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G = (C2×Q8).F5order 320 = 26·5

1st non-split extension by C2×Q8 of F5 acting via F5/C5=C4

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.11C4≀C2, (C2×Q8).1F5, (C2×D20).6C4, (Q8×C10).1C4, C2.7(Q82F5), C2.6(C23.F5), C10.C422C2, (C2×Dic5).110D4, C20.23D4.2C2, C10.5(C4.D4), (C4×Dic5).5C22, C52(C42.C22), C22.63(C22⋊F5), (C2×C4).18(C2×F5), (C2×C20).15(C2×C4), (C2×C10).40(C22⋊C4), SmallGroup(320,265)

Series: Derived Chief Lower central Upper central

C1C2×C20 — (C2×Q8).F5
C1C5C10C2×C10C2×Dic5C4×Dic5C10.C42 — (C2×Q8).F5
C5C2×C10C2×C20 — (C2×Q8).F5
C1C22C2×C4C2×Q8

Generators and relations for (C2×Q8).F5
 G = < a,b,c,d,e | a2=b4=d5=1, c2=b2, e4=a, ebe-1=ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=d3 >

Subgroups: 362 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, D5, C10, C10 [×2], C42, C22⋊C4 [×2], C2×C8 [×2], C2×D4, C2×Q8, Dic5 [×2], C20 [×2], D10 [×3], C2×C10, C8⋊C4 [×2], C4.4D4, C5⋊C8 [×4], D20, C2×Dic5 [×2], C2×C20, C2×C20, C5×Q8, C22×D5, C42.C22, C4×Dic5, D10⋊C4 [×2], C2×C5⋊C8 [×2], C2×D20, Q8×C10, C10.C42 [×2], C20.23D4, (C2×Q8).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, Q82F5 [×2], C23.F5, (C2×Q8).F5

Character table of (C2×Q8).F5

 class 12A2B2C2D4A4B4C4D4E4F58A8B8C8D8E8F8G8H10A10B10C20A20B20C20D20E20F
 size 111140481010101042020202020202020444888888
ρ111111111111111111111111111111    trivial
ρ21111-11-1111111-1-1-1-1111111-1-1-111-1    linear of order 2
ρ31111-11-111111-11111-1-1-1111-1-1-111-1    linear of order 2
ρ4111111111111-1-1-1-1-1-1-1-1111111111    linear of order 2
ρ5111111-1-1-1-1-11iii-i-i-i-ii111-1-1-111-1    linear of order 4
ρ61111-111-1-1-1-11i-i-iii-i-ii111111111    linear of order 4
ρ71111-111-1-1-1-11-iii-i-iii-i111111111    linear of order 4
ρ8111111-1-1-1-1-11-i-i-iiiii-i111-1-1-111-1    linear of order 4
ρ922220-202-2-22200000000222000-2-20    orthogonal lifted from D4
ρ1022220-20-222-2200000000222000-2-20    orthogonal lifted from D4
ρ112-2-220002i00-2i201+i-1-i1-i-1+i000-22-2000000    complex lifted from C4≀C2
ρ122-22-20000-2i2i02-1+i00001+i-1-i1-i2-2-2000000    complex lifted from C4≀C2
ρ132-22-200002i-2i021+i0000-1+i1-i-1-i2-2-2000000    complex lifted from C4≀C2
ρ142-22-200002i-2i02-1-i00001-i-1+i1+i2-2-2000000    complex lifted from C4≀C2
ρ152-2-22000-2i002i20-1+i1-i-1-i1+i000-22-2000000    complex lifted from C4≀C2
ρ162-22-20000-2i2i021-i0000-1-i1+i-1+i2-2-2000000    complex lifted from C4≀C2
ρ172-2-220002i00-2i20-1-i1+i-1+i1-i000-22-2000000    complex lifted from C4≀C2
ρ182-2-22000-2i002i201-i-1+i1+i-1-i000-22-2000000    complex lifted from C4≀C2
ρ1944440440000-100000000-1-1-1-1-1-1-1-1-1    orthogonal lifted from F5
ρ2044-4-40000000400000000-4-44000000    orthogonal lifted from C4.D4
ρ21444404-40000-100000000-1-1-1111-1-11    orthogonal lifted from C2×F5
ρ2244440-400000-100000000-1-1-1-5-55115    orthogonal lifted from C22⋊F5
ρ2344440-400000-100000000-1-1-155-511-5    orthogonal lifted from C22⋊F5
ρ2444-4-40000000-10000000011-154+2ζ52+153+2ζ5+154+2ζ53+1-5552+2ζ5+1    complex lifted from C23.F5
ρ2544-4-40000000-10000000011-153+2ζ5+154+2ζ52+152+2ζ5+1-5554+2ζ53+1    complex lifted from C23.F5
ρ2644-4-40000000-10000000011-152+2ζ5+154+2ζ53+154+2ζ52+15-553+2ζ5+1    complex lifted from C23.F5
ρ2744-4-40000000-10000000011-154+2ζ53+152+2ζ5+153+2ζ5+15-554+2ζ52+1    complex lifted from C23.F5
ρ288-88-80000000-200000000-222000000    orthogonal lifted from Q82F5
ρ298-8-880000000-2000000002-22000000    orthogonal lifted from Q82F5

Smallest permutation representation of (C2×Q8).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 88 110 115)(2 85 111 120)(3 82 112 117)(4 87 105 114)(5 84 106 119)(6 81 107 116)(7 86 108 113)(8 83 109 118)(9 104 152 26)(10 101 145 31)(11 98 146 28)(12 103 147 25)(13 100 148 30)(14 97 149 27)(15 102 150 32)(16 99 151 29)(17 134 38 78)(18 131 39 75)(19 136 40 80)(20 133 33 77)(21 130 34 74)(22 135 35 79)(23 132 36 76)(24 129 37 73)(41 60 56 125)(42 57 49 122)(43 62 50 127)(44 59 51 124)(45 64 52 121)(46 61 53 126)(47 58 54 123)(48 63 55 128)(65 143 155 93)(66 140 156 90)(67 137 157 95)(68 142 158 92)(69 139 159 89)(70 144 160 94)(71 141 153 91)(72 138 154 96)
(1 112 110 3)(2 118 111 83)(4 81 105 116)(5 108 106 7)(6 114 107 87)(8 85 109 120)(9 135 152 79)(10 36 145 23)(11 77 146 133)(12 21 147 34)(13 131 148 75)(14 40 149 19)(15 73 150 129)(16 17 151 38)(18 30 39 100)(20 98 33 28)(22 26 35 104)(24 102 37 32)(25 130 103 74)(27 80 97 136)(29 134 99 78)(31 76 101 132)(41 144 56 94)(42 153 49 71)(43 92 50 142)(44 69 51 159)(45 140 52 90)(46 157 53 67)(47 96 54 138)(48 65 55 155)(57 141 122 91)(58 154 123 72)(59 89 124 139)(60 70 125 160)(61 137 126 95)(62 158 127 68)(63 93 128 143)(64 66 121 156)(82 115 117 88)(84 86 119 113)
(1 98 141 63 18)(2 64 99 19 142)(3 20 57 143 100)(4 144 21 101 58)(5 102 137 59 22)(6 60 103 23 138)(7 24 61 139 104)(8 140 17 97 62)(9 113 73 46 69)(10 47 114 70 74)(11 71 48 75 115)(12 76 72 116 41)(13 117 77 42 65)(14 43 118 66 78)(15 67 44 79 119)(16 80 68 120 45)(25 36 96 107 125)(26 108 37 126 89)(27 127 109 90 38)(28 91 128 39 110)(29 40 92 111 121)(30 112 33 122 93)(31 123 105 94 34)(32 95 124 35 106)(49 155 148 82 133)(50 83 156 134 149)(51 135 84 150 157)(52 151 136 158 85)(53 159 152 86 129)(54 87 160 130 145)(55 131 88 146 153)(56 147 132 154 81)
(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), (1,88,110,115)(2,85,111,120)(3,82,112,117)(4,87,105,114)(5,84,106,119)(6,81,107,116)(7,86,108,113)(8,83,109,118)(9,104,152,26)(10,101,145,31)(11,98,146,28)(12,103,147,25)(13,100,148,30)(14,97,149,27)(15,102,150,32)(16,99,151,29)(17,134,38,78)(18,131,39,75)(19,136,40,80)(20,133,33,77)(21,130,34,74)(22,135,35,79)(23,132,36,76)(24,129,37,73)(41,60,56,125)(42,57,49,122)(43,62,50,127)(44,59,51,124)(45,64,52,121)(46,61,53,126)(47,58,54,123)(48,63,55,128)(65,143,155,93)(66,140,156,90)(67,137,157,95)(68,142,158,92)(69,139,159,89)(70,144,160,94)(71,141,153,91)(72,138,154,96), (1,112,110,3)(2,118,111,83)(4,81,105,116)(5,108,106,7)(6,114,107,87)(8,85,109,120)(9,135,152,79)(10,36,145,23)(11,77,146,133)(12,21,147,34)(13,131,148,75)(14,40,149,19)(15,73,150,129)(16,17,151,38)(18,30,39,100)(20,98,33,28)(22,26,35,104)(24,102,37,32)(25,130,103,74)(27,80,97,136)(29,134,99,78)(31,76,101,132)(41,144,56,94)(42,153,49,71)(43,92,50,142)(44,69,51,159)(45,140,52,90)(46,157,53,67)(47,96,54,138)(48,65,55,155)(57,141,122,91)(58,154,123,72)(59,89,124,139)(60,70,125,160)(61,137,126,95)(62,158,127,68)(63,93,128,143)(64,66,121,156)(82,115,117,88)(84,86,119,113), (1,98,141,63,18)(2,64,99,19,142)(3,20,57,143,100)(4,144,21,101,58)(5,102,137,59,22)(6,60,103,23,138)(7,24,61,139,104)(8,140,17,97,62)(9,113,73,46,69)(10,47,114,70,74)(11,71,48,75,115)(12,76,72,116,41)(13,117,77,42,65)(14,43,118,66,78)(15,67,44,79,119)(16,80,68,120,45)(25,36,96,107,125)(26,108,37,126,89)(27,127,109,90,38)(28,91,128,39,110)(29,40,92,111,121)(30,112,33,122,93)(31,123,105,94,34)(32,95,124,35,106)(49,155,148,82,133)(50,83,156,134,149)(51,135,84,150,157)(52,151,136,158,85)(53,159,152,86,129)(54,87,160,130,145)(55,131,88,146,153)(56,147,132,154,81), (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), (1,88,110,115)(2,85,111,120)(3,82,112,117)(4,87,105,114)(5,84,106,119)(6,81,107,116)(7,86,108,113)(8,83,109,118)(9,104,152,26)(10,101,145,31)(11,98,146,28)(12,103,147,25)(13,100,148,30)(14,97,149,27)(15,102,150,32)(16,99,151,29)(17,134,38,78)(18,131,39,75)(19,136,40,80)(20,133,33,77)(21,130,34,74)(22,135,35,79)(23,132,36,76)(24,129,37,73)(41,60,56,125)(42,57,49,122)(43,62,50,127)(44,59,51,124)(45,64,52,121)(46,61,53,126)(47,58,54,123)(48,63,55,128)(65,143,155,93)(66,140,156,90)(67,137,157,95)(68,142,158,92)(69,139,159,89)(70,144,160,94)(71,141,153,91)(72,138,154,96), (1,112,110,3)(2,118,111,83)(4,81,105,116)(5,108,106,7)(6,114,107,87)(8,85,109,120)(9,135,152,79)(10,36,145,23)(11,77,146,133)(12,21,147,34)(13,131,148,75)(14,40,149,19)(15,73,150,129)(16,17,151,38)(18,30,39,100)(20,98,33,28)(22,26,35,104)(24,102,37,32)(25,130,103,74)(27,80,97,136)(29,134,99,78)(31,76,101,132)(41,144,56,94)(42,153,49,71)(43,92,50,142)(44,69,51,159)(45,140,52,90)(46,157,53,67)(47,96,54,138)(48,65,55,155)(57,141,122,91)(58,154,123,72)(59,89,124,139)(60,70,125,160)(61,137,126,95)(62,158,127,68)(63,93,128,143)(64,66,121,156)(82,115,117,88)(84,86,119,113), (1,98,141,63,18)(2,64,99,19,142)(3,20,57,143,100)(4,144,21,101,58)(5,102,137,59,22)(6,60,103,23,138)(7,24,61,139,104)(8,140,17,97,62)(9,113,73,46,69)(10,47,114,70,74)(11,71,48,75,115)(12,76,72,116,41)(13,117,77,42,65)(14,43,118,66,78)(15,67,44,79,119)(16,80,68,120,45)(25,36,96,107,125)(26,108,37,126,89)(27,127,109,90,38)(28,91,128,39,110)(29,40,92,111,121)(30,112,33,122,93)(31,123,105,94,34)(32,95,124,35,106)(49,155,148,82,133)(50,83,156,134,149)(51,135,84,150,157)(52,151,136,158,85)(53,159,152,86,129)(54,87,160,130,145)(55,131,88,146,153)(56,147,132,154,81), (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)], [(1,88,110,115),(2,85,111,120),(3,82,112,117),(4,87,105,114),(5,84,106,119),(6,81,107,116),(7,86,108,113),(8,83,109,118),(9,104,152,26),(10,101,145,31),(11,98,146,28),(12,103,147,25),(13,100,148,30),(14,97,149,27),(15,102,150,32),(16,99,151,29),(17,134,38,78),(18,131,39,75),(19,136,40,80),(20,133,33,77),(21,130,34,74),(22,135,35,79),(23,132,36,76),(24,129,37,73),(41,60,56,125),(42,57,49,122),(43,62,50,127),(44,59,51,124),(45,64,52,121),(46,61,53,126),(47,58,54,123),(48,63,55,128),(65,143,155,93),(66,140,156,90),(67,137,157,95),(68,142,158,92),(69,139,159,89),(70,144,160,94),(71,141,153,91),(72,138,154,96)], [(1,112,110,3),(2,118,111,83),(4,81,105,116),(5,108,106,7),(6,114,107,87),(8,85,109,120),(9,135,152,79),(10,36,145,23),(11,77,146,133),(12,21,147,34),(13,131,148,75),(14,40,149,19),(15,73,150,129),(16,17,151,38),(18,30,39,100),(20,98,33,28),(22,26,35,104),(24,102,37,32),(25,130,103,74),(27,80,97,136),(29,134,99,78),(31,76,101,132),(41,144,56,94),(42,153,49,71),(43,92,50,142),(44,69,51,159),(45,140,52,90),(46,157,53,67),(47,96,54,138),(48,65,55,155),(57,141,122,91),(58,154,123,72),(59,89,124,139),(60,70,125,160),(61,137,126,95),(62,158,127,68),(63,93,128,143),(64,66,121,156),(82,115,117,88),(84,86,119,113)], [(1,98,141,63,18),(2,64,99,19,142),(3,20,57,143,100),(4,144,21,101,58),(5,102,137,59,22),(6,60,103,23,138),(7,24,61,139,104),(8,140,17,97,62),(9,113,73,46,69),(10,47,114,70,74),(11,71,48,75,115),(12,76,72,116,41),(13,117,77,42,65),(14,43,118,66,78),(15,67,44,79,119),(16,80,68,120,45),(25,36,96,107,125),(26,108,37,126,89),(27,127,109,90,38),(28,91,128,39,110),(29,40,92,111,121),(30,112,33,122,93),(31,123,105,94,34),(32,95,124,35,106),(49,155,148,82,133),(50,83,156,134,149),(51,135,84,150,157),(52,151,136,158,85),(53,159,152,86,129),(54,87,160,130,145),(55,131,88,146,153),(56,147,132,154,81)], [(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×Q8).F5 in GL8(𝔽41)

400000000
040000000
00100000
00010000
00001000
00000100
00000010
00000001
,
01000000
400000000
000400000
00100000
000040000
000004000
000000400
000000040
,
320000000
09000000
000320000
003200000
0000193038
0000022338
0000383220
0000380319
,
10000000
01000000
00100000
00010000
000000040
000010040
000001040
000000140
,
365000000
55000000
0037370000
004370000
0000343446
00003840840
000013313
0000353777

G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[32,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,19,0,38,38,0,0,0,0,3,22,3,0,0,0,0,0,0,3,22,3,0,0,0,0,38,38,0,19],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,40,40,40,40],[36,5,0,0,0,0,0,0,5,5,0,0,0,0,0,0,0,0,37,4,0,0,0,0,0,0,37,37,0,0,0,0,0,0,0,0,34,38,1,35,0,0,0,0,34,40,33,37,0,0,0,0,4,8,1,7,0,0,0,0,6,40,3,7] >;

(C2×Q8).F5 in GAP, Magma, Sage, TeX

(C_2\times Q_8).F_5
% in TeX

G:=Group("(C2xQ8).F5");
// GroupNames label

G:=SmallGroup(320,265);
// by ID

G=gap.SmallGroup(320,265);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,232,219,268,1571,570,136,6278,3156]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^4=d^5=1,c^2=b^2,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^-1=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×Q8).F5 in TeX

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