direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22⋊C4×Dic5, C24.43D10, (C2×C10)⋊4C42, C10.70(C4×D4), C2.1(D4×Dic5), C23.D5⋊13C4, C22⋊1(C4×Dic5), C23.48(C4×D5), C22.93(D4×D5), C10.39(C2×C42), (C2×Dic5).278D4, (C22×Dic5)⋊10C4, (C22×C4).306D10, (C23×Dic5).1C2, C23.12(C2×Dic5), C2.4(Dic5⋊4D4), (C23×C10).24C22, C23.274(C22×D5), C10.10C42⋊37C2, C10.42(C42⋊C2), C22.40(D4⋊2D5), (C22×C20).340C22, (C22×C10).316C23, C22.19(C22×Dic5), C2.4(C23.11D10), (C22×Dic5).205C22, C5⋊5(C4×C22⋊C4), (C2×C20)⋊33(C2×C4), C2.8(C2×C4×Dic5), (C2×C4×Dic5)⋊20C2, (C2×C4)⋊6(C2×Dic5), C2.4(D5×C22⋊C4), (C5×C22⋊C4)⋊15C4, C22.54(C2×C4×D5), (C2×Dic5)⋊23(C2×C4), (C2×C10).313(C2×D4), C10.67(C2×C22⋊C4), (C2×C22⋊C4).19D5, (C2×C23.D5).3C2, (C10×C22⋊C4).22C2, (C2×C10).137(C4○D4), (C2×C10).203(C22×C4), (C22×C10).112(C2×C4), SmallGroup(320,568)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22⋊C4×Dic5
G = < a,b,c,d,e | a2=b2=c4=d10=1, e2=d5, cac-1=ab=ba, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 734 in 258 conjugacy classes, 111 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, C23, C23, C23, C10, C10, C10, C42, C22⋊C4, C22⋊C4, C22×C4, C22×C4, C24, Dic5, Dic5, C20, C2×C10, C2×C10, C2×C10, C2.C42, C2×C42, C2×C22⋊C4, C2×C22⋊C4, C23×C4, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×C10, C22×C10, C22×C10, C4×C22⋊C4, C4×Dic5, C23.D5, C5×C22⋊C4, C22×Dic5, C22×Dic5, C22×Dic5, C22×C20, C23×C10, C10.10C42, C2×C4×Dic5, C2×C23.D5, C10×C22⋊C4, C23×Dic5, C22⋊C4×Dic5
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C42, C22⋊C4, C22×C4, C2×D4, C4○D4, Dic5, D10, C2×C42, C2×C22⋊C4, C42⋊C2, C4×D4, C4×D5, C2×Dic5, C22×D5, C4×C22⋊C4, C4×Dic5, C2×C4×D5, D4×D5, D4⋊2D5, C22×Dic5, C23.11D10, D5×C22⋊C4, Dic5⋊4D4, C2×C4×Dic5, D4×Dic5, C22⋊C4×Dic5
►On 160 points
Generators in S160
(1 16)(2 17)(3 18)(4 19)(5 20)(6 11)(7 12)(8 13)(9 14)(10 15)(21 149)(22 150)(23 141)(24 142)(25 143)(26 144)(27 145)(28 146)(29 147)(30 148)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 41)(38 42)(39 43)(40 44)(51 87)(52 88)(53 89)(54 90)(55 81)(56 82)(57 83)(58 84)(59 85)(60 86)(61 77)(62 78)(63 79)(64 80)(65 71)(66 72)(67 73)(68 74)(69 75)(70 76)(91 107)(92 108)(93 109)(94 110)(95 101)(96 102)(97 103)(98 104)(99 105)(100 106)(111 122)(112 123)(113 124)(114 125)(115 126)(116 127)(117 128)(118 129)(119 130)(120 121)(131 159)(132 160)(133 151)(134 152)(135 153)(136 154)(137 155)(138 156)(139 157)(140 158)
(1 39)(2 40)(3 31)(4 32)(5 33)(6 34)(7 35)(8 36)(9 37)(10 38)(11 48)(12 49)(13 50)(14 41)(15 42)(16 43)(17 44)(18 45)(19 46)(20 47)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 131)(30 132)(51 76)(52 77)(53 78)(54 79)(55 80)(56 71)(57 72)(58 73)(59 74)(60 75)(61 88)(62 89)(63 90)(64 81)(65 82)(66 83)(67 84)(68 85)(69 86)(70 87)(91 130)(92 121)(93 122)(94 123)(95 124)(96 125)(97 126)(98 127)(99 128)(100 129)(101 113)(102 114)(103 115)(104 116)(105 117)(106 118)(107 119)(108 120)(109 111)(110 112)(141 153)(142 154)(143 155)(144 156)(145 157)(146 158)(147 159)(148 160)(149 151)(150 152)
(1 68 11 54)(2 69 12 55)(3 70 13 56)(4 61 14 57)(5 62 15 58)(6 63 16 59)(7 64 17 60)(8 65 18 51)(9 66 19 52)(10 67 20 53)(21 122 156 116)(22 123 157 117)(23 124 158 118)(24 125 159 119)(25 126 160 120)(26 127 151 111)(27 128 152 112)(28 129 153 113)(29 130 154 114)(30 121 155 115)(31 87 50 71)(32 88 41 72)(33 89 42 73)(34 90 43 74)(35 81 44 75)(36 82 45 76)(37 83 46 77)(38 84 47 78)(39 85 48 79)(40 86 49 80)(91 142 102 131)(92 143 103 132)(93 144 104 133)(94 145 105 134)(95 146 106 135)(96 147 107 136)(97 148 108 137)(98 149 109 138)(99 150 110 139)(100 141 101 140)
(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)
(1 104 6 109)(2 103 7 108)(3 102 8 107)(4 101 9 106)(5 110 10 105)(11 93 16 98)(12 92 17 97)(13 91 18 96)(14 100 19 95)(15 99 20 94)(21 90 26 85)(22 89 27 84)(23 88 28 83)(24 87 29 82)(25 86 30 81)(31 114 36 119)(32 113 37 118)(33 112 38 117)(34 111 39 116)(35 120 40 115)(41 129 46 124)(42 128 47 123)(43 127 48 122)(44 126 49 121)(45 125 50 130)(51 147 56 142)(52 146 57 141)(53 145 58 150)(54 144 59 149)(55 143 60 148)(61 140 66 135)(62 139 67 134)(63 138 68 133)(64 137 69 132)(65 136 70 131)(71 154 76 159)(72 153 77 158)(73 152 78 157)(74 151 79 156)(75 160 80 155)
G:=sub<Sym(160)| (1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15)(21,149)(22,150)(23,141)(24,142)(25,143)(26,144)(27,145)(28,146)(29,147)(30,148)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,41)(38,42)(39,43)(40,44)(51,87)(52,88)(53,89)(54,90)(55,81)(56,82)(57,83)(58,84)(59,85)(60,86)(61,77)(62,78)(63,79)(64,80)(65,71)(66,72)(67,73)(68,74)(69,75)(70,76)(91,107)(92,108)(93,109)(94,110)(95,101)(96,102)(97,103)(98,104)(99,105)(100,106)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,121)(131,159)(132,160)(133,151)(134,152)(135,153)(136,154)(137,155)(138,156)(139,157)(140,158), (1,39)(2,40)(3,31)(4,32)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,48)(12,49)(13,50)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,131)(30,132)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(61,88)(62,89)(63,90)(64,81)(65,82)(66,83)(67,84)(68,85)(69,86)(70,87)(91,130)(92,121)(93,122)(94,123)(95,124)(96,125)(97,126)(98,127)(99,128)(100,129)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,111)(110,112)(141,153)(142,154)(143,155)(144,156)(145,157)(146,158)(147,159)(148,160)(149,151)(150,152), (1,68,11,54)(2,69,12,55)(3,70,13,56)(4,61,14,57)(5,62,15,58)(6,63,16,59)(7,64,17,60)(8,65,18,51)(9,66,19,52)(10,67,20,53)(21,122,156,116)(22,123,157,117)(23,124,158,118)(24,125,159,119)(25,126,160,120)(26,127,151,111)(27,128,152,112)(28,129,153,113)(29,130,154,114)(30,121,155,115)(31,87,50,71)(32,88,41,72)(33,89,42,73)(34,90,43,74)(35,81,44,75)(36,82,45,76)(37,83,46,77)(38,84,47,78)(39,85,48,79)(40,86,49,80)(91,142,102,131)(92,143,103,132)(93,144,104,133)(94,145,105,134)(95,146,106,135)(96,147,107,136)(97,148,108,137)(98,149,109,138)(99,150,110,139)(100,141,101,140), (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), (1,104,6,109)(2,103,7,108)(3,102,8,107)(4,101,9,106)(5,110,10,105)(11,93,16,98)(12,92,17,97)(13,91,18,96)(14,100,19,95)(15,99,20,94)(21,90,26,85)(22,89,27,84)(23,88,28,83)(24,87,29,82)(25,86,30,81)(31,114,36,119)(32,113,37,118)(33,112,38,117)(34,111,39,116)(35,120,40,115)(41,129,46,124)(42,128,47,123)(43,127,48,122)(44,126,49,121)(45,125,50,130)(51,147,56,142)(52,146,57,141)(53,145,58,150)(54,144,59,149)(55,143,60,148)(61,140,66,135)(62,139,67,134)(63,138,68,133)(64,137,69,132)(65,136,70,131)(71,154,76,159)(72,153,77,158)(73,152,78,157)(74,151,79,156)(75,160,80,155)>;
G:=Group( (1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15)(21,149)(22,150)(23,141)(24,142)(25,143)(26,144)(27,145)(28,146)(29,147)(30,148)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,41)(38,42)(39,43)(40,44)(51,87)(52,88)(53,89)(54,90)(55,81)(56,82)(57,83)(58,84)(59,85)(60,86)(61,77)(62,78)(63,79)(64,80)(65,71)(66,72)(67,73)(68,74)(69,75)(70,76)(91,107)(92,108)(93,109)(94,110)(95,101)(96,102)(97,103)(98,104)(99,105)(100,106)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,121)(131,159)(132,160)(133,151)(134,152)(135,153)(136,154)(137,155)(138,156)(139,157)(140,158), (1,39)(2,40)(3,31)(4,32)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,48)(12,49)(13,50)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,131)(30,132)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(61,88)(62,89)(63,90)(64,81)(65,82)(66,83)(67,84)(68,85)(69,86)(70,87)(91,130)(92,121)(93,122)(94,123)(95,124)(96,125)(97,126)(98,127)(99,128)(100,129)(101,113)(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,111)(110,112)(141,153)(142,154)(143,155)(144,156)(145,157)(146,158)(147,159)(148,160)(149,151)(150,152), (1,68,11,54)(2,69,12,55)(3,70,13,56)(4,61,14,57)(5,62,15,58)(6,63,16,59)(7,64,17,60)(8,65,18,51)(9,66,19,52)(10,67,20,53)(21,122,156,116)(22,123,157,117)(23,124,158,118)(24,125,159,119)(25,126,160,120)(26,127,151,111)(27,128,152,112)(28,129,153,113)(29,130,154,114)(30,121,155,115)(31,87,50,71)(32,88,41,72)(33,89,42,73)(34,90,43,74)(35,81,44,75)(36,82,45,76)(37,83,46,77)(38,84,47,78)(39,85,48,79)(40,86,49,80)(91,142,102,131)(92,143,103,132)(93,144,104,133)(94,145,105,134)(95,146,106,135)(96,147,107,136)(97,148,108,137)(98,149,109,138)(99,150,110,139)(100,141,101,140), (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), (1,104,6,109)(2,103,7,108)(3,102,8,107)(4,101,9,106)(5,110,10,105)(11,93,16,98)(12,92,17,97)(13,91,18,96)(14,100,19,95)(15,99,20,94)(21,90,26,85)(22,89,27,84)(23,88,28,83)(24,87,29,82)(25,86,30,81)(31,114,36,119)(32,113,37,118)(33,112,38,117)(34,111,39,116)(35,120,40,115)(41,129,46,124)(42,128,47,123)(43,127,48,122)(44,126,49,121)(45,125,50,130)(51,147,56,142)(52,146,57,141)(53,145,58,150)(54,144,59,149)(55,143,60,148)(61,140,66,135)(62,139,67,134)(63,138,68,133)(64,137,69,132)(65,136,70,131)(71,154,76,159)(72,153,77,158)(73,152,78,157)(74,151,79,156)(75,160,80,155) );
G=PermutationGroup([[(1,16),(2,17),(3,18),(4,19),(5,20),(6,11),(7,12),(8,13),(9,14),(10,15),(21,149),(22,150),(23,141),(24,142),(25,143),(26,144),(27,145),(28,146),(29,147),(30,148),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,41),(38,42),(39,43),(40,44),(51,87),(52,88),(53,89),(54,90),(55,81),(56,82),(57,83),(58,84),(59,85),(60,86),(61,77),(62,78),(63,79),(64,80),(65,71),(66,72),(67,73),(68,74),(69,75),(70,76),(91,107),(92,108),(93,109),(94,110),(95,101),(96,102),(97,103),(98,104),(99,105),(100,106),(111,122),(112,123),(113,124),(114,125),(115,126),(116,127),(117,128),(118,129),(119,130),(120,121),(131,159),(132,160),(133,151),(134,152),(135,153),(136,154),(137,155),(138,156),(139,157),(140,158)], [(1,39),(2,40),(3,31),(4,32),(5,33),(6,34),(7,35),(8,36),(9,37),(10,38),(11,48),(12,49),(13,50),(14,41),(15,42),(16,43),(17,44),(18,45),(19,46),(20,47),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,131),(30,132),(51,76),(52,77),(53,78),(54,79),(55,80),(56,71),(57,72),(58,73),(59,74),(60,75),(61,88),(62,89),(63,90),(64,81),(65,82),(66,83),(67,84),(68,85),(69,86),(70,87),(91,130),(92,121),(93,122),(94,123),(95,124),(96,125),(97,126),(98,127),(99,128),(100,129),(101,113),(102,114),(103,115),(104,116),(105,117),(106,118),(107,119),(108,120),(109,111),(110,112),(141,153),(142,154),(143,155),(144,156),(145,157),(146,158),(147,159),(148,160),(149,151),(150,152)], [(1,68,11,54),(2,69,12,55),(3,70,13,56),(4,61,14,57),(5,62,15,58),(6,63,16,59),(7,64,17,60),(8,65,18,51),(9,66,19,52),(10,67,20,53),(21,122,156,116),(22,123,157,117),(23,124,158,118),(24,125,159,119),(25,126,160,120),(26,127,151,111),(27,128,152,112),(28,129,153,113),(29,130,154,114),(30,121,155,115),(31,87,50,71),(32,88,41,72),(33,89,42,73),(34,90,43,74),(35,81,44,75),(36,82,45,76),(37,83,46,77),(38,84,47,78),(39,85,48,79),(40,86,49,80),(91,142,102,131),(92,143,103,132),(93,144,104,133),(94,145,105,134),(95,146,106,135),(96,147,107,136),(97,148,108,137),(98,149,109,138),(99,150,110,139),(100,141,101,140)], [(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)], [(1,104,6,109),(2,103,7,108),(3,102,8,107),(4,101,9,106),(5,110,10,105),(11,93,16,98),(12,92,17,97),(13,91,18,96),(14,100,19,95),(15,99,20,94),(21,90,26,85),(22,89,27,84),(23,88,28,83),(24,87,29,82),(25,86,30,81),(31,114,36,119),(32,113,37,118),(33,112,38,117),(34,111,39,116),(35,120,40,115),(41,129,46,124),(42,128,47,123),(43,127,48,122),(44,126,49,121),(45,125,50,130),(51,147,56,142),(52,146,57,141),(53,145,58,150),(54,144,59,149),(55,143,60,148),(61,140,66,135),(62,139,67,134),(63,138,68,133),(64,137,69,132),(65,136,70,131),(71,154,76,159),(72,153,77,158),(73,152,78,157),(74,151,79,156),(75,160,80,155)]])
80 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | ··· | 4P | 4Q | ··· | 4AB | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10V | 20A | ··· | 20P |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 5 | ··· | 5 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 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 | C4 | C4 | C4 | D4 | D5 | C4○D4 | Dic5 | D10 | D10 | C4×D5 | D4×D5 | D4⋊2D5 |
| kernel | C22⋊C4×Dic5 | C10.10C42 | C2×C4×Dic5 | C2×C23.D5 | C10×C22⋊C4 | C23×Dic5 | C23.D5 | C5×C22⋊C4 | C22×Dic5 | C2×Dic5 | C2×C22⋊C4 | C2×C10 | C22⋊C4 | C22×C4 | C24 | C23 | C22 | C22 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 8 | 8 | 4 | 2 | 4 | 8 | 4 | 2 | 16 | 4 | 4 |
Matrix representation of C22⋊C4×Dic5 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 9 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 35 | 36 |
| 0 | 0 | 0 | 40 | 40 |
| 32 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 0 | 39 | 37 |
| 0 | 0 | 0 | 11 | 2 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[9,0,0,0,0,0,0,40,0,0,0,1,0,0,0,0,0,0,9,0,0,0,0,0,9],[40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,35,40,0,0,0,36,40],[32,0,0,0,0,0,32,0,0,0,0,0,32,0,0,0,0,0,39,11,0,0,0,37,2] >;
C22⋊C4×Dic5 in GAP, Magma, Sage, TeX
C_2^2\rtimes C_4\times {\rm Dic}_5 % in TeX
G:=Group("C2^2:C4xDic5"); // GroupNames label
G:=SmallGroup(320,568);
// by ID
G=gap.SmallGroup(320,568);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,387,100,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^10=1,e^2=d^5,c*a*c^-1=a*b=b*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations