direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C5×D4⋊6D4, C10.1172- 1+4, D4⋊6(C5×D4), (C5×D4)⋊24D4, C4⋊Q8⋊13C10, (C4×D4)⋊16C10, (D4×C20)⋊45C2, C4.41(D4×C10), C20⋊16(C4○D4), C4⋊D4⋊12C10, C20.402(C2×D4), C22⋊Q8⋊12C10, C22.6(D4×C10), C42.42(C2×C10), (C2×C20).675C23, (C4×C20).283C22, (C2×C10).367C24, C22.D4⋊9C10, C10.195(C22×D4), C2.9(C5×2- 1+4), (D4×C10).321C22, (C22×C10).99C23, C23.41(C22×C10), C22.41(C23×C10), (Q8×C10).273C22, (C22×C20).453C22, C4⋊2(C5×C4○D4), (C5×C4⋊Q8)⋊34C2, (C10×C4⋊C4)⋊47C2, (C2×C4⋊C4)⋊20C10, C2.19(D4×C2×C10), (C2×C4○D4)⋊7C10, (C10×C4○D4)⋊23C2, C4⋊C4.31(C2×C10), (C5×C4⋊D4)⋊39C2, C2.21(C10×C4○D4), (C5×C22⋊Q8)⋊39C2, (C2×D4).66(C2×C10), C10.240(C2×C4○D4), (C2×C10).183(C2×D4), C22⋊C4.5(C2×C10), (C2×Q8).60(C2×C10), (C5×C4⋊C4).395C22, (C2×C4).33(C22×C10), (C22×C4).65(C2×C10), (C5×C22.D4)⋊28C2, (C5×C22⋊C4).87C22, SmallGroup(320,1549)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×D4⋊6D4
G = < a,b,c,d,e | a5=b4=c2=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ece=b2c, ede=d-1 >
Subgroups: 426 in 292 conjugacy classes, 166 normal (34 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, D4, Q8, C23, C10, C10, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, C20, C20, C2×C10, C2×C10, C2×C10, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C4⋊Q8, C2×C4○D4, C2×C20, C2×C20, C2×C20, C5×D4, C5×D4, C5×Q8, C22×C10, D4⋊6D4, C4×C20, C5×C22⋊C4, C5×C4⋊C4, C5×C4⋊C4, C22×C20, D4×C10, D4×C10, Q8×C10, C5×C4○D4, C10×C4⋊C4, D4×C20, C5×C4⋊D4, C5×C22⋊Q8, C5×C22.D4, C5×C4⋊Q8, C10×C4○D4, C5×D4⋊6D4
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, D4⋊6D4, D4×C10, C5×C4○D4, C23×C10, D4×C2×C10, C10×C4○D4, C5×2- 1+4, C5×D4⋊6D4
►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)
(1 135 35 116)(2 131 31 117)(3 132 32 118)(4 133 33 119)(5 134 34 120)(6 74 160 60)(7 75 156 56)(8 71 157 57)(9 72 158 58)(10 73 159 59)(11 62 17 68)(12 63 18 69)(13 64 19 70)(14 65 20 66)(15 61 16 67)(21 127 27 121)(22 128 28 122)(23 129 29 123)(24 130 30 124)(25 126 26 125)(36 115 55 96)(37 111 51 97)(38 112 52 98)(39 113 53 99)(40 114 54 100)(41 107 47 101)(42 108 48 102)(43 109 49 103)(44 110 50 104)(45 106 46 105)(76 155 95 136)(77 151 91 137)(78 152 92 138)(79 153 93 139)(80 154 94 140)(81 147 87 141)(82 148 88 142)(83 149 89 143)(84 150 90 144)(85 146 86 145)
(1 101)(2 102)(3 103)(4 104)(5 105)(6 86)(7 87)(8 88)(9 89)(10 90)(11 77)(12 78)(13 79)(14 80)(15 76)(16 95)(17 91)(18 92)(19 93)(20 94)(21 96)(22 97)(23 98)(24 99)(25 100)(26 114)(27 115)(28 111)(29 112)(30 113)(31 108)(32 109)(33 110)(34 106)(35 107)(36 121)(37 122)(38 123)(39 124)(40 125)(41 116)(42 117)(43 118)(44 119)(45 120)(46 134)(47 135)(48 131)(49 132)(50 133)(51 128)(52 129)(53 130)(54 126)(55 127)(56 141)(57 142)(58 143)(59 144)(60 145)(61 136)(62 137)(63 138)(64 139)(65 140)(66 154)(67 155)(68 151)(69 152)(70 153)(71 148)(72 149)(73 150)(74 146)(75 147)(81 156)(82 157)(83 158)(84 159)(85 160)
(1 15 21 156)(2 11 22 157)(3 12 23 158)(4 13 24 159)(5 14 25 160)(6 34 20 26)(7 35 16 27)(8 31 17 28)(9 32 18 29)(10 33 19 30)(36 147 41 155)(37 148 42 151)(38 149 43 152)(39 150 44 153)(40 146 45 154)(46 140 54 145)(47 136 55 141)(48 137 51 142)(49 138 52 143)(50 139 53 144)(56 135 61 127)(57 131 62 128)(58 132 63 129)(59 133 64 130)(60 134 65 126)(66 125 74 120)(67 121 75 116)(68 122 71 117)(69 123 72 118)(70 124 73 119)(76 96 81 101)(77 97 82 102)(78 98 83 103)(79 99 84 104)(80 100 85 105)(86 106 94 114)(87 107 95 115)(88 108 91 111)(89 109 92 112)(90 110 93 113)
(1 21)(2 22)(3 23)(4 24)(5 25)(26 34)(27 35)(28 31)(29 32)(30 33)(36 47)(37 48)(38 49)(39 50)(40 46)(41 55)(42 51)(43 52)(44 53)(45 54)(76 95)(77 91)(78 92)(79 93)(80 94)(81 87)(82 88)(83 89)(84 90)(85 86)(96 107)(97 108)(98 109)(99 110)(100 106)(101 115)(102 111)(103 112)(104 113)(105 114)(116 121)(117 122)(118 123)(119 124)(120 125)(126 134)(127 135)(128 131)(129 132)(130 133)(136 155)(137 151)(138 152)(139 153)(140 154)(141 147)(142 148)(143 149)(144 150)(145 146)
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), (1,135,35,116)(2,131,31,117)(3,132,32,118)(4,133,33,119)(5,134,34,120)(6,74,160,60)(7,75,156,56)(8,71,157,57)(9,72,158,58)(10,73,159,59)(11,62,17,68)(12,63,18,69)(13,64,19,70)(14,65,20,66)(15,61,16,67)(21,127,27,121)(22,128,28,122)(23,129,29,123)(24,130,30,124)(25,126,26,125)(36,115,55,96)(37,111,51,97)(38,112,52,98)(39,113,53,99)(40,114,54,100)(41,107,47,101)(42,108,48,102)(43,109,49,103)(44,110,50,104)(45,106,46,105)(76,155,95,136)(77,151,91,137)(78,152,92,138)(79,153,93,139)(80,154,94,140)(81,147,87,141)(82,148,88,142)(83,149,89,143)(84,150,90,144)(85,146,86,145), (1,101)(2,102)(3,103)(4,104)(5,105)(6,86)(7,87)(8,88)(9,89)(10,90)(11,77)(12,78)(13,79)(14,80)(15,76)(16,95)(17,91)(18,92)(19,93)(20,94)(21,96)(22,97)(23,98)(24,99)(25,100)(26,114)(27,115)(28,111)(29,112)(30,113)(31,108)(32,109)(33,110)(34,106)(35,107)(36,121)(37,122)(38,123)(39,124)(40,125)(41,116)(42,117)(43,118)(44,119)(45,120)(46,134)(47,135)(48,131)(49,132)(50,133)(51,128)(52,129)(53,130)(54,126)(55,127)(56,141)(57,142)(58,143)(59,144)(60,145)(61,136)(62,137)(63,138)(64,139)(65,140)(66,154)(67,155)(68,151)(69,152)(70,153)(71,148)(72,149)(73,150)(74,146)(75,147)(81,156)(82,157)(83,158)(84,159)(85,160), (1,15,21,156)(2,11,22,157)(3,12,23,158)(4,13,24,159)(5,14,25,160)(6,34,20,26)(7,35,16,27)(8,31,17,28)(9,32,18,29)(10,33,19,30)(36,147,41,155)(37,148,42,151)(38,149,43,152)(39,150,44,153)(40,146,45,154)(46,140,54,145)(47,136,55,141)(48,137,51,142)(49,138,52,143)(50,139,53,144)(56,135,61,127)(57,131,62,128)(58,132,63,129)(59,133,64,130)(60,134,65,126)(66,125,74,120)(67,121,75,116)(68,122,71,117)(69,123,72,118)(70,124,73,119)(76,96,81,101)(77,97,82,102)(78,98,83,103)(79,99,84,104)(80,100,85,105)(86,106,94,114)(87,107,95,115)(88,108,91,111)(89,109,92,112)(90,110,93,113), (1,21)(2,22)(3,23)(4,24)(5,25)(26,34)(27,35)(28,31)(29,32)(30,33)(36,47)(37,48)(38,49)(39,50)(40,46)(41,55)(42,51)(43,52)(44,53)(45,54)(76,95)(77,91)(78,92)(79,93)(80,94)(81,87)(82,88)(83,89)(84,90)(85,86)(96,107)(97,108)(98,109)(99,110)(100,106)(101,115)(102,111)(103,112)(104,113)(105,114)(116,121)(117,122)(118,123)(119,124)(120,125)(126,134)(127,135)(128,131)(129,132)(130,133)(136,155)(137,151)(138,152)(139,153)(140,154)(141,147)(142,148)(143,149)(144,150)(145,146)>;
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), (1,135,35,116)(2,131,31,117)(3,132,32,118)(4,133,33,119)(5,134,34,120)(6,74,160,60)(7,75,156,56)(8,71,157,57)(9,72,158,58)(10,73,159,59)(11,62,17,68)(12,63,18,69)(13,64,19,70)(14,65,20,66)(15,61,16,67)(21,127,27,121)(22,128,28,122)(23,129,29,123)(24,130,30,124)(25,126,26,125)(36,115,55,96)(37,111,51,97)(38,112,52,98)(39,113,53,99)(40,114,54,100)(41,107,47,101)(42,108,48,102)(43,109,49,103)(44,110,50,104)(45,106,46,105)(76,155,95,136)(77,151,91,137)(78,152,92,138)(79,153,93,139)(80,154,94,140)(81,147,87,141)(82,148,88,142)(83,149,89,143)(84,150,90,144)(85,146,86,145), (1,101)(2,102)(3,103)(4,104)(5,105)(6,86)(7,87)(8,88)(9,89)(10,90)(11,77)(12,78)(13,79)(14,80)(15,76)(16,95)(17,91)(18,92)(19,93)(20,94)(21,96)(22,97)(23,98)(24,99)(25,100)(26,114)(27,115)(28,111)(29,112)(30,113)(31,108)(32,109)(33,110)(34,106)(35,107)(36,121)(37,122)(38,123)(39,124)(40,125)(41,116)(42,117)(43,118)(44,119)(45,120)(46,134)(47,135)(48,131)(49,132)(50,133)(51,128)(52,129)(53,130)(54,126)(55,127)(56,141)(57,142)(58,143)(59,144)(60,145)(61,136)(62,137)(63,138)(64,139)(65,140)(66,154)(67,155)(68,151)(69,152)(70,153)(71,148)(72,149)(73,150)(74,146)(75,147)(81,156)(82,157)(83,158)(84,159)(85,160), (1,15,21,156)(2,11,22,157)(3,12,23,158)(4,13,24,159)(5,14,25,160)(6,34,20,26)(7,35,16,27)(8,31,17,28)(9,32,18,29)(10,33,19,30)(36,147,41,155)(37,148,42,151)(38,149,43,152)(39,150,44,153)(40,146,45,154)(46,140,54,145)(47,136,55,141)(48,137,51,142)(49,138,52,143)(50,139,53,144)(56,135,61,127)(57,131,62,128)(58,132,63,129)(59,133,64,130)(60,134,65,126)(66,125,74,120)(67,121,75,116)(68,122,71,117)(69,123,72,118)(70,124,73,119)(76,96,81,101)(77,97,82,102)(78,98,83,103)(79,99,84,104)(80,100,85,105)(86,106,94,114)(87,107,95,115)(88,108,91,111)(89,109,92,112)(90,110,93,113), (1,21)(2,22)(3,23)(4,24)(5,25)(26,34)(27,35)(28,31)(29,32)(30,33)(36,47)(37,48)(38,49)(39,50)(40,46)(41,55)(42,51)(43,52)(44,53)(45,54)(76,95)(77,91)(78,92)(79,93)(80,94)(81,87)(82,88)(83,89)(84,90)(85,86)(96,107)(97,108)(98,109)(99,110)(100,106)(101,115)(102,111)(103,112)(104,113)(105,114)(116,121)(117,122)(118,123)(119,124)(120,125)(126,134)(127,135)(128,131)(129,132)(130,133)(136,155)(137,151)(138,152)(139,153)(140,154)(141,147)(142,148)(143,149)(144,150)(145,146) );
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)], [(1,135,35,116),(2,131,31,117),(3,132,32,118),(4,133,33,119),(5,134,34,120),(6,74,160,60),(7,75,156,56),(8,71,157,57),(9,72,158,58),(10,73,159,59),(11,62,17,68),(12,63,18,69),(13,64,19,70),(14,65,20,66),(15,61,16,67),(21,127,27,121),(22,128,28,122),(23,129,29,123),(24,130,30,124),(25,126,26,125),(36,115,55,96),(37,111,51,97),(38,112,52,98),(39,113,53,99),(40,114,54,100),(41,107,47,101),(42,108,48,102),(43,109,49,103),(44,110,50,104),(45,106,46,105),(76,155,95,136),(77,151,91,137),(78,152,92,138),(79,153,93,139),(80,154,94,140),(81,147,87,141),(82,148,88,142),(83,149,89,143),(84,150,90,144),(85,146,86,145)], [(1,101),(2,102),(3,103),(4,104),(5,105),(6,86),(7,87),(8,88),(9,89),(10,90),(11,77),(12,78),(13,79),(14,80),(15,76),(16,95),(17,91),(18,92),(19,93),(20,94),(21,96),(22,97),(23,98),(24,99),(25,100),(26,114),(27,115),(28,111),(29,112),(30,113),(31,108),(32,109),(33,110),(34,106),(35,107),(36,121),(37,122),(38,123),(39,124),(40,125),(41,116),(42,117),(43,118),(44,119),(45,120),(46,134),(47,135),(48,131),(49,132),(50,133),(51,128),(52,129),(53,130),(54,126),(55,127),(56,141),(57,142),(58,143),(59,144),(60,145),(61,136),(62,137),(63,138),(64,139),(65,140),(66,154),(67,155),(68,151),(69,152),(70,153),(71,148),(72,149),(73,150),(74,146),(75,147),(81,156),(82,157),(83,158),(84,159),(85,160)], [(1,15,21,156),(2,11,22,157),(3,12,23,158),(4,13,24,159),(5,14,25,160),(6,34,20,26),(7,35,16,27),(8,31,17,28),(9,32,18,29),(10,33,19,30),(36,147,41,155),(37,148,42,151),(38,149,43,152),(39,150,44,153),(40,146,45,154),(46,140,54,145),(47,136,55,141),(48,137,51,142),(49,138,52,143),(50,139,53,144),(56,135,61,127),(57,131,62,128),(58,132,63,129),(59,133,64,130),(60,134,65,126),(66,125,74,120),(67,121,75,116),(68,122,71,117),(69,123,72,118),(70,124,73,119),(76,96,81,101),(77,97,82,102),(78,98,83,103),(79,99,84,104),(80,100,85,105),(86,106,94,114),(87,107,95,115),(88,108,91,111),(89,109,92,112),(90,110,93,113)], [(1,21),(2,22),(3,23),(4,24),(5,25),(26,34),(27,35),(28,31),(29,32),(30,33),(36,47),(37,48),(38,49),(39,50),(40,46),(41,55),(42,51),(43,52),(44,53),(45,54),(76,95),(77,91),(78,92),(79,93),(80,94),(81,87),(82,88),(83,89),(84,90),(85,86),(96,107),(97,108),(98,109),(99,110),(100,106),(101,115),(102,111),(103,112),(104,113),(105,114),(116,121),(117,122),(118,123),(119,124),(120,125),(126,134),(127,135),(128,131),(129,132),(130,133),(136,155),(137,151),(138,152),(139,153),(140,154),(141,147),(142,148),(143,149),(144,150),(145,146)]])
125 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4H | 4I | ··· | 4O | 5A | 5B | 5C | 5D | 10A | ··· | 10L | 10M | ··· | 10AB | 10AC | ··· | 10AJ | 20A | ··· | 20AF | 20AG | ··· | 20BH |
| order | 1 | 2 | 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 | 2 | 2 | 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×D4⋊6D4 | C10×C4⋊C4 | D4×C20 | C5×C4⋊D4 | C5×C22⋊Q8 | C5×C22.D4 | C5×C4⋊Q8 | C10×C4○D4 | D4⋊6D4 | C2×C4⋊C4 | C4×D4 | C4⋊D4 | C22⋊Q8 | C22.D4 | C4⋊Q8 | C2×C4○D4 | C5×D4 | C20 | D4 | C4 | C10 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 4 | 1 | 2 | 4 | 8 | 8 | 8 | 8 | 16 | 4 | 8 | 4 | 4 | 16 | 16 | 1 | 4 |
Matrix representation of C5×D4⋊6D4 ►in GL5(𝔽41)
| 37 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 6 | 2 |
| 0 | 0 | 0 | 2 | 35 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 6 | 1 |
G:=sub<GL(5,GF(41))| [37,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,9,0,0,0,0,0,32,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,0,32,0,0,0,9,0,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,6,2,0,0,0,2,35],[40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,40,6,0,0,0,0,1] >;
C5×D4⋊6D4 in GAP, Magma, Sage, TeX
C_5\times D_4\rtimes_6D_4
% in TeX
G:=Group("C5xD4:6D4"); // GroupNames label
G:=SmallGroup(320,1549);
// by ID
G=gap.SmallGroup(320,1549);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-2,560,1149,3446,436,1242]);
// Polycyclic
G:=Group<a,b,c,d,e|a^5=b^4=c^2=d^4=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^2*c,e*d*e=d^-1>;
// generators/relations