metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.55D10, (C2×C20).70D4, C4⋊D4.3D5, (C2×D4).35D10, C20.55D4⋊8C2, D4⋊Dic5⋊13C2, C20.Q8⋊33C2, (C2×C10).15SD16, C10.54(C2×SD16), (C22×C10).80D4, C20.181(C4○D4), C4.91(D4⋊2D5), (C2×C20).353C23, (D4×C10).51C22, (C22×C4).117D10, C23.57(C5⋊D4), C5⋊5(C23.46D4), C22.3(D4.D5), C2.11(D4⋊D10), C10.113(C8⋊C22), C4⋊Dic5.335C22, (C22×C20).157C22, C10.78(C22.D4), C2.12(C23.18D10), C2.8(C2×D4.D5), (C2×C4⋊Dic5)⋊32C2, (C5×C4⋊D4).2C2, (C2×C10).484(C2×D4), (C2×C4).48(C5⋊D4), (C5×C4⋊C4).102C22, (C2×C4).453(C22×D5), C22.159(C2×C5⋊D4), (C2×C5⋊2C8).106C22, SmallGroup(320,661)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊D4.D5
G = < a,b,c,d,e | a4=b4=c2=d5=1, e2=a2b2, bab-1=cac=eae-1=a-1, ad=da, cbc=b-1, bd=db, ebe-1=a-1b, cd=dc, ece-1=a-1c, ede-1=d-1 >
Subgroups: 382 in 114 conjugacy classes, 43 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C8, C2×C4, C2×C4, D4, C23, C23, C10, C10, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×D4, C2×D4, Dic5, C20, C20, C2×C10, C2×C10, C2×C10, C22⋊C8, D4⋊C4, C4.Q8, C2×C4⋊C4, C4⋊D4, C5⋊2C8, C2×Dic5, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C23.46D4, C2×C5⋊2C8, C4⋊Dic5, C4⋊Dic5, C5×C22⋊C4, C5×C4⋊C4, C22×Dic5, C22×C20, D4×C10, D4×C10, C20.Q8, C20.55D4, D4⋊Dic5, C2×C4⋊Dic5, C5×C4⋊D4, C4⋊D4.D5
Quotients: C1, C2, C22, D4, C23, D5, SD16, C2×D4, C4○D4, D10, C22.D4, C2×SD16, C8⋊C22, C5⋊D4, C22×D5, C23.46D4, D4.D5, D4⋊2D5, C2×C5⋊D4, C2×D4.D5, C23.18D10, D4⋊D10, C4⋊D4.D5
►On 160 points
Generators in S160
(1 29 9 24)(2 30 10 25)(3 26 6 21)(4 27 7 22)(5 28 8 23)(11 36 16 31)(12 37 17 32)(13 38 18 33)(14 39 19 34)(15 40 20 35)(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)(121 141 126 146)(122 142 127 147)(123 143 128 148)(124 144 129 149)(125 145 130 150)(131 151 136 156)(132 152 137 157)(133 153 138 158)(134 154 139 159)(135 155 140 160)
(1 44 14 54)(2 45 15 55)(3 41 11 51)(4 42 12 52)(5 43 13 53)(6 46 16 56)(7 47 17 57)(8 48 18 58)(9 49 19 59)(10 50 20 60)(21 66 31 76)(22 67 32 77)(23 68 33 78)(24 69 34 79)(25 70 35 80)(26 61 36 71)(27 62 37 72)(28 63 38 73)(29 64 39 74)(30 65 40 75)(81 146 91 156)(82 147 92 157)(83 148 93 158)(84 149 94 159)(85 150 95 160)(86 141 96 151)(87 142 97 152)(88 143 98 153)(89 144 99 154)(90 145 100 155)(101 126 111 136)(102 127 112 137)(103 128 113 138)(104 129 114 139)(105 130 115 140)(106 121 116 131)(107 122 117 132)(108 123 118 133)(109 124 119 134)(110 125 120 135)
(21 26)(22 27)(23 28)(24 29)(25 30)(31 36)(32 37)(33 38)(34 39)(35 40)(41 51)(42 52)(43 53)(44 54)(45 55)(46 56)(47 57)(48 58)(49 59)(50 60)(61 76)(62 77)(63 78)(64 79)(65 80)(66 71)(67 72)(68 73)(69 74)(70 75)(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)(121 156)(122 157)(123 158)(124 159)(125 160)(126 151)(127 152)(128 153)(129 154)(130 155)(131 146)(132 147)(133 148)(134 149)(135 150)(136 141)(137 142)(138 143)(139 144)(140 145)
(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)
(1 100 19 85)(2 99 20 84)(3 98 16 83)(4 97 17 82)(5 96 18 81)(6 93 11 88)(7 92 12 87)(8 91 13 86)(9 95 14 90)(10 94 15 89)(21 118 36 103)(22 117 37 102)(23 116 38 101)(24 120 39 105)(25 119 40 104)(26 113 31 108)(27 112 32 107)(28 111 33 106)(29 115 34 110)(30 114 35 109)(41 138 56 123)(42 137 57 122)(43 136 58 121)(44 140 59 125)(45 139 60 124)(46 133 51 128)(47 132 52 127)(48 131 53 126)(49 135 54 130)(50 134 55 129)(61 158 76 143)(62 157 77 142)(63 156 78 141)(64 160 79 145)(65 159 80 144)(66 153 71 148)(67 152 72 147)(68 151 73 146)(69 155 74 150)(70 154 75 149)
G:=sub<Sym(160)| (1,29,9,24)(2,30,10,25)(3,26,6,21)(4,27,7,22)(5,28,8,23)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)(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)(121,141,126,146)(122,142,127,147)(123,143,128,148)(124,144,129,149)(125,145,130,150)(131,151,136,156)(132,152,137,157)(133,153,138,158)(134,154,139,159)(135,155,140,160), (1,44,14,54)(2,45,15,55)(3,41,11,51)(4,42,12,52)(5,43,13,53)(6,46,16,56)(7,47,17,57)(8,48,18,58)(9,49,19,59)(10,50,20,60)(21,66,31,76)(22,67,32,77)(23,68,33,78)(24,69,34,79)(25,70,35,80)(26,61,36,71)(27,62,37,72)(28,63,38,73)(29,64,39,74)(30,65,40,75)(81,146,91,156)(82,147,92,157)(83,148,93,158)(84,149,94,159)(85,150,95,160)(86,141,96,151)(87,142,97,152)(88,143,98,153)(89,144,99,154)(90,145,100,155)(101,126,111,136)(102,127,112,137)(103,128,113,138)(104,129,114,139)(105,130,115,140)(106,121,116,131)(107,122,117,132)(108,123,118,133)(109,124,119,134)(110,125,120,135), (21,26)(22,27)(23,28)(24,29)(25,30)(31,36)(32,37)(33,38)(34,39)(35,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(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)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145), (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), (1,100,19,85)(2,99,20,84)(3,98,16,83)(4,97,17,82)(5,96,18,81)(6,93,11,88)(7,92,12,87)(8,91,13,86)(9,95,14,90)(10,94,15,89)(21,118,36,103)(22,117,37,102)(23,116,38,101)(24,120,39,105)(25,119,40,104)(26,113,31,108)(27,112,32,107)(28,111,33,106)(29,115,34,110)(30,114,35,109)(41,138,56,123)(42,137,57,122)(43,136,58,121)(44,140,59,125)(45,139,60,124)(46,133,51,128)(47,132,52,127)(48,131,53,126)(49,135,54,130)(50,134,55,129)(61,158,76,143)(62,157,77,142)(63,156,78,141)(64,160,79,145)(65,159,80,144)(66,153,71,148)(67,152,72,147)(68,151,73,146)(69,155,74,150)(70,154,75,149)>;
G:=Group( (1,29,9,24)(2,30,10,25)(3,26,6,21)(4,27,7,22)(5,28,8,23)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)(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)(121,141,126,146)(122,142,127,147)(123,143,128,148)(124,144,129,149)(125,145,130,150)(131,151,136,156)(132,152,137,157)(133,153,138,158)(134,154,139,159)(135,155,140,160), (1,44,14,54)(2,45,15,55)(3,41,11,51)(4,42,12,52)(5,43,13,53)(6,46,16,56)(7,47,17,57)(8,48,18,58)(9,49,19,59)(10,50,20,60)(21,66,31,76)(22,67,32,77)(23,68,33,78)(24,69,34,79)(25,70,35,80)(26,61,36,71)(27,62,37,72)(28,63,38,73)(29,64,39,74)(30,65,40,75)(81,146,91,156)(82,147,92,157)(83,148,93,158)(84,149,94,159)(85,150,95,160)(86,141,96,151)(87,142,97,152)(88,143,98,153)(89,144,99,154)(90,145,100,155)(101,126,111,136)(102,127,112,137)(103,128,113,138)(104,129,114,139)(105,130,115,140)(106,121,116,131)(107,122,117,132)(108,123,118,133)(109,124,119,134)(110,125,120,135), (21,26)(22,27)(23,28)(24,29)(25,30)(31,36)(32,37)(33,38)(34,39)(35,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,76)(62,77)(63,78)(64,79)(65,80)(66,71)(67,72)(68,73)(69,74)(70,75)(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)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145), (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), (1,100,19,85)(2,99,20,84)(3,98,16,83)(4,97,17,82)(5,96,18,81)(6,93,11,88)(7,92,12,87)(8,91,13,86)(9,95,14,90)(10,94,15,89)(21,118,36,103)(22,117,37,102)(23,116,38,101)(24,120,39,105)(25,119,40,104)(26,113,31,108)(27,112,32,107)(28,111,33,106)(29,115,34,110)(30,114,35,109)(41,138,56,123)(42,137,57,122)(43,136,58,121)(44,140,59,125)(45,139,60,124)(46,133,51,128)(47,132,52,127)(48,131,53,126)(49,135,54,130)(50,134,55,129)(61,158,76,143)(62,157,77,142)(63,156,78,141)(64,160,79,145)(65,159,80,144)(66,153,71,148)(67,152,72,147)(68,151,73,146)(69,155,74,150)(70,154,75,149) );
G=PermutationGroup([[(1,29,9,24),(2,30,10,25),(3,26,6,21),(4,27,7,22),(5,28,8,23),(11,36,16,31),(12,37,17,32),(13,38,18,33),(14,39,19,34),(15,40,20,35),(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),(121,141,126,146),(122,142,127,147),(123,143,128,148),(124,144,129,149),(125,145,130,150),(131,151,136,156),(132,152,137,157),(133,153,138,158),(134,154,139,159),(135,155,140,160)], [(1,44,14,54),(2,45,15,55),(3,41,11,51),(4,42,12,52),(5,43,13,53),(6,46,16,56),(7,47,17,57),(8,48,18,58),(9,49,19,59),(10,50,20,60),(21,66,31,76),(22,67,32,77),(23,68,33,78),(24,69,34,79),(25,70,35,80),(26,61,36,71),(27,62,37,72),(28,63,38,73),(29,64,39,74),(30,65,40,75),(81,146,91,156),(82,147,92,157),(83,148,93,158),(84,149,94,159),(85,150,95,160),(86,141,96,151),(87,142,97,152),(88,143,98,153),(89,144,99,154),(90,145,100,155),(101,126,111,136),(102,127,112,137),(103,128,113,138),(104,129,114,139),(105,130,115,140),(106,121,116,131),(107,122,117,132),(108,123,118,133),(109,124,119,134),(110,125,120,135)], [(21,26),(22,27),(23,28),(24,29),(25,30),(31,36),(32,37),(33,38),(34,39),(35,40),(41,51),(42,52),(43,53),(44,54),(45,55),(46,56),(47,57),(48,58),(49,59),(50,60),(61,76),(62,77),(63,78),(64,79),(65,80),(66,71),(67,72),(68,73),(69,74),(70,75),(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),(121,156),(122,157),(123,158),(124,159),(125,160),(126,151),(127,152),(128,153),(129,154),(130,155),(131,146),(132,147),(133,148),(134,149),(135,150),(136,141),(137,142),(138,143),(139,144),(140,145)], [(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)], [(1,100,19,85),(2,99,20,84),(3,98,16,83),(4,97,17,82),(5,96,18,81),(6,93,11,88),(7,92,12,87),(8,91,13,86),(9,95,14,90),(10,94,15,89),(21,118,36,103),(22,117,37,102),(23,116,38,101),(24,120,39,105),(25,119,40,104),(26,113,31,108),(27,112,32,107),(28,111,33,106),(29,115,34,110),(30,114,35,109),(41,138,56,123),(42,137,57,122),(43,136,58,121),(44,140,59,125),(45,139,60,124),(46,133,51,128),(47,132,52,127),(48,131,53,126),(49,135,54,130),(50,134,55,129),(61,158,76,143),(62,157,77,142),(63,156,78,141),(64,160,79,145),(65,159,80,144),(66,153,71,148),(67,152,72,147),(68,151,73,146),(69,155,74,150),(70,154,75,149)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 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 | 2 | 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 | 2 | 2 | 8 | 2 | 2 | 4 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | SD16 | D10 | D10 | D10 | C5⋊D4 | C5⋊D4 | C8⋊C22 | D4⋊2D5 | D4.D5 | D4⋊D10 |
| kernel | C4⋊D4.D5 | C20.Q8 | C20.55D4 | D4⋊Dic5 | C2×C4⋊Dic5 | C5×C4⋊D4 | C2×C20 | C22×C10 | C4⋊D4 | C20 | C2×C10 | C4⋊C4 | C22×C4 | C2×D4 | C2×C4 | C23 | C10 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 2 | 2 | 2 | 4 | 4 | 1 | 4 | 4 | 4 |
Matrix representation of C4⋊D4.D5 ►in GL6(𝔽41)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 0 | 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 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 4 |
| 0 | 0 | 0 | 0 | 5 | 26 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 13 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 0 | 0 | 0 |
| 0 | 0 | 0 | 37 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 26 | 15 | 0 | 0 | 0 | 0 |
| 15 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 37 | 0 | 0 |
| 0 | 0 | 10 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 29 | 5 |
| 0 | 0 | 0 | 0 | 12 | 12 |
G:=sub<GL(6,GF(41))| [0,40,0,0,0,0,1,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,15,5,0,0,0,0,4,26],[1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,13,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,0,0,0,0,37,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[26,15,0,0,0,0,15,15,0,0,0,0,0,0,0,10,0,0,0,0,37,0,0,0,0,0,0,0,29,12,0,0,0,0,5,12] >;
C4⋊D4.D5 in GAP, Magma, Sage, TeX
C_4\rtimes D_4.D_5
% in TeX
G:=Group("C4:D4.D5"); // GroupNames label
G:=SmallGroup(320,661);
// by ID
G=gap.SmallGroup(320,661);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,336,254,219,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=c^2=d^5=1,e^2=a^2*b^2,b*a*b^-1=c*a*c=e*a*e^-1=a^-1,a*d=d*a,c*b*c=b^-1,b*d=d*b,e*b*e^-1=a^-1*b,c*d=d*c,e*c*e^-1=a^-1*c,e*d*e^-1=d^-1>;
// generators/relations