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G = (C2×D4).F5order 320 = 26·5

1st non-split extension by C2×D4 of F5 acting via F5/C5=C4

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.5C4≀C2, (C2×D4).1F5, (D4×C10).1C4, C2.7(D4⋊F5), (C2×Dic10).5C4, C2.4(C23.F5), C10.C421C2, (C2×Dic5).106D4, C20.17D4.2C2, C10.3(C4.D4), (C4×Dic5).3C22, C51(C42.C22), C22.60(C22⋊F5), (C2×C4).15(C2×F5), (C2×C20).10(C2×C4), (C2×C10).34(C22⋊C4), SmallGroup(320,259)

Series: Derived Chief Lower central Upper central

C1C2×C20 — (C2×D4).F5
C1C5C10C2×C10C2×Dic5C4×Dic5C10.C42 — (C2×D4).F5
C5C2×C10C2×C20 — (C2×D4).F5
C1C22C2×C4C2×D4

Generators and relations for (C2×D4).F5
 G = < a,b,c,d,e | a2=b4=c2=d5=1, e4=a, ebe-1=ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=d3 >

Subgroups: 298 in 70 conjugacy classes, 22 normal (14 characteristic)
C1, C2, C2 [×2], C2, C4 [×4], C22, C22 [×3], C5, C8 [×4], C2×C4, C2×C4 [×3], D4, Q8, C23, C10, C10 [×2], C10, C42, C22⋊C4 [×2], C2×C8 [×2], C2×D4, C2×Q8, Dic5 [×3], C20, C2×C10, C2×C10 [×3], C8⋊C4 [×2], C4.4D4, C5⋊C8 [×4], Dic10, C2×Dic5 [×2], C2×Dic5, C2×C20, C5×D4, C22×C10, C42.C22, C4×Dic5, C23.D5 [×2], C2×C5⋊C8 [×2], C2×Dic10, D4×C10, C10.C42 [×2], C20.17D4, (C2×D4).F5
Quotients: C1, C2 [×3], C4 [×2], C22, C2×C4, D4 [×2], C22⋊C4, F5, C4.D4, C4≀C2 [×2], C2×F5, C42.C22, C22⋊F5, D4⋊F5 [×2], C23.F5, (C2×D4).F5

Character table of (C2×D4).F5

 class 12A2B2C2D4A4B4C4D4E4F58A8B8C8D8E8F8G8H10A10B10C10D10E10F10G20A20B
 size 111184101010104042020202020202020444888888
ρ111111111111111111111111111111    trivial
ρ21111-111111-111-1-1-1-1111111-1-1-1-111    linear of order 2
ρ31111-111111-11-11111-1-1-1111-1-1-1-111    linear of order 2
ρ4111111111111-1-1-1-1-1-1-1-1111111111    linear of order 2
ρ5111111-1-1-1-1-11-iii-i-iii-i111111111    linear of order 4
ρ61111-11-1-1-1-111-i-i-iiiii-i111-1-1-1-111    linear of order 4
ρ71111-11-1-1-1-111iii-i-i-i-ii111-1-1-1-111    linear of order 4
ρ8111111-1-1-1-1-11i-i-iii-i-ii111111111    linear of order 4
ρ922220-222-2-202000000002220000-2-2    orthogonal lifted from D4
ρ1022220-2-2-22202000000002220000-2-2    orthogonal lifted from D4
ρ112-22-20000-2i2i02-1-i0000-1+i1-i1+i2-2-2000000    complex lifted from C4≀C2
ρ122-22-20000-2i2i021+i00001-i-1+i-1-i2-2-2000000    complex lifted from C4≀C2
ρ1322-2-2002i-2i000201+i-1-i1-i-1+i000-2-22000000    complex lifted from C4≀C2
ρ1422-2-200-2i2i00020-1+i1-i-1-i1+i000-2-22000000    complex lifted from C4≀C2
ρ1522-2-2002i-2i00020-1-i1+i-1+i1-i000-2-22000000    complex lifted from C4≀C2
ρ162-22-200002i-2i02-1+i0000-1-i1+i1-i2-2-2000000    complex lifted from C4≀C2
ρ172-22-200002i-2i021-i00001+i-1-i-1+i2-2-2000000    complex lifted from C4≀C2
ρ1822-2-200-2i2i000201-i-1+i1+i-1-i000-2-22000000    complex lifted from C4≀C2
ρ1944444400000-100000000-1-1-1-1-1-1-1-1-1    orthogonal lifted from F5
ρ204444-4400000-100000000-1-1-11111-1-1    orthogonal lifted from C2×F5
ρ214-4-440000000400000000-44-4000000    orthogonal lifted from C4.D4
ρ2244440-400000-100000000-1-1-155-5-511    orthogonal lifted from C22⋊F5
ρ2344440-400000-100000000-1-1-1-5-55511    orthogonal lifted from C22⋊F5
ρ244-4-440000000-1000000001-1154+2ζ53+152+2ζ5+154+2ζ52+153+2ζ5+1-55    complex lifted from C23.F5
ρ254-4-440000000-1000000001-1152+2ζ5+154+2ζ53+153+2ζ5+154+2ζ52+1-55    complex lifted from C23.F5
ρ264-4-440000000-1000000001-1153+2ζ5+154+2ζ52+154+2ζ53+152+2ζ5+15-5    complex lifted from C23.F5
ρ274-4-440000000-1000000001-1154+2ζ52+153+2ζ5+152+2ζ5+154+2ζ53+15-5    complex lifted from C23.F5
ρ2888-8-80000000-20000000022-2000000    symplectic lifted from D4⋊F5, Schur index 2
ρ298-88-80000000-200000000-222000000    symplectic lifted from D4⋊F5, Schur index 2

Smallest permutation representation of (C2×D4).F5
On 160 points
Generators in S160
(1 5)(2 6)(3 7)(4 8)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(33 37)(34 38)(35 39)(36 40)(41 45)(42 46)(43 47)(44 48)(49 53)(50 54)(51 55)(52 56)(57 61)(58 62)(59 63)(60 64)(65 69)(66 70)(67 71)(68 72)(73 77)(74 78)(75 79)(76 80)(81 85)(82 86)(83 87)(84 88)(89 93)(90 94)(91 95)(92 96)(97 101)(98 102)(99 103)(100 104)(105 109)(106 110)(107 111)(108 112)(113 117)(114 118)(115 119)(116 120)(121 125)(122 126)(123 127)(124 128)(129 133)(130 134)(131 135)(132 136)(137 141)(138 142)(139 143)(140 144)(145 149)(146 150)(147 151)(148 152)(153 157)(154 158)(155 159)(156 160)
(1 128 88 115)(2 125 81 120)(3 122 82 117)(4 127 83 114)(5 124 84 119)(6 121 85 116)(7 126 86 113)(8 123 87 118)(9 97 106 30)(10 102 107 27)(11 99 108 32)(12 104 109 29)(13 101 110 26)(14 98 111 31)(15 103 112 28)(16 100 105 25)(17 131 152 153)(18 136 145 158)(19 133 146 155)(20 130 147 160)(21 135 148 157)(22 132 149 154)(23 129 150 159)(24 134 151 156)(33 51 68 91)(34 56 69 96)(35 53 70 93)(36 50 71 90)(37 55 72 95)(38 52 65 92)(39 49 66 89)(40 54 67 94)(41 144 76 62)(42 141 77 59)(43 138 78 64)(44 143 79 61)(45 140 80 58)(46 137 73 63)(47 142 74 60)(48 139 75 57)
(2 121)(3 86)(4 114)(6 125)(7 82)(8 118)(9 110)(10 27)(12 100)(13 106)(14 31)(16 104)(18 132)(19 150)(20 160)(22 136)(23 146)(24 156)(25 109)(26 30)(28 103)(29 105)(32 99)(34 52)(35 66)(36 90)(38 56)(39 70)(40 94)(41 58)(42 46)(43 138)(44 79)(45 62)(47 142)(48 75)(49 53)(50 71)(51 91)(54 67)(55 95)(59 137)(60 74)(63 141)(64 78)(65 96)(69 92)(73 77)(76 140)(80 144)(81 116)(83 127)(85 120)(87 123)(89 93)(97 101)(98 111)(102 107)(113 117)(115 128)(119 124)(122 126)(129 133)(130 147)(131 153)(134 151)(135 157)(145 154)(149 158)(155 159)
(1 143 108 37 17)(2 38 144 18 109)(3 19 39 110 137)(4 111 20 138 40)(5 139 112 33 21)(6 34 140 22 105)(7 23 35 106 141)(8 107 24 142 36)(9 59 86 150 70)(10 151 60 71 87)(11 72 152 88 61)(12 81 65 62 145)(13 63 82 146 66)(14 147 64 67 83)(15 68 148 84 57)(16 85 69 58 149)(25 121 56 80 132)(26 73 122 133 49)(27 134 74 50 123)(28 51 135 124 75)(29 125 52 76 136)(30 77 126 129 53)(31 130 78 54 127)(32 55 131 128 79)(41 158 104 120 92)(42 113 159 93 97)(43 94 114 98 160)(44 99 95 153 115)(45 154 100 116 96)(46 117 155 89 101)(47 90 118 102 156)(48 103 91 157 119)
(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)

G:=sub<Sym(160)| (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160), (1,128,88,115)(2,125,81,120)(3,122,82,117)(4,127,83,114)(5,124,84,119)(6,121,85,116)(7,126,86,113)(8,123,87,118)(9,97,106,30)(10,102,107,27)(11,99,108,32)(12,104,109,29)(13,101,110,26)(14,98,111,31)(15,103,112,28)(16,100,105,25)(17,131,152,153)(18,136,145,158)(19,133,146,155)(20,130,147,160)(21,135,148,157)(22,132,149,154)(23,129,150,159)(24,134,151,156)(33,51,68,91)(34,56,69,96)(35,53,70,93)(36,50,71,90)(37,55,72,95)(38,52,65,92)(39,49,66,89)(40,54,67,94)(41,144,76,62)(42,141,77,59)(43,138,78,64)(44,143,79,61)(45,140,80,58)(46,137,73,63)(47,142,74,60)(48,139,75,57), (2,121)(3,86)(4,114)(6,125)(7,82)(8,118)(9,110)(10,27)(12,100)(13,106)(14,31)(16,104)(18,132)(19,150)(20,160)(22,136)(23,146)(24,156)(25,109)(26,30)(28,103)(29,105)(32,99)(34,52)(35,66)(36,90)(38,56)(39,70)(40,94)(41,58)(42,46)(43,138)(44,79)(45,62)(47,142)(48,75)(49,53)(50,71)(51,91)(54,67)(55,95)(59,137)(60,74)(63,141)(64,78)(65,96)(69,92)(73,77)(76,140)(80,144)(81,116)(83,127)(85,120)(87,123)(89,93)(97,101)(98,111)(102,107)(113,117)(115,128)(119,124)(122,126)(129,133)(130,147)(131,153)(134,151)(135,157)(145,154)(149,158)(155,159), (1,143,108,37,17)(2,38,144,18,109)(3,19,39,110,137)(4,111,20,138,40)(5,139,112,33,21)(6,34,140,22,105)(7,23,35,106,141)(8,107,24,142,36)(9,59,86,150,70)(10,151,60,71,87)(11,72,152,88,61)(12,81,65,62,145)(13,63,82,146,66)(14,147,64,67,83)(15,68,148,84,57)(16,85,69,58,149)(25,121,56,80,132)(26,73,122,133,49)(27,134,74,50,123)(28,51,135,124,75)(29,125,52,76,136)(30,77,126,129,53)(31,130,78,54,127)(32,55,131,128,79)(41,158,104,120,92)(42,113,159,93,97)(43,94,114,98,160)(44,99,95,153,115)(45,154,100,116,96)(46,117,155,89,101)(47,90,118,102,156)(48,103,91,157,119), (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)>;

G:=Group( (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160), (1,128,88,115)(2,125,81,120)(3,122,82,117)(4,127,83,114)(5,124,84,119)(6,121,85,116)(7,126,86,113)(8,123,87,118)(9,97,106,30)(10,102,107,27)(11,99,108,32)(12,104,109,29)(13,101,110,26)(14,98,111,31)(15,103,112,28)(16,100,105,25)(17,131,152,153)(18,136,145,158)(19,133,146,155)(20,130,147,160)(21,135,148,157)(22,132,149,154)(23,129,150,159)(24,134,151,156)(33,51,68,91)(34,56,69,96)(35,53,70,93)(36,50,71,90)(37,55,72,95)(38,52,65,92)(39,49,66,89)(40,54,67,94)(41,144,76,62)(42,141,77,59)(43,138,78,64)(44,143,79,61)(45,140,80,58)(46,137,73,63)(47,142,74,60)(48,139,75,57), (2,121)(3,86)(4,114)(6,125)(7,82)(8,118)(9,110)(10,27)(12,100)(13,106)(14,31)(16,104)(18,132)(19,150)(20,160)(22,136)(23,146)(24,156)(25,109)(26,30)(28,103)(29,105)(32,99)(34,52)(35,66)(36,90)(38,56)(39,70)(40,94)(41,58)(42,46)(43,138)(44,79)(45,62)(47,142)(48,75)(49,53)(50,71)(51,91)(54,67)(55,95)(59,137)(60,74)(63,141)(64,78)(65,96)(69,92)(73,77)(76,140)(80,144)(81,116)(83,127)(85,120)(87,123)(89,93)(97,101)(98,111)(102,107)(113,117)(115,128)(119,124)(122,126)(129,133)(130,147)(131,153)(134,151)(135,157)(145,154)(149,158)(155,159), (1,143,108,37,17)(2,38,144,18,109)(3,19,39,110,137)(4,111,20,138,40)(5,139,112,33,21)(6,34,140,22,105)(7,23,35,106,141)(8,107,24,142,36)(9,59,86,150,70)(10,151,60,71,87)(11,72,152,88,61)(12,81,65,62,145)(13,63,82,146,66)(14,147,64,67,83)(15,68,148,84,57)(16,85,69,58,149)(25,121,56,80,132)(26,73,122,133,49)(27,134,74,50,123)(28,51,135,124,75)(29,125,52,76,136)(30,77,126,129,53)(31,130,78,54,127)(32,55,131,128,79)(41,158,104,120,92)(42,113,159,93,97)(43,94,114,98,160)(44,99,95,153,115)(45,154,100,116,96)(46,117,155,89,101)(47,90,118,102,156)(48,103,91,157,119), (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) );

G=PermutationGroup([(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32),(33,37),(34,38),(35,39),(36,40),(41,45),(42,46),(43,47),(44,48),(49,53),(50,54),(51,55),(52,56),(57,61),(58,62),(59,63),(60,64),(65,69),(66,70),(67,71),(68,72),(73,77),(74,78),(75,79),(76,80),(81,85),(82,86),(83,87),(84,88),(89,93),(90,94),(91,95),(92,96),(97,101),(98,102),(99,103),(100,104),(105,109),(106,110),(107,111),(108,112),(113,117),(114,118),(115,119),(116,120),(121,125),(122,126),(123,127),(124,128),(129,133),(130,134),(131,135),(132,136),(137,141),(138,142),(139,143),(140,144),(145,149),(146,150),(147,151),(148,152),(153,157),(154,158),(155,159),(156,160)], [(1,128,88,115),(2,125,81,120),(3,122,82,117),(4,127,83,114),(5,124,84,119),(6,121,85,116),(7,126,86,113),(8,123,87,118),(9,97,106,30),(10,102,107,27),(11,99,108,32),(12,104,109,29),(13,101,110,26),(14,98,111,31),(15,103,112,28),(16,100,105,25),(17,131,152,153),(18,136,145,158),(19,133,146,155),(20,130,147,160),(21,135,148,157),(22,132,149,154),(23,129,150,159),(24,134,151,156),(33,51,68,91),(34,56,69,96),(35,53,70,93),(36,50,71,90),(37,55,72,95),(38,52,65,92),(39,49,66,89),(40,54,67,94),(41,144,76,62),(42,141,77,59),(43,138,78,64),(44,143,79,61),(45,140,80,58),(46,137,73,63),(47,142,74,60),(48,139,75,57)], [(2,121),(3,86),(4,114),(6,125),(7,82),(8,118),(9,110),(10,27),(12,100),(13,106),(14,31),(16,104),(18,132),(19,150),(20,160),(22,136),(23,146),(24,156),(25,109),(26,30),(28,103),(29,105),(32,99),(34,52),(35,66),(36,90),(38,56),(39,70),(40,94),(41,58),(42,46),(43,138),(44,79),(45,62),(47,142),(48,75),(49,53),(50,71),(51,91),(54,67),(55,95),(59,137),(60,74),(63,141),(64,78),(65,96),(69,92),(73,77),(76,140),(80,144),(81,116),(83,127),(85,120),(87,123),(89,93),(97,101),(98,111),(102,107),(113,117),(115,128),(119,124),(122,126),(129,133),(130,147),(131,153),(134,151),(135,157),(145,154),(149,158),(155,159)], [(1,143,108,37,17),(2,38,144,18,109),(3,19,39,110,137),(4,111,20,138,40),(5,139,112,33,21),(6,34,140,22,105),(7,23,35,106,141),(8,107,24,142,36),(9,59,86,150,70),(10,151,60,71,87),(11,72,152,88,61),(12,81,65,62,145),(13,63,82,146,66),(14,147,64,67,83),(15,68,148,84,57),(16,85,69,58,149),(25,121,56,80,132),(26,73,122,133,49),(27,134,74,50,123),(28,51,135,124,75),(29,125,52,76,136),(30,77,126,129,53),(31,130,78,54,127),(32,55,131,128,79),(41,158,104,120,92),(42,113,159,93,97),(43,94,114,98,160),(44,99,95,153,115),(45,154,100,116,96),(46,117,155,89,101),(47,90,118,102,156),(48,103,91,157,119)], [(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)])

Matrix representation of (C2×D4).F5 in GL8(𝔽41)

10000000
01000000
004000000
000400000
00001000
00000100
00000010
00000001
,
040000000
10000000
0034300000
001270000
00001000
00000100
00000010
00000001
,
10000000
040000000
00100000
0036400000
00001000
00000100
00000010
00000001
,
10000000
01000000
00100000
00010000
000040404040
00001000
00000100
00000010
,
3636000000
536000000
0040140000
002410000
00001633414
000031113813
00002723020
000028183925

G:=sub<GL(8,GF(41))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,34,12,0,0,0,0,0,0,30,7,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,36,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,1,0,0,0,0,0,0,40,0,1,0,0,0,0,0,40,0,0,1,0,0,0,0,40,0,0,0],[36,5,0,0,0,0,0,0,36,36,0,0,0,0,0,0,0,0,40,24,0,0,0,0,0,0,14,1,0,0,0,0,0,0,0,0,16,31,27,28,0,0,0,0,3,11,2,18,0,0,0,0,34,38,30,39,0,0,0,0,14,13,20,25] >;

(C2×D4).F5 in GAP, Magma, Sage, TeX

(C_2\times D_4).F_5
% in TeX

G:=Group("(C2xD4).F5");
// GroupNames label

G:=SmallGroup(320,259);
// by ID

G=gap.SmallGroup(320,259);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,219,268,1571,570,136,6278,3156]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^5=1,e^4=a,e*b*e^-1=a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^3>;
// generators/relations

Export

Character table of (C2×D4).F5 in TeX

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