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G = C2×Dic5.A4order 480 = 25·3·5

Direct product of C2 and Dic5.A4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — C5×Q8 — C2×Dic5.A4
 Chief series C1 — C2 — C10 — C5×Q8 — C5×SL2(𝔽3) — Dic5.A4 — C2×Dic5.A4
 Lower central C5×Q8 — C2×Dic5.A4
 Upper central C1 — C22

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, Q82D5, Q82D5, Q8×C10, C2×C4.A4, C5×SL2(𝔽3), C6×Dic5, C2×Q82D5, 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

Smallest permutation representation of 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

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