D10⋊C4 | C22×D20 | C2×Dic5 | C2×C20 | C22×D5 | C2.C42 | C2×C10 | C22×C4 | C2×C4 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 4 | 1 | 2 | 2 | 4 | 2 | 6 | 6 | 8 | 16 | 6 | 2 |
Matrix representation of (C2×Dic5)⋊3D4 ►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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 1 | 0 | 0 |
| 0 | 0 | 5 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 40 | 2 | 0 | 0 | 0 | 0 |
| 40 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 32 | 0 | 0 |
| 0 | 0 | 28 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 9 | 23 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 9 | 0 | 0 |
| 0 | 0 | 4 | 39 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 1 | 0 | 0 |
| 0 | 0 | 6 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,6,5,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,40,0,0,0,0,2,1,0,0,0,0,0,0,28,28,0,0,0,0,32,13,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[9,0,0,0,0,0,23,32,0,0,0,0,0,0,2,4,0,0,0,0,9,39,0,0,0,0,0,0,0,1,0,0,0,0,40,0],[1,1,0,0,0,0,0,40,0,0,0,0,0,0,6,6,0,0,0,0,1,35,0,0,0,0,0,0,1,0,0,0,0,0,0,40] >;
(C2×Dic5)⋊3D4 in GAP, Magma, Sage, TeX
(C_2\times {\rm Dic}_5)\rtimes_3D_4 % in TeX
G:=Group("(C2xDic5):3D4"); // GroupNames label
G:=SmallGroup(320,299);
// by ID
G=gap.SmallGroup(320,299);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,64,254,387,268,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^10=d^4=e^2=1,c^2=b^5,a*b=b*a,e*c*e=a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e=b^-1,b*d=d*b,d*c*d^-1=b^5*c,e*d*e=d^-1>;
// generators/relations