direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C5×Q8⋊5D4, C10.1182- 1+4, Q8⋊5(C5×D4), (C5×Q8)⋊23D4, (C4×D4)⋊17C10, (D4×C20)⋊46C2, (Q8×C20)⋊31C2, (C4×Q8)⋊11C10, C4.42(D4×C10), C4⋊D4⋊13C10, C20.403(C2×D4), C22⋊Q8⋊13C10, (C22×Q8)⋊6C10, C4.4D4⋊11C10, C42.43(C2×C10), (C2×C10).368C24, (C4×C20).284C22, (C2×C20).714C23, C10.196(C22×D4), (D4×C10).322C22, C22.42(C23×C10), C23.42(C22×C10), (Q8×C10).274C22, C2.10(C5×2- 1+4), (C22×C10).100C23, (C22×C20).454C22, (Q8×C2×C10)⋊18C2, C2.20(D4×C2×C10), (C2×C4○D4)⋊8C10, C22⋊3(C5×C4○D4), (C10×C4○D4)⋊24C2, (C5×C4⋊D4)⋊40C2, C4⋊C4.71(C2×C10), C2.22(C10×C4○D4), (C5×C22⋊Q8)⋊40C2, (C2×C10)⋊17(C4○D4), (C2×D4).67(C2×C10), C10.241(C2×C4○D4), (C5×C4.4D4)⋊31C2, (C2×Q8).61(C2×C10), C22⋊C4.19(C2×C10), (C5×C4⋊C4).396C22, (C22×C4).66(C2×C10), (C2×C4).60(C22×C10), (C5×C22⋊C4).88C22, SmallGroup(320,1550)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×Q8⋊5D4
G = < a,b,c,d,e | a5=b4=d4=e2=1, c2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, dcd-1=ece=b2c, ede=d-1 >
Subgroups: 426 in 290 conjugacy classes, 166 normal (28 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C2×Q8, C4○D4, C20, C20, C2×C10, C2×C10, C2×C10, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C4.4D4, C22×Q8, C2×C4○D4, C2×C20, C2×C20, C2×C20, C5×D4, C5×Q8, C5×Q8, C22×C10, C22×C10, Q8⋊5D4, C4×C20, C5×C22⋊C4, C5×C22⋊C4, C5×C4⋊C4, C22×C20, D4×C10, Q8×C10, Q8×C10, Q8×C10, C5×C4○D4, D4×C20, Q8×C20, C5×C4⋊D4, C5×C22⋊Q8, C5×C4.4D4, Q8×C2×C10, C10×C4○D4, C5×Q8⋊5D4
Quotients: C1, C2, C22, C5, D4, C23, C10, C2×D4, C4○D4, C24, C2×C10, C22×D4, C2×C4○D4, 2- 1+4, C5×D4, C22×C10, Q8⋊5D4, D4×C10, C5×C4○D4, C23×C10, D4×C2×C10, C10×C4○D4, C5×2- 1+4, C5×Q8⋊5D4
►On 160 points
Generators in S160
(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 51 26 41)(2 52 27 42)(3 53 28 43)(4 54 29 44)(5 55 30 45)(6 146 16 136)(7 147 17 137)(8 148 18 138)(9 149 19 139)(10 150 20 140)(11 141 156 151)(12 142 157 152)(13 143 158 153)(14 144 159 154)(15 145 160 155)(21 46 31 36)(22 47 32 37)(23 48 33 38)(24 49 34 39)(25 50 35 40)(56 91 66 81)(57 92 67 82)(58 93 68 83)(59 94 69 84)(60 95 70 85)(61 86 71 76)(62 87 72 77)(63 88 73 78)(64 89 74 79)(65 90 75 80)(96 121 106 131)(97 122 107 132)(98 123 108 133)(99 124 109 134)(100 125 110 135)(101 116 111 126)(102 117 112 127)(103 118 113 128)(104 119 114 129)(105 120 115 130)
(1 111 26 101)(2 112 27 102)(3 113 28 103)(4 114 29 104)(5 115 30 105)(6 76 16 86)(7 77 17 87)(8 78 18 88)(9 79 19 89)(10 80 20 90)(11 91 156 81)(12 92 157 82)(13 93 158 83)(14 94 159 84)(15 95 160 85)(21 106 31 96)(22 107 32 97)(23 108 33 98)(24 109 34 99)(25 110 35 100)(36 131 46 121)(37 132 47 122)(38 133 48 123)(39 134 49 124)(40 135 50 125)(41 126 51 116)(42 127 52 117)(43 128 53 118)(44 129 54 119)(45 130 55 120)(56 151 66 141)(57 152 67 142)(58 153 68 143)(59 154 69 144)(60 155 70 145)(61 146 71 136)(62 147 72 137)(63 148 73 138)(64 149 74 139)(65 150 75 140)
(1 136 21 141)(2 137 22 142)(3 138 23 143)(4 139 24 144)(5 140 25 145)(6 46 156 51)(7 47 157 52)(8 48 158 53)(9 49 159 54)(10 50 160 55)(11 41 16 36)(12 42 17 37)(13 43 18 38)(14 44 19 39)(15 45 20 40)(26 146 31 151)(27 147 32 152)(28 148 33 153)(29 149 34 154)(30 150 35 155)(56 101 61 96)(57 102 62 97)(58 103 63 98)(59 104 64 99)(60 105 65 100)(66 111 71 106)(67 112 72 107)(68 113 73 108)(69 114 74 109)(70 115 75 110)(76 131 81 126)(77 132 82 127)(78 133 83 128)(79 134 84 129)(80 135 85 130)(86 121 91 116)(87 122 92 117)(88 123 93 118)(89 124 94 119)(90 125 95 120)
(1 96)(2 97)(3 98)(4 99)(5 100)(6 86)(7 87)(8 88)(9 89)(10 90)(11 81)(12 82)(13 83)(14 84)(15 85)(16 76)(17 77)(18 78)(19 79)(20 80)(21 101)(22 102)(23 103)(24 104)(25 105)(26 106)(27 107)(28 108)(29 109)(30 110)(31 111)(32 112)(33 113)(34 114)(35 115)(36 126)(37 127)(38 128)(39 129)(40 130)(41 131)(42 132)(43 133)(44 134)(45 135)(46 116)(47 117)(48 118)(49 119)(50 120)(51 121)(52 122)(53 123)(54 124)(55 125)(56 141)(57 142)(58 143)(59 144)(60 145)(61 136)(62 137)(63 138)(64 139)(65 140)(66 151)(67 152)(68 153)(69 154)(70 155)(71 146)(72 147)(73 148)(74 149)(75 150)(91 156)(92 157)(93 158)(94 159)(95 160)
G:=sub<Sym(160)| (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), (1,51,26,41)(2,52,27,42)(3,53,28,43)(4,54,29,44)(5,55,30,45)(6,146,16,136)(7,147,17,137)(8,148,18,138)(9,149,19,139)(10,150,20,140)(11,141,156,151)(12,142,157,152)(13,143,158,153)(14,144,159,154)(15,145,160,155)(21,46,31,36)(22,47,32,37)(23,48,33,38)(24,49,34,39)(25,50,35,40)(56,91,66,81)(57,92,67,82)(58,93,68,83)(59,94,69,84)(60,95,70,85)(61,86,71,76)(62,87,72,77)(63,88,73,78)(64,89,74,79)(65,90,75,80)(96,121,106,131)(97,122,107,132)(98,123,108,133)(99,124,109,134)(100,125,110,135)(101,116,111,126)(102,117,112,127)(103,118,113,128)(104,119,114,129)(105,120,115,130), (1,111,26,101)(2,112,27,102)(3,113,28,103)(4,114,29,104)(5,115,30,105)(6,76,16,86)(7,77,17,87)(8,78,18,88)(9,79,19,89)(10,80,20,90)(11,91,156,81)(12,92,157,82)(13,93,158,83)(14,94,159,84)(15,95,160,85)(21,106,31,96)(22,107,32,97)(23,108,33,98)(24,109,34,99)(25,110,35,100)(36,131,46,121)(37,132,47,122)(38,133,48,123)(39,134,49,124)(40,135,50,125)(41,126,51,116)(42,127,52,117)(43,128,53,118)(44,129,54,119)(45,130,55,120)(56,151,66,141)(57,152,67,142)(58,153,68,143)(59,154,69,144)(60,155,70,145)(61,146,71,136)(62,147,72,137)(63,148,73,138)(64,149,74,139)(65,150,75,140), (1,136,21,141)(2,137,22,142)(3,138,23,143)(4,139,24,144)(5,140,25,145)(6,46,156,51)(7,47,157,52)(8,48,158,53)(9,49,159,54)(10,50,160,55)(11,41,16,36)(12,42,17,37)(13,43,18,38)(14,44,19,39)(15,45,20,40)(26,146,31,151)(27,147,32,152)(28,148,33,153)(29,149,34,154)(30,150,35,155)(56,101,61,96)(57,102,62,97)(58,103,63,98)(59,104,64,99)(60,105,65,100)(66,111,71,106)(67,112,72,107)(68,113,73,108)(69,114,74,109)(70,115,75,110)(76,131,81,126)(77,132,82,127)(78,133,83,128)(79,134,84,129)(80,135,85,130)(86,121,91,116)(87,122,92,117)(88,123,93,118)(89,124,94,119)(90,125,95,120), (1,96)(2,97)(3,98)(4,99)(5,100)(6,86)(7,87)(8,88)(9,89)(10,90)(11,81)(12,82)(13,83)(14,84)(15,85)(16,76)(17,77)(18,78)(19,79)(20,80)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,126)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,133)(44,134)(45,135)(46,116)(47,117)(48,118)(49,119)(50,120)(51,121)(52,122)(53,123)(54,124)(55,125)(56,141)(57,142)(58,143)(59,144)(60,145)(61,136)(62,137)(63,138)(64,139)(65,140)(66,151)(67,152)(68,153)(69,154)(70,155)(71,146)(72,147)(73,148)(74,149)(75,150)(91,156)(92,157)(93,158)(94,159)(95,160)>;
G:=Group( (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), (1,51,26,41)(2,52,27,42)(3,53,28,43)(4,54,29,44)(5,55,30,45)(6,146,16,136)(7,147,17,137)(8,148,18,138)(9,149,19,139)(10,150,20,140)(11,141,156,151)(12,142,157,152)(13,143,158,153)(14,144,159,154)(15,145,160,155)(21,46,31,36)(22,47,32,37)(23,48,33,38)(24,49,34,39)(25,50,35,40)(56,91,66,81)(57,92,67,82)(58,93,68,83)(59,94,69,84)(60,95,70,85)(61,86,71,76)(62,87,72,77)(63,88,73,78)(64,89,74,79)(65,90,75,80)(96,121,106,131)(97,122,107,132)(98,123,108,133)(99,124,109,134)(100,125,110,135)(101,116,111,126)(102,117,112,127)(103,118,113,128)(104,119,114,129)(105,120,115,130), (1,111,26,101)(2,112,27,102)(3,113,28,103)(4,114,29,104)(5,115,30,105)(6,76,16,86)(7,77,17,87)(8,78,18,88)(9,79,19,89)(10,80,20,90)(11,91,156,81)(12,92,157,82)(13,93,158,83)(14,94,159,84)(15,95,160,85)(21,106,31,96)(22,107,32,97)(23,108,33,98)(24,109,34,99)(25,110,35,100)(36,131,46,121)(37,132,47,122)(38,133,48,123)(39,134,49,124)(40,135,50,125)(41,126,51,116)(42,127,52,117)(43,128,53,118)(44,129,54,119)(45,130,55,120)(56,151,66,141)(57,152,67,142)(58,153,68,143)(59,154,69,144)(60,155,70,145)(61,146,71,136)(62,147,72,137)(63,148,73,138)(64,149,74,139)(65,150,75,140), (1,136,21,141)(2,137,22,142)(3,138,23,143)(4,139,24,144)(5,140,25,145)(6,46,156,51)(7,47,157,52)(8,48,158,53)(9,49,159,54)(10,50,160,55)(11,41,16,36)(12,42,17,37)(13,43,18,38)(14,44,19,39)(15,45,20,40)(26,146,31,151)(27,147,32,152)(28,148,33,153)(29,149,34,154)(30,150,35,155)(56,101,61,96)(57,102,62,97)(58,103,63,98)(59,104,64,99)(60,105,65,100)(66,111,71,106)(67,112,72,107)(68,113,73,108)(69,114,74,109)(70,115,75,110)(76,131,81,126)(77,132,82,127)(78,133,83,128)(79,134,84,129)(80,135,85,130)(86,121,91,116)(87,122,92,117)(88,123,93,118)(89,124,94,119)(90,125,95,120), (1,96)(2,97)(3,98)(4,99)(5,100)(6,86)(7,87)(8,88)(9,89)(10,90)(11,81)(12,82)(13,83)(14,84)(15,85)(16,76)(17,77)(18,78)(19,79)(20,80)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,126)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,133)(44,134)(45,135)(46,116)(47,117)(48,118)(49,119)(50,120)(51,121)(52,122)(53,123)(54,124)(55,125)(56,141)(57,142)(58,143)(59,144)(60,145)(61,136)(62,137)(63,138)(64,139)(65,140)(66,151)(67,152)(68,153)(69,154)(70,155)(71,146)(72,147)(73,148)(74,149)(75,150)(91,156)(92,157)(93,158)(94,159)(95,160) );
G=PermutationGroup([[(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)], [(1,51,26,41),(2,52,27,42),(3,53,28,43),(4,54,29,44),(5,55,30,45),(6,146,16,136),(7,147,17,137),(8,148,18,138),(9,149,19,139),(10,150,20,140),(11,141,156,151),(12,142,157,152),(13,143,158,153),(14,144,159,154),(15,145,160,155),(21,46,31,36),(22,47,32,37),(23,48,33,38),(24,49,34,39),(25,50,35,40),(56,91,66,81),(57,92,67,82),(58,93,68,83),(59,94,69,84),(60,95,70,85),(61,86,71,76),(62,87,72,77),(63,88,73,78),(64,89,74,79),(65,90,75,80),(96,121,106,131),(97,122,107,132),(98,123,108,133),(99,124,109,134),(100,125,110,135),(101,116,111,126),(102,117,112,127),(103,118,113,128),(104,119,114,129),(105,120,115,130)], [(1,111,26,101),(2,112,27,102),(3,113,28,103),(4,114,29,104),(5,115,30,105),(6,76,16,86),(7,77,17,87),(8,78,18,88),(9,79,19,89),(10,80,20,90),(11,91,156,81),(12,92,157,82),(13,93,158,83),(14,94,159,84),(15,95,160,85),(21,106,31,96),(22,107,32,97),(23,108,33,98),(24,109,34,99),(25,110,35,100),(36,131,46,121),(37,132,47,122),(38,133,48,123),(39,134,49,124),(40,135,50,125),(41,126,51,116),(42,127,52,117),(43,128,53,118),(44,129,54,119),(45,130,55,120),(56,151,66,141),(57,152,67,142),(58,153,68,143),(59,154,69,144),(60,155,70,145),(61,146,71,136),(62,147,72,137),(63,148,73,138),(64,149,74,139),(65,150,75,140)], [(1,136,21,141),(2,137,22,142),(3,138,23,143),(4,139,24,144),(5,140,25,145),(6,46,156,51),(7,47,157,52),(8,48,158,53),(9,49,159,54),(10,50,160,55),(11,41,16,36),(12,42,17,37),(13,43,18,38),(14,44,19,39),(15,45,20,40),(26,146,31,151),(27,147,32,152),(28,148,33,153),(29,149,34,154),(30,150,35,155),(56,101,61,96),(57,102,62,97),(58,103,63,98),(59,104,64,99),(60,105,65,100),(66,111,71,106),(67,112,72,107),(68,113,73,108),(69,114,74,109),(70,115,75,110),(76,131,81,126),(77,132,82,127),(78,133,83,128),(79,134,84,129),(80,135,85,130),(86,121,91,116),(87,122,92,117),(88,123,93,118),(89,124,94,119),(90,125,95,120)], [(1,96),(2,97),(3,98),(4,99),(5,100),(6,86),(7,87),(8,88),(9,89),(10,90),(11,81),(12,82),(13,83),(14,84),(15,85),(16,76),(17,77),(18,78),(19,79),(20,80),(21,101),(22,102),(23,103),(24,104),(25,105),(26,106),(27,107),(28,108),(29,109),(30,110),(31,111),(32,112),(33,113),(34,114),(35,115),(36,126),(37,127),(38,128),(39,129),(40,130),(41,131),(42,132),(43,133),(44,134),(45,135),(46,116),(47,117),(48,118),(49,119),(50,120),(51,121),(52,122),(53,123),(54,124),(55,125),(56,141),(57,142),(58,143),(59,144),(60,145),(61,136),(62,137),(63,138),(64,139),(65,140),(66,151),(67,152),(68,153),(69,154),(70,155),(71,146),(72,147),(73,148),(74,149),(75,150),(91,156),(92,157),(93,158),(94,159),(95,160)]])
125 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4J | 4K | ··· | 4P | 5A | 5B | 5C | 5D | 10A | ··· | 10L | 10M | ··· | 10T | 10U | ··· | 10AF | 20A | ··· | 20AN | 20AO | ··· | 20BL |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
125 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C5 | C10 | C10 | C10 | C10 | C10 | C10 | C10 | D4 | C4○D4 | C5×D4 | C5×C4○D4 | 2- 1+4 | C5×2- 1+4 |
| kernel | C5×Q8⋊5D4 | D4×C20 | Q8×C20 | C5×C4⋊D4 | C5×C22⋊Q8 | C5×C4.4D4 | Q8×C2×C10 | C10×C4○D4 | Q8⋊5D4 | C4×D4 | C4×Q8 | C4⋊D4 | C22⋊Q8 | C4.4D4 | C22×Q8 | C2×C4○D4 | C5×Q8 | C2×C10 | Q8 | C22 | C10 | C2 |
| # reps | 1 | 3 | 1 | 3 | 3 | 3 | 1 | 1 | 4 | 12 | 4 | 12 | 12 | 12 | 4 | 4 | 4 | 4 | 16 | 16 | 1 | 4 |
Matrix representation of C5×Q8⋊5D4 ►in GL4(𝔽41) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 16 | 0 |
| 0 | 0 | 0 | 16 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 29 | 39 |
| 0 | 0 | 11 | 12 |
| 40 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 |
| 0 | 0 | 15 | 23 |
| 0 | 0 | 8 | 26 |
| 40 | 2 | 0 | 0 |
| 40 | 1 | 0 | 0 |
| 0 | 0 | 15 | 23 |
| 0 | 0 | 17 | 26 |
| 1 | 0 | 0 | 0 |
| 1 | 40 | 0 | 0 |
| 0 | 0 | 15 | 23 |
| 0 | 0 | 17 | 26 |
G:=sub<GL(4,GF(41))| [1,0,0,0,0,1,0,0,0,0,16,0,0,0,0,16],[1,0,0,0,0,1,0,0,0,0,29,11,0,0,39,12],[40,0,0,0,0,40,0,0,0,0,15,8,0,0,23,26],[40,40,0,0,2,1,0,0,0,0,15,17,0,0,23,26],[1,1,0,0,0,40,0,0,0,0,15,17,0,0,23,26] >;
C5×Q8⋊5D4 in GAP, Magma, Sage, TeX
C_5\times Q_8\rtimes_5D_4
% in TeX
G:=Group("C5xQ8:5D4"); // GroupNames label
G:=SmallGroup(320,1550);
// by ID
G=gap.SmallGroup(320,1550);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-2,1149,568,3446,1242,304]);
// Polycyclic
G:=Group<a,b,c,d,e|a^5=b^4=d^4=e^2=1,c^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=e*c*e=b^2*c,e*d*e=d^-1>;
// generators/relations