metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D4.D5⋊5C4, D4.1(C4×D5), C40⋊8C4⋊15C2, C10.61(C4×D4), C4⋊C4.129D10, D4⋊C4.7D5, (C2×C8).165D10, C10.D8⋊2C2, (D4×Dic5).1C2, C22.66(D4×D5), Dic10⋊10(C2×C4), Dic5⋊3Q8⋊1C2, (C2×D4).124D10, C2.1(D8⋊D5), C5⋊3(SD16⋊C4), C20.37(C22×C4), C20.143(C4○D4), C4.44(D4⋊2D5), C20.44D4⋊14C2, C10.24(C8⋊C22), (C2×C40).176C22, (C2×C20).197C23, (C2×Dic5).189D4, C2.1(SD16⋊D5), (D4×C10).18C22, C4⋊Dic5.57C22, (C4×Dic5).9C22, C10.24(C8.C22), C2.15(Dic5⋊4D4), (C2×Dic10).53C22, C4.2(C2×C4×D5), C5⋊2C8⋊1(C2×C4), (C5×D4).15(C2×C4), (C5×C4⋊C4).2C22, (C2×D4.D5).1C2, (C5×D4⋊C4).7C2, (C2×C10).210(C2×D4), (C2×C5⋊2C8).5C22, (C2×C4).304(C22×D5), SmallGroup(320,384)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4.D5⋊5C4
G = < a,b,c,d,e | a4=b2=c5=e4=1, d2=a2, bab=dad-1=eae-1=a-1, ac=ca, bc=cb, dbd-1=ebe-1=ab, dcd-1=c-1, ce=ec, ede-1=a2d >
Subgroups: 422 in 120 conjugacy classes, 49 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, D4, D4, Q8, C23, C10, C10, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic5, C20, C20, C2×C10, C2×C10, C8⋊C4, D4⋊C4, Q8⋊C4, C2.D8, C4×D4, C4×Q8, C2×SD16, C5⋊2C8, C40, Dic10, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×D4, C5×D4, C22×C10, SD16⋊C4, C2×C5⋊2C8, C4×Dic5, C4×Dic5, C10.D4, C4⋊Dic5, D4.D5, C23.D5, C5×C4⋊C4, C2×C40, C2×Dic10, C22×Dic5, D4×C10, C10.D8, C40⋊8C4, C20.44D4, C5×D4⋊C4, Dic5⋊3Q8, C2×D4.D5, D4×Dic5, D4.D5⋊5C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22×C4, C2×D4, C4○D4, D10, C4×D4, C8⋊C22, C8.C22, C4×D5, C22×D5, SD16⋊C4, C2×C4×D5, D4×D5, D4⋊2D5, Dic5⋊4D4, D8⋊D5, SD16⋊D5, D4.D5⋊5C4
►On 160 points
Generators in S160
(1 21 6 26)(2 22 7 27)(3 23 8 28)(4 24 9 29)(5 25 10 30)(11 31 16 36)(12 32 17 37)(13 33 18 38)(14 34 19 39)(15 35 20 40)(41 66 46 61)(42 67 47 62)(43 68 48 63)(44 69 49 64)(45 70 50 65)(51 76 56 71)(52 77 57 72)(53 78 58 73)(54 79 59 74)(55 80 60 75)(81 101 86 106)(82 102 87 107)(83 103 88 108)(84 104 89 109)(85 105 90 110)(91 111 96 116)(92 112 97 117)(93 113 98 118)(94 114 99 119)(95 115 100 120)(121 146 126 141)(122 147 127 142)(123 148 128 143)(124 149 129 144)(125 150 130 145)(131 156 136 151)(132 157 137 152)(133 158 138 153)(134 159 139 154)(135 160 140 155)
(1 26)(2 27)(3 28)(4 29)(5 30)(6 21)(7 22)(8 23)(9 24)(10 25)(11 36)(12 37)(13 38)(14 39)(15 40)(16 31)(17 32)(18 33)(19 34)(20 35)(41 46)(42 47)(43 48)(44 49)(45 50)(51 56)(52 57)(53 58)(54 59)(55 60)(81 106)(82 107)(83 108)(84 109)(85 110)(86 101)(87 102)(88 103)(89 104)(90 105)(91 116)(92 117)(93 118)(94 119)(95 120)(96 111)(97 112)(98 113)(99 114)(100 115)(121 126)(122 127)(123 128)(124 129)(125 130)(131 136)(132 137)(133 138)(134 139)(135 140)
(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)
(1 138 6 133)(2 137 7 132)(3 136 8 131)(4 140 9 135)(5 139 10 134)(11 128 16 123)(12 127 17 122)(13 126 18 121)(14 130 19 125)(15 129 20 124)(21 158 26 153)(22 157 27 152)(23 156 28 151)(24 160 29 155)(25 159 30 154)(31 148 36 143)(32 147 37 142)(33 146 38 141)(34 150 39 145)(35 149 40 144)(41 88 46 83)(42 87 47 82)(43 86 48 81)(44 90 49 85)(45 89 50 84)(51 98 56 93)(52 97 57 92)(53 96 58 91)(54 100 59 95)(55 99 60 94)(61 108 66 103)(62 107 67 102)(63 106 68 101)(64 110 69 105)(65 109 70 104)(71 118 76 113)(72 117 77 112)(73 116 78 111)(74 120 79 115)(75 119 80 114)
(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)(81 136 91 126)(82 137 92 127)(83 138 93 128)(84 139 94 129)(85 140 95 130)(86 131 96 121)(87 132 97 122)(88 133 98 123)(89 134 99 124)(90 135 100 125)(101 156 111 146)(102 157 112 147)(103 158 113 148)(104 159 114 149)(105 160 115 150)(106 151 116 141)(107 152 117 142)(108 153 118 143)(109 154 119 144)(110 155 120 145)
G:=sub<Sym(160)| (1,21,6,26)(2,22,7,27)(3,23,8,28)(4,24,9,29)(5,25,10,30)(11,31,16,36)(12,32,17,37)(13,33,18,38)(14,34,19,39)(15,35,20,40)(41,66,46,61)(42,67,47,62)(43,68,48,63)(44,69,49,64)(45,70,50,65)(51,76,56,71)(52,77,57,72)(53,78,58,73)(54,79,59,74)(55,80,60,75)(81,101,86,106)(82,102,87,107)(83,103,88,108)(84,104,89,109)(85,105,90,110)(91,111,96,116)(92,112,97,117)(93,113,98,118)(94,114,99,119)(95,115,100,120)(121,146,126,141)(122,147,127,142)(123,148,128,143)(124,149,129,144)(125,150,130,145)(131,156,136,151)(132,157,137,152)(133,158,138,153)(134,159,139,154)(135,160,140,155), (1,26)(2,27)(3,28)(4,29)(5,30)(6,21)(7,22)(8,23)(9,24)(10,25)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35)(41,46)(42,47)(43,48)(44,49)(45,50)(51,56)(52,57)(53,58)(54,59)(55,60)(81,106)(82,107)(83,108)(84,109)(85,110)(86,101)(87,102)(88,103)(89,104)(90,105)(91,116)(92,117)(93,118)(94,119)(95,120)(96,111)(97,112)(98,113)(99,114)(100,115)(121,126)(122,127)(123,128)(124,129)(125,130)(131,136)(132,137)(133,138)(134,139)(135,140), (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), (1,138,6,133)(2,137,7,132)(3,136,8,131)(4,140,9,135)(5,139,10,134)(11,128,16,123)(12,127,17,122)(13,126,18,121)(14,130,19,125)(15,129,20,124)(21,158,26,153)(22,157,27,152)(23,156,28,151)(24,160,29,155)(25,159,30,154)(31,148,36,143)(32,147,37,142)(33,146,38,141)(34,150,39,145)(35,149,40,144)(41,88,46,83)(42,87,47,82)(43,86,48,81)(44,90,49,85)(45,89,50,84)(51,98,56,93)(52,97,57,92)(53,96,58,91)(54,100,59,95)(55,99,60,94)(61,108,66,103)(62,107,67,102)(63,106,68,101)(64,110,69,105)(65,109,70,104)(71,118,76,113)(72,117,77,112)(73,116,78,111)(74,120,79,115)(75,119,80,114), (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)(81,136,91,126)(82,137,92,127)(83,138,93,128)(84,139,94,129)(85,140,95,130)(86,131,96,121)(87,132,97,122)(88,133,98,123)(89,134,99,124)(90,135,100,125)(101,156,111,146)(102,157,112,147)(103,158,113,148)(104,159,114,149)(105,160,115,150)(106,151,116,141)(107,152,117,142)(108,153,118,143)(109,154,119,144)(110,155,120,145)>;
G:=Group( (1,21,6,26)(2,22,7,27)(3,23,8,28)(4,24,9,29)(5,25,10,30)(11,31,16,36)(12,32,17,37)(13,33,18,38)(14,34,19,39)(15,35,20,40)(41,66,46,61)(42,67,47,62)(43,68,48,63)(44,69,49,64)(45,70,50,65)(51,76,56,71)(52,77,57,72)(53,78,58,73)(54,79,59,74)(55,80,60,75)(81,101,86,106)(82,102,87,107)(83,103,88,108)(84,104,89,109)(85,105,90,110)(91,111,96,116)(92,112,97,117)(93,113,98,118)(94,114,99,119)(95,115,100,120)(121,146,126,141)(122,147,127,142)(123,148,128,143)(124,149,129,144)(125,150,130,145)(131,156,136,151)(132,157,137,152)(133,158,138,153)(134,159,139,154)(135,160,140,155), (1,26)(2,27)(3,28)(4,29)(5,30)(6,21)(7,22)(8,23)(9,24)(10,25)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35)(41,46)(42,47)(43,48)(44,49)(45,50)(51,56)(52,57)(53,58)(54,59)(55,60)(81,106)(82,107)(83,108)(84,109)(85,110)(86,101)(87,102)(88,103)(89,104)(90,105)(91,116)(92,117)(93,118)(94,119)(95,120)(96,111)(97,112)(98,113)(99,114)(100,115)(121,126)(122,127)(123,128)(124,129)(125,130)(131,136)(132,137)(133,138)(134,139)(135,140), (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), (1,138,6,133)(2,137,7,132)(3,136,8,131)(4,140,9,135)(5,139,10,134)(11,128,16,123)(12,127,17,122)(13,126,18,121)(14,130,19,125)(15,129,20,124)(21,158,26,153)(22,157,27,152)(23,156,28,151)(24,160,29,155)(25,159,30,154)(31,148,36,143)(32,147,37,142)(33,146,38,141)(34,150,39,145)(35,149,40,144)(41,88,46,83)(42,87,47,82)(43,86,48,81)(44,90,49,85)(45,89,50,84)(51,98,56,93)(52,97,57,92)(53,96,58,91)(54,100,59,95)(55,99,60,94)(61,108,66,103)(62,107,67,102)(63,106,68,101)(64,110,69,105)(65,109,70,104)(71,118,76,113)(72,117,77,112)(73,116,78,111)(74,120,79,115)(75,119,80,114), (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)(81,136,91,126)(82,137,92,127)(83,138,93,128)(84,139,94,129)(85,140,95,130)(86,131,96,121)(87,132,97,122)(88,133,98,123)(89,134,99,124)(90,135,100,125)(101,156,111,146)(102,157,112,147)(103,158,113,148)(104,159,114,149)(105,160,115,150)(106,151,116,141)(107,152,117,142)(108,153,118,143)(109,154,119,144)(110,155,120,145) );
G=PermutationGroup([[(1,21,6,26),(2,22,7,27),(3,23,8,28),(4,24,9,29),(5,25,10,30),(11,31,16,36),(12,32,17,37),(13,33,18,38),(14,34,19,39),(15,35,20,40),(41,66,46,61),(42,67,47,62),(43,68,48,63),(44,69,49,64),(45,70,50,65),(51,76,56,71),(52,77,57,72),(53,78,58,73),(54,79,59,74),(55,80,60,75),(81,101,86,106),(82,102,87,107),(83,103,88,108),(84,104,89,109),(85,105,90,110),(91,111,96,116),(92,112,97,117),(93,113,98,118),(94,114,99,119),(95,115,100,120),(121,146,126,141),(122,147,127,142),(123,148,128,143),(124,149,129,144),(125,150,130,145),(131,156,136,151),(132,157,137,152),(133,158,138,153),(134,159,139,154),(135,160,140,155)], [(1,26),(2,27),(3,28),(4,29),(5,30),(6,21),(7,22),(8,23),(9,24),(10,25),(11,36),(12,37),(13,38),(14,39),(15,40),(16,31),(17,32),(18,33),(19,34),(20,35),(41,46),(42,47),(43,48),(44,49),(45,50),(51,56),(52,57),(53,58),(54,59),(55,60),(81,106),(82,107),(83,108),(84,109),(85,110),(86,101),(87,102),(88,103),(89,104),(90,105),(91,116),(92,117),(93,118),(94,119),(95,120),(96,111),(97,112),(98,113),(99,114),(100,115),(121,126),(122,127),(123,128),(124,129),(125,130),(131,136),(132,137),(133,138),(134,139),(135,140)], [(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)], [(1,138,6,133),(2,137,7,132),(3,136,8,131),(4,140,9,135),(5,139,10,134),(11,128,16,123),(12,127,17,122),(13,126,18,121),(14,130,19,125),(15,129,20,124),(21,158,26,153),(22,157,27,152),(23,156,28,151),(24,160,29,155),(25,159,30,154),(31,148,36,143),(32,147,37,142),(33,146,38,141),(34,150,39,145),(35,149,40,144),(41,88,46,83),(42,87,47,82),(43,86,48,81),(44,90,49,85),(45,89,50,84),(51,98,56,93),(52,97,57,92),(53,96,58,91),(54,100,59,95),(55,99,60,94),(61,108,66,103),(62,107,67,102),(63,106,68,101),(64,110,69,105),(65,109,70,104),(71,118,76,113),(72,117,77,112),(73,116,78,111),(74,120,79,115),(75,119,80,114)], [(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),(81,136,91,126),(82,137,92,127),(83,138,93,128),(84,139,94,129),(85,140,95,130),(86,131,96,121),(87,132,97,122),(88,133,98,123),(89,134,99,124),(90,135,100,125),(101,156,111,146),(102,157,112,147),(103,158,113,148),(104,159,114,149),(105,160,115,150),(106,151,116,141),(107,152,117,142),(108,153,118,143),(109,154,119,144),(110,155,120,145)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | ··· | 2 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4×D5 | C8⋊C22 | C8.C22 | D4⋊2D5 | D4×D5 | D8⋊D5 | SD16⋊D5 |
| kernel | D4.D5⋊5C4 | C10.D8 | C40⋊8C4 | C20.44D4 | C5×D4⋊C4 | Dic5⋊3Q8 | C2×D4.D5 | D4×Dic5 | D4.D5 | C2×Dic5 | D4⋊C4 | C20 | C4⋊C4 | C2×C8 | C2×D4 | D4 | C10 | C10 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 2 | 2 | 2 | 2 | 2 | 8 | 1 | 1 | 2 | 2 | 4 | 4 |
Matrix representation of D4.D5⋊5C4 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 2 | 0 | 0 |
| 0 | 0 | 40 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 39 |
| 0 | 0 | 0 | 0 | 1 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 2 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 | 1 |
| 6 | 40 | 0 | 0 | 0 | 0 |
| 1 | 0 | 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 |
| 36 | 38 | 0 | 0 | 0 | 0 |
| 8 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 32 | 26 | 0 |
| 0 | 0 | 25 | 32 | 0 | 26 |
| 0 | 0 | 26 | 0 | 32 | 9 |
| 0 | 0 | 0 | 26 | 16 | 9 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 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 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,40,0,0,0,0,2,1,0,0,0,0,0,0,1,1,0,0,0,0,39,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,2,1,0,0,0,0,0,0,40,40,0,0,0,0,0,1],[6,1,0,0,0,0,40,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[36,8,0,0,0,0,38,5,0,0,0,0,0,0,9,25,26,0,0,0,32,32,0,26,0,0,26,0,32,16,0,0,0,26,9,9],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,1,0,0,0,0,0,0,1,0,0] >;
D4.D5⋊5C4 in GAP, Magma, Sage, TeX
D_4.D_5\rtimes_5C_4
% in TeX
G:=Group("D4.D5:5C4"); // GroupNames label
G:=SmallGroup(320,384);
// by ID
G=gap.SmallGroup(320,384);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,758,135,100,570,297,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^2=c^5=e^4=1,d^2=a^2,b*a*b=d*a*d^-1=e*a*e^-1=a^-1,a*c=c*a,b*c=c*b,d*b*d^-1=e*b*e^-1=a*b,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=a^2*d>;
// generators/relations