direct product, non-abelian, soluble
Aliases: C2×Dic5.A4, SL2(𝔽3)⋊5D10, C10⋊(C4.A4), Q8.1(C6×D5), Q8⋊2D5⋊2C6, (Q8×C10).2C6, C22.7(D5×A4), C10.4(C22×A4), (C2×Dic5).2A4, Dic5.6(C2×A4), (C2×SL2(𝔽3))⋊4D5, (C10×SL2(𝔽3))⋊4C2, (C5×SL2(𝔽3))⋊5C22, C5⋊1(C2×C4.A4), C2.5(C2×D5×A4), (C2×Q8⋊2D5)⋊C3, (C5×Q8).1(C2×C6), (C2×Q8).2(C3×D5), (C2×C10).11(C2×A4), SmallGroup(480,1038)
Series: Derived ►Chief ►Lower central ►Upper central
| C5×Q8 — C2×Dic5.A4 |
Generators and relations for C2×Dic5.A4
G = < a,b,c,d,e,f | a2=b10=f3=1, c2=d2=e2=b5, ab=ba, ac=ca, ad=da, ae=ea, af=fa, cbc-1=b-1, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, ede-1=b5d, fdf-1=b5de, fef-1=d >
Subgroups: 622 in 98 conjugacy classes, 27 normal (17 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, C5, C6, C2×C4, D4, Q8, Q8, C23, D5, C10, C10, C12, C2×C6, C15, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, C20, D10, C2×C10, SL2(𝔽3), C2×C12, C30, C2×C4○D4, C4×D5, D20, C2×Dic5, C2×C20, C5×Q8, C5×Q8, C22×D5, C2×SL2(𝔽3), C4.A4, C3×Dic5, C2×C30, C2×C4×D5, C2×D20, Q8⋊2D5, Q8⋊2D5, Q8×C10, C2×C4.A4, C5×SL2(𝔽3), C6×Dic5, C2×Q8⋊2D5, Dic5.A4, C10×SL2(𝔽3), C2×Dic5.A4
Quotients: C1, C2, C3, C22, C6, D5, A4, C2×C6, D10, C2×A4, C3×D5, C4.A4, C22×A4, C6×D5, C2×C4.A4, D5×A4, Dic5.A4, C2×D5×A4, C2×Dic5.A4
►On 160 points
Generators in S160
(1 46)(2 47)(3 48)(4 49)(5 50)(6 41)(7 42)(8 43)(9 44)(10 45)(11 56)(12 57)(13 58)(14 59)(15 60)(16 51)(17 52)(18 53)(19 54)(20 55)(21 66)(22 67)(23 68)(24 69)(25 70)(26 61)(27 62)(28 63)(29 64)(30 65)(31 76)(32 77)(33 78)(34 79)(35 80)(36 71)(37 72)(38 73)(39 74)(40 75)(81 126)(82 127)(83 128)(84 129)(85 130)(86 121)(87 122)(88 123)(89 124)(90 125)(91 136)(92 137)(93 138)(94 139)(95 140)(96 131)(97 132)(98 133)(99 134)(100 135)(101 146)(102 147)(103 148)(104 149)(105 150)(106 141)(107 142)(108 143)(109 144)(110 145)(111 156)(112 157)(113 158)(114 159)(115 160)(116 151)(117 152)(118 153)(119 154)(120 155)
(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)
(1 124 6 129)(2 123 7 128)(3 122 8 127)(4 121 9 126)(5 130 10 125)(11 134 16 139)(12 133 17 138)(13 132 18 137)(14 131 19 136)(15 140 20 135)(21 144 26 149)(22 143 27 148)(23 142 28 147)(24 141 29 146)(25 150 30 145)(31 154 36 159)(32 153 37 158)(33 152 38 157)(34 151 39 156)(35 160 40 155)(41 84 46 89)(42 83 47 88)(43 82 48 87)(44 81 49 86)(45 90 50 85)(51 94 56 99)(52 93 57 98)(53 92 58 97)(54 91 59 96)(55 100 60 95)(61 104 66 109)(62 103 67 108)(63 102 68 107)(64 101 69 106)(65 110 70 105)(71 114 76 119)(72 113 77 118)(73 112 78 117)(74 111 79 116)(75 120 80 115)
(1 21 6 26)(2 22 7 27)(3 23 8 28)(4 24 9 29)(5 25 10 30)(11 31 16 36)(12 32 17 37)(13 33 18 38)(14 34 19 39)(15 35 20 40)(41 61 46 66)(42 62 47 67)(43 63 48 68)(44 64 49 69)(45 65 50 70)(51 71 56 76)(52 72 57 77)(53 73 58 78)(54 74 59 79)(55 75 60 80)(81 101 86 106)(82 102 87 107)(83 103 88 108)(84 104 89 109)(85 105 90 110)(91 111 96 116)(92 112 97 117)(93 113 98 118)(94 114 99 119)(95 115 100 120)(121 141 126 146)(122 142 127 147)(123 143 128 148)(124 144 129 149)(125 145 130 150)(131 151 136 156)(132 152 137 157)(133 153 138 158)(134 154 139 159)(135 155 140 160)
(1 11 6 16)(2 12 7 17)(3 13 8 18)(4 14 9 19)(5 15 10 20)(21 36 26 31)(22 37 27 32)(23 38 28 33)(24 39 29 34)(25 40 30 35)(41 51 46 56)(42 52 47 57)(43 53 48 58)(44 54 49 59)(45 55 50 60)(61 76 66 71)(62 77 67 72)(63 78 68 73)(64 79 69 74)(65 80 70 75)(81 91 86 96)(82 92 87 97)(83 93 88 98)(84 94 89 99)(85 95 90 100)(101 116 106 111)(102 117 107 112)(103 118 108 113)(104 119 109 114)(105 120 110 115)(121 131 126 136)(122 132 127 137)(123 133 128 138)(124 134 129 139)(125 135 130 140)(141 156 146 151)(142 157 147 152)(143 158 148 153)(144 159 149 154)(145 160 150 155)
(11 31 21)(12 32 22)(13 33 23)(14 34 24)(15 35 25)(16 36 26)(17 37 27)(18 38 28)(19 39 29)(20 40 30)(51 71 61)(52 72 62)(53 73 63)(54 74 64)(55 75 65)(56 76 66)(57 77 67)(58 78 68)(59 79 69)(60 80 70)(91 111 101)(92 112 102)(93 113 103)(94 114 104)(95 115 105)(96 116 106)(97 117 107)(98 118 108)(99 119 109)(100 120 110)(131 151 141)(132 152 142)(133 153 143)(134 154 144)(135 155 145)(136 156 146)(137 157 147)(138 158 148)(139 159 149)(140 160 150)
G:=sub<Sym(160)| (1,46)(2,47)(3,48)(4,49)(5,50)(6,41)(7,42)(8,43)(9,44)(10,45)(11,56)(12,57)(13,58)(14,59)(15,60)(16,51)(17,52)(18,53)(19,54)(20,55)(21,66)(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75)(81,126)(82,127)(83,128)(84,129)(85,130)(86,121)(87,122)(88,123)(89,124)(90,125)(91,136)(92,137)(93,138)(94,139)(95,140)(96,131)(97,132)(98,133)(99,134)(100,135)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)(117,152)(118,153)(119,154)(120,155), (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), (1,124,6,129)(2,123,7,128)(3,122,8,127)(4,121,9,126)(5,130,10,125)(11,134,16,139)(12,133,17,138)(13,132,18,137)(14,131,19,136)(15,140,20,135)(21,144,26,149)(22,143,27,148)(23,142,28,147)(24,141,29,146)(25,150,30,145)(31,154,36,159)(32,153,37,158)(33,152,38,157)(34,151,39,156)(35,160,40,155)(41,84,46,89)(42,83,47,88)(43,82,48,87)(44,81,49,86)(45,90,50,85)(51,94,56,99)(52,93,57,98)(53,92,58,97)(54,91,59,96)(55,100,60,95)(61,104,66,109)(62,103,67,108)(63,102,68,107)(64,101,69,106)(65,110,70,105)(71,114,76,119)(72,113,77,118)(73,112,78,117)(74,111,79,116)(75,120,80,115), (1,21,6,26)(2,22,7,27)(3,23,8,28)(4,24,9,29)(5,25,10,30)(11,31,16,36)(12,32,17,37)(13,33,18,38)(14,34,19,39)(15,35,20,40)(41,61,46,66)(42,62,47,67)(43,63,48,68)(44,64,49,69)(45,65,50,70)(51,71,56,76)(52,72,57,77)(53,73,58,78)(54,74,59,79)(55,75,60,80)(81,101,86,106)(82,102,87,107)(83,103,88,108)(84,104,89,109)(85,105,90,110)(91,111,96,116)(92,112,97,117)(93,113,98,118)(94,114,99,119)(95,115,100,120)(121,141,126,146)(122,142,127,147)(123,143,128,148)(124,144,129,149)(125,145,130,150)(131,151,136,156)(132,152,137,157)(133,153,138,158)(134,154,139,159)(135,155,140,160), (1,11,6,16)(2,12,7,17)(3,13,8,18)(4,14,9,19)(5,15,10,20)(21,36,26,31)(22,37,27,32)(23,38,28,33)(24,39,29,34)(25,40,30,35)(41,51,46,56)(42,52,47,57)(43,53,48,58)(44,54,49,59)(45,55,50,60)(61,76,66,71)(62,77,67,72)(63,78,68,73)(64,79,69,74)(65,80,70,75)(81,91,86,96)(82,92,87,97)(83,93,88,98)(84,94,89,99)(85,95,90,100)(101,116,106,111)(102,117,107,112)(103,118,108,113)(104,119,109,114)(105,120,110,115)(121,131,126,136)(122,132,127,137)(123,133,128,138)(124,134,129,139)(125,135,130,140)(141,156,146,151)(142,157,147,152)(143,158,148,153)(144,159,149,154)(145,160,150,155), (11,31,21)(12,32,22)(13,33,23)(14,34,24)(15,35,25)(16,36,26)(17,37,27)(18,38,28)(19,39,29)(20,40,30)(51,71,61)(52,72,62)(53,73,63)(54,74,64)(55,75,65)(56,76,66)(57,77,67)(58,78,68)(59,79,69)(60,80,70)(91,111,101)(92,112,102)(93,113,103)(94,114,104)(95,115,105)(96,116,106)(97,117,107)(98,118,108)(99,119,109)(100,120,110)(131,151,141)(132,152,142)(133,153,143)(134,154,144)(135,155,145)(136,156,146)(137,157,147)(138,158,148)(139,159,149)(140,160,150)>;
G:=Group( (1,46)(2,47)(3,48)(4,49)(5,50)(6,41)(7,42)(8,43)(9,44)(10,45)(11,56)(12,57)(13,58)(14,59)(15,60)(16,51)(17,52)(18,53)(19,54)(20,55)(21,66)(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75)(81,126)(82,127)(83,128)(84,129)(85,130)(86,121)(87,122)(88,123)(89,124)(90,125)(91,136)(92,137)(93,138)(94,139)(95,140)(96,131)(97,132)(98,133)(99,134)(100,135)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)(117,152)(118,153)(119,154)(120,155), (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), (1,124,6,129)(2,123,7,128)(3,122,8,127)(4,121,9,126)(5,130,10,125)(11,134,16,139)(12,133,17,138)(13,132,18,137)(14,131,19,136)(15,140,20,135)(21,144,26,149)(22,143,27,148)(23,142,28,147)(24,141,29,146)(25,150,30,145)(31,154,36,159)(32,153,37,158)(33,152,38,157)(34,151,39,156)(35,160,40,155)(41,84,46,89)(42,83,47,88)(43,82,48,87)(44,81,49,86)(45,90,50,85)(51,94,56,99)(52,93,57,98)(53,92,58,97)(54,91,59,96)(55,100,60,95)(61,104,66,109)(62,103,67,108)(63,102,68,107)(64,101,69,106)(65,110,70,105)(71,114,76,119)(72,113,77,118)(73,112,78,117)(74,111,79,116)(75,120,80,115), (1,21,6,26)(2,22,7,27)(3,23,8,28)(4,24,9,29)(5,25,10,30)(11,31,16,36)(12,32,17,37)(13,33,18,38)(14,34,19,39)(15,35,20,40)(41,61,46,66)(42,62,47,67)(43,63,48,68)(44,64,49,69)(45,65,50,70)(51,71,56,76)(52,72,57,77)(53,73,58,78)(54,74,59,79)(55,75,60,80)(81,101,86,106)(82,102,87,107)(83,103,88,108)(84,104,89,109)(85,105,90,110)(91,111,96,116)(92,112,97,117)(93,113,98,118)(94,114,99,119)(95,115,100,120)(121,141,126,146)(122,142,127,147)(123,143,128,148)(124,144,129,149)(125,145,130,150)(131,151,136,156)(132,152,137,157)(133,153,138,158)(134,154,139,159)(135,155,140,160), (1,11,6,16)(2,12,7,17)(3,13,8,18)(4,14,9,19)(5,15,10,20)(21,36,26,31)(22,37,27,32)(23,38,28,33)(24,39,29,34)(25,40,30,35)(41,51,46,56)(42,52,47,57)(43,53,48,58)(44,54,49,59)(45,55,50,60)(61,76,66,71)(62,77,67,72)(63,78,68,73)(64,79,69,74)(65,80,70,75)(81,91,86,96)(82,92,87,97)(83,93,88,98)(84,94,89,99)(85,95,90,100)(101,116,106,111)(102,117,107,112)(103,118,108,113)(104,119,109,114)(105,120,110,115)(121,131,126,136)(122,132,127,137)(123,133,128,138)(124,134,129,139)(125,135,130,140)(141,156,146,151)(142,157,147,152)(143,158,148,153)(144,159,149,154)(145,160,150,155), (11,31,21)(12,32,22)(13,33,23)(14,34,24)(15,35,25)(16,36,26)(17,37,27)(18,38,28)(19,39,29)(20,40,30)(51,71,61)(52,72,62)(53,73,63)(54,74,64)(55,75,65)(56,76,66)(57,77,67)(58,78,68)(59,79,69)(60,80,70)(91,111,101)(92,112,102)(93,113,103)(94,114,104)(95,115,105)(96,116,106)(97,117,107)(98,118,108)(99,119,109)(100,120,110)(131,151,141)(132,152,142)(133,153,143)(134,154,144)(135,155,145)(136,156,146)(137,157,147)(138,158,148)(139,159,149)(140,160,150) );
G=PermutationGroup([[(1,46),(2,47),(3,48),(4,49),(5,50),(6,41),(7,42),(8,43),(9,44),(10,45),(11,56),(12,57),(13,58),(14,59),(15,60),(16,51),(17,52),(18,53),(19,54),(20,55),(21,66),(22,67),(23,68),(24,69),(25,70),(26,61),(27,62),(28,63),(29,64),(30,65),(31,76),(32,77),(33,78),(34,79),(35,80),(36,71),(37,72),(38,73),(39,74),(40,75),(81,126),(82,127),(83,128),(84,129),(85,130),(86,121),(87,122),(88,123),(89,124),(90,125),(91,136),(92,137),(93,138),(94,139),(95,140),(96,131),(97,132),(98,133),(99,134),(100,135),(101,146),(102,147),(103,148),(104,149),(105,150),(106,141),(107,142),(108,143),(109,144),(110,145),(111,156),(112,157),(113,158),(114,159),(115,160),(116,151),(117,152),(118,153),(119,154),(120,155)], [(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)], [(1,124,6,129),(2,123,7,128),(3,122,8,127),(4,121,9,126),(5,130,10,125),(11,134,16,139),(12,133,17,138),(13,132,18,137),(14,131,19,136),(15,140,20,135),(21,144,26,149),(22,143,27,148),(23,142,28,147),(24,141,29,146),(25,150,30,145),(31,154,36,159),(32,153,37,158),(33,152,38,157),(34,151,39,156),(35,160,40,155),(41,84,46,89),(42,83,47,88),(43,82,48,87),(44,81,49,86),(45,90,50,85),(51,94,56,99),(52,93,57,98),(53,92,58,97),(54,91,59,96),(55,100,60,95),(61,104,66,109),(62,103,67,108),(63,102,68,107),(64,101,69,106),(65,110,70,105),(71,114,76,119),(72,113,77,118),(73,112,78,117),(74,111,79,116),(75,120,80,115)], [(1,21,6,26),(2,22,7,27),(3,23,8,28),(4,24,9,29),(5,25,10,30),(11,31,16,36),(12,32,17,37),(13,33,18,38),(14,34,19,39),(15,35,20,40),(41,61,46,66),(42,62,47,67),(43,63,48,68),(44,64,49,69),(45,65,50,70),(51,71,56,76),(52,72,57,77),(53,73,58,78),(54,74,59,79),(55,75,60,80),(81,101,86,106),(82,102,87,107),(83,103,88,108),(84,104,89,109),(85,105,90,110),(91,111,96,116),(92,112,97,117),(93,113,98,118),(94,114,99,119),(95,115,100,120),(121,141,126,146),(122,142,127,147),(123,143,128,148),(124,144,129,149),(125,145,130,150),(131,151,136,156),(132,152,137,157),(133,153,138,158),(134,154,139,159),(135,155,140,160)], [(1,11,6,16),(2,12,7,17),(3,13,8,18),(4,14,9,19),(5,15,10,20),(21,36,26,31),(22,37,27,32),(23,38,28,33),(24,39,29,34),(25,40,30,35),(41,51,46,56),(42,52,47,57),(43,53,48,58),(44,54,49,59),(45,55,50,60),(61,76,66,71),(62,77,67,72),(63,78,68,73),(64,79,69,74),(65,80,70,75),(81,91,86,96),(82,92,87,97),(83,93,88,98),(84,94,89,99),(85,95,90,100),(101,116,106,111),(102,117,107,112),(103,118,108,113),(104,119,109,114),(105,120,110,115),(121,131,126,136),(122,132,127,137),(123,133,128,138),(124,134,129,139),(125,135,130,140),(141,156,146,151),(142,157,147,152),(143,158,148,153),(144,159,149,154),(145,160,150,155)], [(11,31,21),(12,32,22),(13,33,23),(14,34,24),(15,35,25),(16,36,26),(17,37,27),(18,38,28),(19,39,29),(20,40,30),(51,71,61),(52,72,62),(53,73,63),(54,74,64),(55,75,65),(56,76,66),(57,77,67),(58,78,68),(59,79,69),(60,80,70),(91,111,101),(92,112,102),(93,113,103),(94,114,104),(95,115,105),(96,116,106),(97,117,107),(98,118,108),(99,119,109),(100,120,110),(131,151,141),(132,152,142),(133,153,143),(134,154,144),(135,155,145),(136,156,146),(137,157,147),(138,158,148),(139,159,149),(140,160,150)]])
56 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6A | ··· | 6F | 10A | ··· | 10F | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 20A | 20B | 20C | 20D | 30A | ··· | 30L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | 20 | 20 | 20 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 30 | 30 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 20 | ··· | 20 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 8 | ··· | 8 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 6 | 6 |
| type | + | + | + | + | + | + | + | + | + | + | + | |||||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | D5 | D10 | C3×D5 | C4.A4 | C6×D5 | A4 | C2×A4 | C2×A4 | Dic5.A4 | Dic5.A4 | D5×A4 | C2×D5×A4 |
| kernel | C2×Dic5.A4 | Dic5.A4 | C10×SL2(𝔽3) | C2×Q8⋊2D5 | Q8⋊2D5 | Q8×C10 | C2×SL2(𝔽3) | SL2(𝔽3) | C2×Q8 | C10 | Q8 | C2×Dic5 | Dic5 | C2×C10 | C2 | C2 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 4 | 2 | 2 | 2 | 4 | 12 | 4 | 1 | 2 | 1 | 4 | 8 | 2 | 2 |
Matrix representation of C2×Dic5.A4 ►in GL4(𝔽61) generated by
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 17 | 60 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 53 | 20 | 0 | 0 |
| 6 | 8 | 0 | 0 |
| 0 | 0 | 50 | 0 |
| 0 | 0 | 0 | 50 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 13 | 14 |
| 0 | 0 | 14 | 48 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 60 |
| 0 | 0 | 1 | 0 |
| 47 | 0 | 0 | 0 |
| 0 | 47 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 48 | 47 |
G:=sub<GL(4,GF(61))| [60,0,0,0,0,60,0,0,0,0,60,0,0,0,0,60],[17,1,0,0,60,0,0,0,0,0,60,0,0,0,0,60],[53,6,0,0,20,8,0,0,0,0,50,0,0,0,0,50],[1,0,0,0,0,1,0,0,0,0,13,14,0,0,14,48],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,60,0],[47,0,0,0,0,47,0,0,0,0,1,48,0,0,0,47] >;
C2×Dic5.A4 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_5.A_4 % in TeX
G:=Group("C2xDic5.A4"); // GroupNames label
G:=SmallGroup(480,1038);
// by ID
G=gap.SmallGroup(480,1038);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,2,-5,-2,1680,269,584,123,795,382,8069]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^10=f^3=1,c^2=d^2=e^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,e*d*e^-1=b^5*d,f*d*f^-1=b^5*d*e,f*e*f^-1=d>;
// generators/relations