direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic5.5D4, C24.28D10, C22⋊C4⋊41D10, C10⋊2(C4.4D4), (C2×C10).35C24, Dic5.13(C2×D4), C10.38(C22×D4), C22.128(D4×D5), (C2×C20).574C23, (C2×Dic5).164D4, (C22×Dic10)⋊6C2, (C4×Dic5)⋊74C22, (C22×C4).314D10, C23.D5⋊46C22, D10⋊C4⋊47C22, (C22×D5).7C23, C22.74(C23×D5), C23.81(C22×D5), (C2×Dic10)⋊49C22, C22.74(C4○D20), (C23×C10).61C22, (C23×D5).32C22, C22.68(D4⋊2D5), (C22×C10).388C23, (C22×C20).354C22, (C2×Dic5).191C23, (C22×Dic5).79C22, C2.12(C2×D4×D5), C5⋊2(C2×C4.4D4), (C2×C4×Dic5)⋊31C2, (C2×C22⋊C4)⋊14D5, C2.17(C2×C4○D20), C10.15(C2×C4○D4), (C10×C22⋊C4)⋊19C2, (C2×C10).384(C2×D4), C2.10(C2×D4⋊2D5), (C2×C23.D5)⋊17C2, (C2×D10⋊C4)⋊18C2, (C5×C22⋊C4)⋊54C22, (C2×C4).260(C22×D5), (C22×C5⋊D4).11C2, (C2×C5⋊D4).98C22, (C2×C10).103(C4○D4), SmallGroup(320,1163)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic5.5D4
G = < a,b,c,d,e | a2=b10=d4=1, c2=e2=b5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, cd=dc, ece-1=b5c, ede-1=b5d-1 >
Subgroups: 1214 in 330 conjugacy classes, 119 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D5, C10, C10, C10, C42, C22⋊C4, C22⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C24, C24, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C2×C42, C2×C22⋊C4, C2×C22⋊C4, C4.4D4, C22×D4, C22×Q8, Dic10, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×D5, C22×C10, C22×C10, C22×C10, C2×C4.4D4, C4×Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C2×Dic10, C2×Dic10, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, C23×D5, C23×C10, Dic5.5D4, C2×C4×Dic5, C2×D10⋊C4, C2×C23.D5, C10×C22⋊C4, C22×Dic10, C22×C5⋊D4, C2×Dic5.5D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C4.4D4, C22×D4, C2×C4○D4, C22×D5, C2×C4.4D4, C4○D20, D4×D5, D4⋊2D5, C23×D5, Dic5.5D4, C2×C4○D20, C2×D4×D5, C2×D4⋊2D5, C2×Dic5.5D4
►On 160 points
Generators in S160
(1 96)(2 97)(3 98)(4 99)(5 100)(6 91)(7 92)(8 93)(9 94)(10 95)(11 79)(12 80)(13 71)(14 72)(15 73)(16 74)(17 75)(18 76)(19 77)(20 78)(21 105)(22 106)(23 107)(24 108)(25 109)(26 110)(27 101)(28 102)(29 103)(30 104)(31 127)(32 128)(33 129)(34 130)(35 121)(36 122)(37 123)(38 124)(39 125)(40 126)(41 115)(42 116)(43 117)(44 118)(45 119)(46 120)(47 111)(48 112)(49 113)(50 114)(51 147)(52 148)(53 149)(54 150)(55 141)(56 142)(57 143)(58 144)(59 145)(60 146)(61 135)(62 136)(63 137)(64 138)(65 139)(66 140)(67 131)(68 132)(69 133)(70 134)(81 155)(82 156)(83 157)(84 158)(85 159)(86 160)(87 151)(88 152)(89 153)(90 154)
(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)
(1 116 6 111)(2 115 7 120)(3 114 8 119)(4 113 9 118)(5 112 10 117)(11 58 16 53)(12 57 17 52)(13 56 18 51)(14 55 19 60)(15 54 20 59)(21 129 26 124)(22 128 27 123)(23 127 28 122)(24 126 29 121)(25 125 30 130)(31 102 36 107)(32 101 37 106)(33 110 38 105)(34 109 39 104)(35 108 40 103)(41 92 46 97)(42 91 47 96)(43 100 48 95)(44 99 49 94)(45 98 50 93)(61 157 66 152)(62 156 67 151)(63 155 68 160)(64 154 69 159)(65 153 70 158)(71 142 76 147)(72 141 77 146)(73 150 78 145)(74 149 79 144)(75 148 80 143)(81 132 86 137)(82 131 87 136)(83 140 88 135)(84 139 89 134)(85 138 90 133)
(1 56 23 67)(2 57 24 68)(3 58 25 69)(4 59 26 70)(5 60 27 61)(6 51 28 62)(7 52 29 63)(8 53 30 64)(9 54 21 65)(10 55 22 66)(11 130 154 119)(12 121 155 120)(13 122 156 111)(14 123 157 112)(15 124 158 113)(16 125 159 114)(17 126 160 115)(18 127 151 116)(19 128 152 117)(20 129 153 118)(31 87 42 76)(32 88 43 77)(33 89 44 78)(34 90 45 79)(35 81 46 80)(36 82 47 71)(37 83 48 72)(38 84 49 73)(39 85 50 74)(40 86 41 75)(91 147 102 136)(92 148 103 137)(93 149 104 138)(94 150 105 139)(95 141 106 140)(96 142 107 131)(97 143 108 132)(98 144 109 133)(99 145 110 134)(100 146 101 135)
(1 51 6 56)(2 60 7 55)(3 59 8 54)(4 58 9 53)(5 57 10 52)(11 118 16 113)(12 117 17 112)(13 116 18 111)(14 115 19 120)(15 114 20 119)(21 64 26 69)(22 63 27 68)(23 62 28 67)(24 61 29 66)(25 70 30 65)(31 87 36 82)(32 86 37 81)(33 85 38 90)(34 84 39 89)(35 83 40 88)(41 77 46 72)(42 76 47 71)(43 75 48 80)(44 74 49 79)(45 73 50 78)(91 142 96 147)(92 141 97 146)(93 150 98 145)(94 149 99 144)(95 148 100 143)(101 132 106 137)(102 131 107 136)(103 140 108 135)(104 139 109 134)(105 138 110 133)(121 157 126 152)(122 156 127 151)(123 155 128 160)(124 154 129 159)(125 153 130 158)
G:=sub<Sym(160)| (1,96)(2,97)(3,98)(4,99)(5,100)(6,91)(7,92)(8,93)(9,94)(10,95)(11,79)(12,80)(13,71)(14,72)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,105)(22,106)(23,107)(24,108)(25,109)(26,110)(27,101)(28,102)(29,103)(30,104)(31,127)(32,128)(33,129)(34,130)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,115)(42,116)(43,117)(44,118)(45,119)(46,120)(47,111)(48,112)(49,113)(50,114)(51,147)(52,148)(53,149)(54,150)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(61,135)(62,136)(63,137)(64,138)(65,139)(66,140)(67,131)(68,132)(69,133)(70,134)(81,155)(82,156)(83,157)(84,158)(85,159)(86,160)(87,151)(88,152)(89,153)(90,154), (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), (1,116,6,111)(2,115,7,120)(3,114,8,119)(4,113,9,118)(5,112,10,117)(11,58,16,53)(12,57,17,52)(13,56,18,51)(14,55,19,60)(15,54,20,59)(21,129,26,124)(22,128,27,123)(23,127,28,122)(24,126,29,121)(25,125,30,130)(31,102,36,107)(32,101,37,106)(33,110,38,105)(34,109,39,104)(35,108,40,103)(41,92,46,97)(42,91,47,96)(43,100,48,95)(44,99,49,94)(45,98,50,93)(61,157,66,152)(62,156,67,151)(63,155,68,160)(64,154,69,159)(65,153,70,158)(71,142,76,147)(72,141,77,146)(73,150,78,145)(74,149,79,144)(75,148,80,143)(81,132,86,137)(82,131,87,136)(83,140,88,135)(84,139,89,134)(85,138,90,133), (1,56,23,67)(2,57,24,68)(3,58,25,69)(4,59,26,70)(5,60,27,61)(6,51,28,62)(7,52,29,63)(8,53,30,64)(9,54,21,65)(10,55,22,66)(11,130,154,119)(12,121,155,120)(13,122,156,111)(14,123,157,112)(15,124,158,113)(16,125,159,114)(17,126,160,115)(18,127,151,116)(19,128,152,117)(20,129,153,118)(31,87,42,76)(32,88,43,77)(33,89,44,78)(34,90,45,79)(35,81,46,80)(36,82,47,71)(37,83,48,72)(38,84,49,73)(39,85,50,74)(40,86,41,75)(91,147,102,136)(92,148,103,137)(93,149,104,138)(94,150,105,139)(95,141,106,140)(96,142,107,131)(97,143,108,132)(98,144,109,133)(99,145,110,134)(100,146,101,135), (1,51,6,56)(2,60,7,55)(3,59,8,54)(4,58,9,53)(5,57,10,52)(11,118,16,113)(12,117,17,112)(13,116,18,111)(14,115,19,120)(15,114,20,119)(21,64,26,69)(22,63,27,68)(23,62,28,67)(24,61,29,66)(25,70,30,65)(31,87,36,82)(32,86,37,81)(33,85,38,90)(34,84,39,89)(35,83,40,88)(41,77,46,72)(42,76,47,71)(43,75,48,80)(44,74,49,79)(45,73,50,78)(91,142,96,147)(92,141,97,146)(93,150,98,145)(94,149,99,144)(95,148,100,143)(101,132,106,137)(102,131,107,136)(103,140,108,135)(104,139,109,134)(105,138,110,133)(121,157,126,152)(122,156,127,151)(123,155,128,160)(124,154,129,159)(125,153,130,158)>;
G:=Group( (1,96)(2,97)(3,98)(4,99)(5,100)(6,91)(7,92)(8,93)(9,94)(10,95)(11,79)(12,80)(13,71)(14,72)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,105)(22,106)(23,107)(24,108)(25,109)(26,110)(27,101)(28,102)(29,103)(30,104)(31,127)(32,128)(33,129)(34,130)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,115)(42,116)(43,117)(44,118)(45,119)(46,120)(47,111)(48,112)(49,113)(50,114)(51,147)(52,148)(53,149)(54,150)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(61,135)(62,136)(63,137)(64,138)(65,139)(66,140)(67,131)(68,132)(69,133)(70,134)(81,155)(82,156)(83,157)(84,158)(85,159)(86,160)(87,151)(88,152)(89,153)(90,154), (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), (1,116,6,111)(2,115,7,120)(3,114,8,119)(4,113,9,118)(5,112,10,117)(11,58,16,53)(12,57,17,52)(13,56,18,51)(14,55,19,60)(15,54,20,59)(21,129,26,124)(22,128,27,123)(23,127,28,122)(24,126,29,121)(25,125,30,130)(31,102,36,107)(32,101,37,106)(33,110,38,105)(34,109,39,104)(35,108,40,103)(41,92,46,97)(42,91,47,96)(43,100,48,95)(44,99,49,94)(45,98,50,93)(61,157,66,152)(62,156,67,151)(63,155,68,160)(64,154,69,159)(65,153,70,158)(71,142,76,147)(72,141,77,146)(73,150,78,145)(74,149,79,144)(75,148,80,143)(81,132,86,137)(82,131,87,136)(83,140,88,135)(84,139,89,134)(85,138,90,133), (1,56,23,67)(2,57,24,68)(3,58,25,69)(4,59,26,70)(5,60,27,61)(6,51,28,62)(7,52,29,63)(8,53,30,64)(9,54,21,65)(10,55,22,66)(11,130,154,119)(12,121,155,120)(13,122,156,111)(14,123,157,112)(15,124,158,113)(16,125,159,114)(17,126,160,115)(18,127,151,116)(19,128,152,117)(20,129,153,118)(31,87,42,76)(32,88,43,77)(33,89,44,78)(34,90,45,79)(35,81,46,80)(36,82,47,71)(37,83,48,72)(38,84,49,73)(39,85,50,74)(40,86,41,75)(91,147,102,136)(92,148,103,137)(93,149,104,138)(94,150,105,139)(95,141,106,140)(96,142,107,131)(97,143,108,132)(98,144,109,133)(99,145,110,134)(100,146,101,135), (1,51,6,56)(2,60,7,55)(3,59,8,54)(4,58,9,53)(5,57,10,52)(11,118,16,113)(12,117,17,112)(13,116,18,111)(14,115,19,120)(15,114,20,119)(21,64,26,69)(22,63,27,68)(23,62,28,67)(24,61,29,66)(25,70,30,65)(31,87,36,82)(32,86,37,81)(33,85,38,90)(34,84,39,89)(35,83,40,88)(41,77,46,72)(42,76,47,71)(43,75,48,80)(44,74,49,79)(45,73,50,78)(91,142,96,147)(92,141,97,146)(93,150,98,145)(94,149,99,144)(95,148,100,143)(101,132,106,137)(102,131,107,136)(103,140,108,135)(104,139,109,134)(105,138,110,133)(121,157,126,152)(122,156,127,151)(123,155,128,160)(124,154,129,159)(125,153,130,158) );
G=PermutationGroup([[(1,96),(2,97),(3,98),(4,99),(5,100),(6,91),(7,92),(8,93),(9,94),(10,95),(11,79),(12,80),(13,71),(14,72),(15,73),(16,74),(17,75),(18,76),(19,77),(20,78),(21,105),(22,106),(23,107),(24,108),(25,109),(26,110),(27,101),(28,102),(29,103),(30,104),(31,127),(32,128),(33,129),(34,130),(35,121),(36,122),(37,123),(38,124),(39,125),(40,126),(41,115),(42,116),(43,117),(44,118),(45,119),(46,120),(47,111),(48,112),(49,113),(50,114),(51,147),(52,148),(53,149),(54,150),(55,141),(56,142),(57,143),(58,144),(59,145),(60,146),(61,135),(62,136),(63,137),(64,138),(65,139),(66,140),(67,131),(68,132),(69,133),(70,134),(81,155),(82,156),(83,157),(84,158),(85,159),(86,160),(87,151),(88,152),(89,153),(90,154)], [(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)], [(1,116,6,111),(2,115,7,120),(3,114,8,119),(4,113,9,118),(5,112,10,117),(11,58,16,53),(12,57,17,52),(13,56,18,51),(14,55,19,60),(15,54,20,59),(21,129,26,124),(22,128,27,123),(23,127,28,122),(24,126,29,121),(25,125,30,130),(31,102,36,107),(32,101,37,106),(33,110,38,105),(34,109,39,104),(35,108,40,103),(41,92,46,97),(42,91,47,96),(43,100,48,95),(44,99,49,94),(45,98,50,93),(61,157,66,152),(62,156,67,151),(63,155,68,160),(64,154,69,159),(65,153,70,158),(71,142,76,147),(72,141,77,146),(73,150,78,145),(74,149,79,144),(75,148,80,143),(81,132,86,137),(82,131,87,136),(83,140,88,135),(84,139,89,134),(85,138,90,133)], [(1,56,23,67),(2,57,24,68),(3,58,25,69),(4,59,26,70),(5,60,27,61),(6,51,28,62),(7,52,29,63),(8,53,30,64),(9,54,21,65),(10,55,22,66),(11,130,154,119),(12,121,155,120),(13,122,156,111),(14,123,157,112),(15,124,158,113),(16,125,159,114),(17,126,160,115),(18,127,151,116),(19,128,152,117),(20,129,153,118),(31,87,42,76),(32,88,43,77),(33,89,44,78),(34,90,45,79),(35,81,46,80),(36,82,47,71),(37,83,48,72),(38,84,49,73),(39,85,50,74),(40,86,41,75),(91,147,102,136),(92,148,103,137),(93,149,104,138),(94,150,105,139),(95,141,106,140),(96,142,107,131),(97,143,108,132),(98,144,109,133),(99,145,110,134),(100,146,101,135)], [(1,51,6,56),(2,60,7,55),(3,59,8,54),(4,58,9,53),(5,57,10,52),(11,118,16,113),(12,117,17,112),(13,116,18,111),(14,115,19,120),(15,114,20,119),(21,64,26,69),(22,63,27,68),(23,62,28,67),(24,61,29,66),(25,70,30,65),(31,87,36,82),(32,86,37,81),(33,85,38,90),(34,84,39,89),(35,83,40,88),(41,77,46,72),(42,76,47,71),(43,75,48,80),(44,74,49,79),(45,73,50,78),(91,142,96,147),(92,141,97,146),(93,150,98,145),(94,149,99,144),(95,148,100,143),(101,132,106,137),(102,131,107,136),(103,140,108,135),(104,139,109,134),(105,138,110,133),(121,157,126,152),(122,156,127,151),(123,155,128,160),(124,154,129,159),(125,153,130,158)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4N | 4O | 4P | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10V | 20A | ··· | 20P |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4○D20 | D4×D5 | D4⋊2D5 |
| kernel | C2×Dic5.5D4 | Dic5.5D4 | C2×C4×Dic5 | C2×D10⋊C4 | C2×C23.D5 | C10×C22⋊C4 | C22×Dic10 | C22×C5⋊D4 | C2×Dic5 | C2×C22⋊C4 | C2×C10 | C22⋊C4 | C22×C4 | C24 | C22 | C22 | C22 |
| # reps | 1 | 8 | 1 | 2 | 1 | 1 | 1 | 1 | 4 | 2 | 8 | 8 | 4 | 2 | 16 | 4 | 4 |
Matrix representation of C2×Dic5.5D4 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 7 | 1 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 38 | 17 | 0 | 0 |
| 0 | 38 | 3 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 0 | 9 | 39 |
| 0 | 0 | 0 | 0 | 32 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 19 | 32 | 0 | 0 |
| 0 | 22 | 22 | 0 | 0 |
| 0 | 0 | 0 | 32 | 2 |
| 0 | 0 | 0 | 1 | 9 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,7,40,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,38,38,0,0,0,17,3,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,32,0,0,0,0,0,32,0,0,0,0,0,9,0,0,0,0,39,32],[40,0,0,0,0,0,19,22,0,0,0,32,22,0,0,0,0,0,32,1,0,0,0,2,9] >;
C2×Dic5.5D4 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_5._5D_4 % in TeX
G:=Group("C2xDic5.5D4"); // GroupNames label
G:=SmallGroup(320,1163);
// by ID
G=gap.SmallGroup(320,1163);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,100,1571,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^10=d^4=1,c^2=e^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b^5*c,e*d*e^-1=b^5*d^-1>;
// generators/relations