metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C5⋊2C8⋊1D4, C5⋊1(C8⋊D4), C4⋊C4.11D10, C4.160(D4×D5), D4⋊C4⋊18D5, D10⋊2Q8⋊3C2, (C2×D4).28D10, C20.9(C4○D4), C10.D8⋊8C2, C20⋊2D4.6C2, C20.110(C2×D4), (C2×C8).169D10, C4.26(C4○D20), (C2×Dic5).30D4, (C22×D5).20D4, C22.178(D4×D5), C20.44D4⋊21C2, C2.16(D8⋊D5), C10.17(C4⋊D4), C10.34(C8⋊C22), (C2×C20).220C23, (C2×C40).186C22, (D4×C10).41C22, C4⋊Dic5.74C22, C2.20(D10⋊D4), C2.12(SD16⋊D5), C10.30(C8.C22), (C2×Dic10).62C22, (C2×D4.D5)⋊5C2, (C2×C8⋊D5)⋊17C2, (C5×D4⋊C4)⋊24C2, (C2×C4×D5).16C22, (C2×C10).233(C2×D4), (C5×C4⋊C4).21C22, (C2×C5⋊2C8).18C22, (C2×C4).327(C22×D5), SmallGroup(320,407)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5⋊2C8⋊D4
G = < a,b,c,d | a5=b8=c4=d2=1, bab-1=cac-1=dad=a-1, cbc-1=b-1, dbd=b5, dcd=c-1 >
Subgroups: 518 in 120 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, D4, Q8, C23, D5, C10, C10, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), SD16, C22×C4, C2×D4, C2×D4, C2×Q8, Dic5, C20, C20, D10, C2×C10, C2×C10, D4⋊C4, Q8⋊C4, C2.D8, C4⋊D4, C22⋊Q8, C2×M4(2), C2×SD16, C5⋊2C8, C40, Dic10, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C8⋊D4, C8⋊D5, C2×C5⋊2C8, C4⋊Dic5, C4⋊Dic5, D10⋊C4, D4.D5, C23.D5, C5×C4⋊C4, C2×C40, C2×Dic10, C2×C4×D5, C2×C5⋊D4, D4×C10, C10.D8, C20.44D4, C5×D4⋊C4, D10⋊2Q8, C2×C8⋊D5, C2×D4.D5, C20⋊2D4, C5⋊2C8⋊D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, D10, C4⋊D4, C8⋊C22, C8.C22, C22×D5, C8⋊D4, C4○D20, D4×D5, D10⋊D4, D8⋊D5, SD16⋊D5, C5⋊2C8⋊D4
►On 160 points
Generators in S160
(1 109 130 97 30)(2 31 98 131 110)(3 111 132 99 32)(4 25 100 133 112)(5 105 134 101 26)(6 27 102 135 106)(7 107 136 103 28)(8 29 104 129 108)(9 52 67 128 81)(10 82 121 68 53)(11 54 69 122 83)(12 84 123 70 55)(13 56 71 124 85)(14 86 125 72 49)(15 50 65 126 87)(16 88 127 66 51)(17 62 159 91 113)(18 114 92 160 63)(19 64 153 93 115)(20 116 94 154 57)(21 58 155 95 117)(22 118 96 156 59)(23 60 157 89 119)(24 120 90 158 61)(33 80 142 46 151)(34 152 47 143 73)(35 74 144 48 145)(36 146 41 137 75)(37 76 138 42 147)(38 148 43 139 77)(39 78 140 44 149)(40 150 45 141 79)
(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 57 74 121)(2 64 75 128)(3 63 76 127)(4 62 77 126)(5 61 78 125)(6 60 79 124)(7 59 80 123)(8 58 73 122)(9 131 93 41)(10 130 94 48)(11 129 95 47)(12 136 96 46)(13 135 89 45)(14 134 90 44)(15 133 91 43)(16 132 92 42)(17 38 65 25)(18 37 66 32)(19 36 67 31)(20 35 68 30)(21 34 69 29)(22 33 70 28)(23 40 71 27)(24 39 72 26)(49 101 120 149)(50 100 113 148)(51 99 114 147)(52 98 115 146)(53 97 116 145)(54 104 117 152)(55 103 118 151)(56 102 119 150)(81 110 153 137)(82 109 154 144)(83 108 155 143)(84 107 156 142)(85 106 157 141)(86 105 158 140)(87 112 159 139)(88 111 160 138)
(2 6)(4 8)(9 119)(10 116)(11 113)(12 118)(13 115)(14 120)(15 117)(16 114)(17 83)(18 88)(19 85)(20 82)(21 87)(22 84)(23 81)(24 86)(25 108)(26 105)(27 110)(28 107)(29 112)(30 109)(31 106)(32 111)(33 142)(34 139)(35 144)(36 141)(37 138)(38 143)(39 140)(40 137)(41 150)(42 147)(43 152)(44 149)(45 146)(46 151)(47 148)(48 145)(49 90)(50 95)(51 92)(52 89)(53 94)(54 91)(55 96)(56 93)(57 121)(58 126)(59 123)(60 128)(61 125)(62 122)(63 127)(64 124)(65 155)(66 160)(67 157)(68 154)(69 159)(70 156)(71 153)(72 158)(73 77)(75 79)(97 130)(98 135)(99 132)(100 129)(101 134)(102 131)(103 136)(104 133)
G:=sub<Sym(160)| (1,109,130,97,30)(2,31,98,131,110)(3,111,132,99,32)(4,25,100,133,112)(5,105,134,101,26)(6,27,102,135,106)(7,107,136,103,28)(8,29,104,129,108)(9,52,67,128,81)(10,82,121,68,53)(11,54,69,122,83)(12,84,123,70,55)(13,56,71,124,85)(14,86,125,72,49)(15,50,65,126,87)(16,88,127,66,51)(17,62,159,91,113)(18,114,92,160,63)(19,64,153,93,115)(20,116,94,154,57)(21,58,155,95,117)(22,118,96,156,59)(23,60,157,89,119)(24,120,90,158,61)(33,80,142,46,151)(34,152,47,143,73)(35,74,144,48,145)(36,146,41,137,75)(37,76,138,42,147)(38,148,43,139,77)(39,78,140,44,149)(40,150,45,141,79), (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), (1,57,74,121)(2,64,75,128)(3,63,76,127)(4,62,77,126)(5,61,78,125)(6,60,79,124)(7,59,80,123)(8,58,73,122)(9,131,93,41)(10,130,94,48)(11,129,95,47)(12,136,96,46)(13,135,89,45)(14,134,90,44)(15,133,91,43)(16,132,92,42)(17,38,65,25)(18,37,66,32)(19,36,67,31)(20,35,68,30)(21,34,69,29)(22,33,70,28)(23,40,71,27)(24,39,72,26)(49,101,120,149)(50,100,113,148)(51,99,114,147)(52,98,115,146)(53,97,116,145)(54,104,117,152)(55,103,118,151)(56,102,119,150)(81,110,153,137)(82,109,154,144)(83,108,155,143)(84,107,156,142)(85,106,157,141)(86,105,158,140)(87,112,159,139)(88,111,160,138), (2,6)(4,8)(9,119)(10,116)(11,113)(12,118)(13,115)(14,120)(15,117)(16,114)(17,83)(18,88)(19,85)(20,82)(21,87)(22,84)(23,81)(24,86)(25,108)(26,105)(27,110)(28,107)(29,112)(30,109)(31,106)(32,111)(33,142)(34,139)(35,144)(36,141)(37,138)(38,143)(39,140)(40,137)(41,150)(42,147)(43,152)(44,149)(45,146)(46,151)(47,148)(48,145)(49,90)(50,95)(51,92)(52,89)(53,94)(54,91)(55,96)(56,93)(57,121)(58,126)(59,123)(60,128)(61,125)(62,122)(63,127)(64,124)(65,155)(66,160)(67,157)(68,154)(69,159)(70,156)(71,153)(72,158)(73,77)(75,79)(97,130)(98,135)(99,132)(100,129)(101,134)(102,131)(103,136)(104,133)>;
G:=Group( (1,109,130,97,30)(2,31,98,131,110)(3,111,132,99,32)(4,25,100,133,112)(5,105,134,101,26)(6,27,102,135,106)(7,107,136,103,28)(8,29,104,129,108)(9,52,67,128,81)(10,82,121,68,53)(11,54,69,122,83)(12,84,123,70,55)(13,56,71,124,85)(14,86,125,72,49)(15,50,65,126,87)(16,88,127,66,51)(17,62,159,91,113)(18,114,92,160,63)(19,64,153,93,115)(20,116,94,154,57)(21,58,155,95,117)(22,118,96,156,59)(23,60,157,89,119)(24,120,90,158,61)(33,80,142,46,151)(34,152,47,143,73)(35,74,144,48,145)(36,146,41,137,75)(37,76,138,42,147)(38,148,43,139,77)(39,78,140,44,149)(40,150,45,141,79), (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), (1,57,74,121)(2,64,75,128)(3,63,76,127)(4,62,77,126)(5,61,78,125)(6,60,79,124)(7,59,80,123)(8,58,73,122)(9,131,93,41)(10,130,94,48)(11,129,95,47)(12,136,96,46)(13,135,89,45)(14,134,90,44)(15,133,91,43)(16,132,92,42)(17,38,65,25)(18,37,66,32)(19,36,67,31)(20,35,68,30)(21,34,69,29)(22,33,70,28)(23,40,71,27)(24,39,72,26)(49,101,120,149)(50,100,113,148)(51,99,114,147)(52,98,115,146)(53,97,116,145)(54,104,117,152)(55,103,118,151)(56,102,119,150)(81,110,153,137)(82,109,154,144)(83,108,155,143)(84,107,156,142)(85,106,157,141)(86,105,158,140)(87,112,159,139)(88,111,160,138), (2,6)(4,8)(9,119)(10,116)(11,113)(12,118)(13,115)(14,120)(15,117)(16,114)(17,83)(18,88)(19,85)(20,82)(21,87)(22,84)(23,81)(24,86)(25,108)(26,105)(27,110)(28,107)(29,112)(30,109)(31,106)(32,111)(33,142)(34,139)(35,144)(36,141)(37,138)(38,143)(39,140)(40,137)(41,150)(42,147)(43,152)(44,149)(45,146)(46,151)(47,148)(48,145)(49,90)(50,95)(51,92)(52,89)(53,94)(54,91)(55,96)(56,93)(57,121)(58,126)(59,123)(60,128)(61,125)(62,122)(63,127)(64,124)(65,155)(66,160)(67,157)(68,154)(69,159)(70,156)(71,153)(72,158)(73,77)(75,79)(97,130)(98,135)(99,132)(100,129)(101,134)(102,131)(103,136)(104,133) );
G=PermutationGroup([[(1,109,130,97,30),(2,31,98,131,110),(3,111,132,99,32),(4,25,100,133,112),(5,105,134,101,26),(6,27,102,135,106),(7,107,136,103,28),(8,29,104,129,108),(9,52,67,128,81),(10,82,121,68,53),(11,54,69,122,83),(12,84,123,70,55),(13,56,71,124,85),(14,86,125,72,49),(15,50,65,126,87),(16,88,127,66,51),(17,62,159,91,113),(18,114,92,160,63),(19,64,153,93,115),(20,116,94,154,57),(21,58,155,95,117),(22,118,96,156,59),(23,60,157,89,119),(24,120,90,158,61),(33,80,142,46,151),(34,152,47,143,73),(35,74,144,48,145),(36,146,41,137,75),(37,76,138,42,147),(38,148,43,139,77),(39,78,140,44,149),(40,150,45,141,79)], [(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)], [(1,57,74,121),(2,64,75,128),(3,63,76,127),(4,62,77,126),(5,61,78,125),(6,60,79,124),(7,59,80,123),(8,58,73,122),(9,131,93,41),(10,130,94,48),(11,129,95,47),(12,136,96,46),(13,135,89,45),(14,134,90,44),(15,133,91,43),(16,132,92,42),(17,38,65,25),(18,37,66,32),(19,36,67,31),(20,35,68,30),(21,34,69,29),(22,33,70,28),(23,40,71,27),(24,39,72,26),(49,101,120,149),(50,100,113,148),(51,99,114,147),(52,98,115,146),(53,97,116,145),(54,104,117,152),(55,103,118,151),(56,102,119,150),(81,110,153,137),(82,109,154,144),(83,108,155,143),(84,107,156,142),(85,106,157,141),(86,105,158,140),(87,112,159,139),(88,111,160,138)], [(2,6),(4,8),(9,119),(10,116),(11,113),(12,118),(13,115),(14,120),(15,117),(16,114),(17,83),(18,88),(19,85),(20,82),(21,87),(22,84),(23,81),(24,86),(25,108),(26,105),(27,110),(28,107),(29,112),(30,109),(31,106),(32,111),(33,142),(34,139),(35,144),(36,141),(37,138),(38,143),(39,140),(40,137),(41,150),(42,147),(43,152),(44,149),(45,146),(46,151),(47,148),(48,145),(49,90),(50,95),(51,92),(52,89),(53,94),(54,91),(55,96),(56,93),(57,121),(58,126),(59,123),(60,128),(61,125),(62,122),(63,127),(64,124),(65,155),(66,160),(67,157),(68,154),(69,159),(70,156),(71,153),(72,158),(73,77),(75,79),(97,130),(98,135),(99,132),(100,129),(101,134),(102,131),(103,136),(104,133)]])
44 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 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 | 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 | 8 | 20 | 2 | 2 | 8 | 20 | 40 | 40 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | ··· | 2 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4○D20 | C8⋊C22 | C8.C22 | D4×D5 | D4×D5 | D8⋊D5 | SD16⋊D5 |
| kernel | C5⋊2C8⋊D4 | C10.D8 | C20.44D4 | C5×D4⋊C4 | D10⋊2Q8 | C2×C8⋊D5 | C2×D4.D5 | C20⋊2D4 | C5⋊2C8 | C2×Dic5 | C22×D5 | D4⋊C4 | C20 | C4⋊C4 | C2×C8 | C2×D4 | C4 | C10 | C10 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 8 | 1 | 1 | 2 | 2 | 4 | 4 |
Matrix representation of C5⋊2C8⋊D4 ►in GL10(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 9 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 17 | 21 | 1 | 22 |
| 0 | 0 | 0 | 0 | 0 | 0 | 23 | 25 | 0 | 39 |
| 0 | 0 | 0 | 0 | 0 | 0 | 30 | 10 | 17 | 23 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 21 | 32 | 23 |
| 0 | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 40 | 18 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 24 | 38 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 17 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 9 | 3 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 24 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 9 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 10 | 16 | 32 | 7 |
| 0 | 0 | 0 | 0 | 0 | 0 | 40 | 4 | 12 | 9 |
| 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 9 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 30 | 34 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 34 | 23 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 23 | 25 | 0 | 40 |
G:=sub<GL(10,GF(41))| [1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,32,22,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,9,19,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,17,23,30,12,0,0,0,0,0,0,21,25,10,21,0,0,0,0,0,0,1,0,17,32,0,0,0,0,0,0,22,39,23,23],[0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,17,3,32,22,0,0,0,0,0,0,40,24,0,9,0,0,0,0,0,0,18,38,17,3,0,0,0,0,0,0,0,23,40,24,0,0,0,0,0,0,0,0,0,0,24,9,10,40,0,0,0,0,0,0,9,17,16,4,0,0,0,0,0,0,0,0,32,12,0,0,0,0,0,0,0,0,7,9],[40,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,34,11,14,0,0,0,0,0,0,0,40,9,30,0,0,0,0,0,0,0,0,1,34,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,1,0,34,23,0,0,0,0,0,0,0,1,23,25,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,40] >;
C5⋊2C8⋊D4 in GAP, Magma, Sage, TeX
C_5\rtimes_2C_8\rtimes D_4
% in TeX
G:=Group("C5:2C8:D4"); // GroupNames label
G:=SmallGroup(320,407);
// by ID
G=gap.SmallGroup(320,407);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,1094,135,100,570,297,136,12550]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^8=c^4=d^2=1,b*a*b^-1=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=b^-1,d*b*d=b^5,d*c*d=c^-1>;
// generators/relations