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## G = C2×C13⋊C8order 208 = 24·13

### Direct product of C2 and C13⋊C8

Aliases: C2×C13⋊C8, C26⋊C8, Dic13.2C4, Dic13.6C22, C132(C2×C8), (C2×C26).1C4, C26.5(C2×C4), C22.2(C13⋊C4), (C2×Dic13).4C2, C2.3(C2×C13⋊C4), SmallGroup(208,32)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C13 — C2×C13⋊C8
 Chief series C1 — C13 — C26 — Dic13 — C13⋊C8 — C2×C13⋊C8
 Lower central C13 — C2×C13⋊C8
 Upper central C1 — C22

Generators and relations for C2×C13⋊C8
G = < a,b,c | a2=b13=c8=1, ab=ba, ac=ca, cbc-1=b5 >

Character table of C2×C13⋊C8

 class 1 2A 2B 2C 4A 4B 4C 4D 8A 8B 8C 8D 8E 8F 8G 8H 13A 13B 13C 26A 26B 26C 26D 26E 26F 26G 26H 26I size 1 1 1 1 13 13 13 13 13 13 13 13 13 13 13 13 4 4 4 4 4 4 4 4 4 4 4 4 ρ1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 trivial ρ2 1 -1 -1 1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 linear of order 2 ρ3 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 linear of order 2 ρ4 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 2 ρ5 1 1 1 1 -1 -1 -1 -1 -i i i -i -i i i -i 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 4 ρ6 1 -1 -1 1 1 -1 -1 1 i i i -i -i -i -i i 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 linear of order 4 ρ7 1 -1 -1 1 1 -1 -1 1 -i -i -i i i i i -i 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 linear of order 4 ρ8 1 1 1 1 -1 -1 -1 -1 i -i -i i i -i -i i 1 1 1 1 1 1 1 1 1 1 1 1 linear of order 4 ρ9 1 1 -1 -1 -i -i i i ζ8 ζ83 ζ87 ζ8 ζ85 ζ87 ζ83 ζ85 1 1 1 -1 -1 -1 -1 -1 1 1 1 -1 linear of order 8 ρ10 1 -1 1 -1 i -i i -i ζ85 ζ83 ζ87 ζ8 ζ85 ζ83 ζ87 ζ8 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 linear of order 8 ρ11 1 1 -1 -1 i i -i -i ζ83 ζ8 ζ85 ζ83 ζ87 ζ85 ζ8 ζ87 1 1 1 -1 -1 -1 -1 -1 1 1 1 -1 linear of order 8 ρ12 1 -1 1 -1 -i i -i i ζ87 ζ8 ζ85 ζ83 ζ87 ζ8 ζ85 ζ83 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 linear of order 8 ρ13 1 1 -1 -1 -i -i i i ζ85 ζ87 ζ83 ζ85 ζ8 ζ83 ζ87 ζ8 1 1 1 -1 -1 -1 -1 -1 1 1 1 -1 linear of order 8 ρ14 1 -1 1 -1 i -i i -i ζ8 ζ87 ζ83 ζ85 ζ8 ζ87 ζ83 ζ85 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 linear of order 8 ρ15 1 -1 1 -1 -i i -i i ζ83 ζ85 ζ8 ζ87 ζ83 ζ85 ζ8 ζ87 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 linear of order 8 ρ16 1 1 -1 -1 i i -i -i ζ87 ζ85 ζ8 ζ87 ζ83 ζ8 ζ85 ζ83 1 1 1 -1 -1 -1 -1 -1 1 1 1 -1 linear of order 8 ρ17 4 -4 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ139+ζ137+ζ136+ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 ζ1312+ζ138+ζ135+ζ13 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 ζ1311+ζ1310+ζ133+ζ132 orthogonal lifted from C2×C13⋊C4 ρ18 4 -4 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ1311+ζ1310+ζ133+ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 ζ139+ζ137+ζ136+ζ134 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 ζ1312+ζ138+ζ135+ζ13 orthogonal lifted from C2×C13⋊C4 ρ19 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1311+ζ1310+ζ133+ζ132 orthogonal lifted from C13⋊C4 ρ20 4 -4 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1312+ζ138+ζ135+ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 ζ1311+ζ1310+ζ133+ζ132 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 ζ139+ζ137+ζ136+ζ134 orthogonal lifted from C2×C13⋊C4 ρ21 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ139+ζ137+ζ136+ζ134 orthogonal lifted from C13⋊C4 ρ22 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ1312+ζ138+ζ135+ζ13 orthogonal lifted from C13⋊C4 ρ23 4 4 -4 -4 0 0 0 0 0 0 0 0 0 0 0 0 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 -ζ1312-ζ138-ζ135-ζ13 symplectic lifted from C13⋊C8, Schur index 2 ρ24 4 -4 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 -ζ1312-ζ138-ζ135-ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ139-ζ137-ζ136-ζ134 symplectic lifted from C13⋊C8, Schur index 2 ρ25 4 4 -4 -4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 -ζ139-ζ137-ζ136-ζ134 symplectic lifted from C13⋊C8, Schur index 2 ρ26 4 4 -4 -4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 -ζ1311-ζ1310-ζ133-ζ132 symplectic lifted from C13⋊C8, Schur index 2 ρ27 4 -4 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 -ζ1311-ζ1310-ζ133-ζ132 ζ139+ζ137+ζ136+ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ139-ζ137-ζ136-ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ1312-ζ138-ζ135-ζ13 symplectic lifted from C13⋊C8, Schur index 2 ρ28 4 -4 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 -ζ139-ζ137-ζ136-ζ134 ζ1312+ζ138+ζ135+ζ13 ζ1311+ζ1310+ζ133+ζ132 ζ139+ζ137+ζ136+ζ134 -ζ1312-ζ138-ζ135-ζ13 -ζ1312-ζ138-ζ135-ζ13 -ζ1311-ζ1310-ζ133-ζ132 -ζ139-ζ137-ζ136-ζ134 -ζ1311-ζ1310-ζ133-ζ132 symplectic lifted from C13⋊C8, Schur index 2

Smallest permutation representation of C2×C13⋊C8
Regular action on 208 points
Generators in S208
(1 66)(2 67)(3 68)(4 69)(5 70)(6 71)(7 72)(8 73)(9 74)(10 75)(11 76)(12 77)(13 78)(14 53)(15 54)(16 55)(17 56)(18 57)(19 58)(20 59)(21 60)(22 61)(23 62)(24 63)(25 64)(26 65)(27 92)(28 93)(29 94)(30 95)(31 96)(32 97)(33 98)(34 99)(35 100)(36 101)(37 102)(38 103)(39 104)(40 85)(41 86)(42 87)(43 88)(44 89)(45 90)(46 91)(47 79)(48 80)(49 81)(50 82)(51 83)(52 84)(105 170)(106 171)(107 172)(108 173)(109 174)(110 175)(111 176)(112 177)(113 178)(114 179)(115 180)(116 181)(117 182)(118 163)(119 164)(120 165)(121 166)(122 167)(123 168)(124 169)(125 157)(126 158)(127 159)(128 160)(129 161)(130 162)(131 208)(132 196)(133 197)(134 198)(135 199)(136 200)(137 201)(138 202)(139 203)(140 204)(141 205)(142 206)(143 207)(144 191)(145 192)(146 193)(147 194)(148 195)(149 183)(150 184)(151 185)(152 186)(153 187)(154 188)(155 189)(156 190)
(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)(157 158 159 160 161 162 163 164 165 166 167 168 169)(170 171 172 173 174 175 176 177 178 179 180 181 182)(183 184 185 186 187 188 189 190 191 192 193 194 195)(196 197 198 199 200 201 202 203 204 205 206 207 208)
(1 155 44 128 14 134 32 110)(2 150 43 120 15 142 31 115)(3 145 42 125 16 137 30 107)(4 153 41 130 17 132 29 112)(5 148 40 122 18 140 28 117)(6 156 52 127 19 135 27 109)(7 151 51 119 20 143 39 114)(8 146 50 124 21 138 38 106)(9 154 49 129 22 133 37 111)(10 149 48 121 23 141 36 116)(11 144 47 126 24 136 35 108)(12 152 46 118 25 131 34 113)(13 147 45 123 26 139 33 105)(53 198 97 175 66 189 89 160)(54 206 96 180 67 184 88 165)(55 201 95 172 68 192 87 157)(56 196 94 177 69 187 86 162)(57 204 93 182 70 195 85 167)(58 199 92 174 71 190 84 159)(59 207 104 179 72 185 83 164)(60 202 103 171 73 193 82 169)(61 197 102 176 74 188 81 161)(62 205 101 181 75 183 80 166)(63 200 100 173 76 191 79 158)(64 208 99 178 77 186 91 163)(65 203 98 170 78 194 90 168)

G:=sub<Sym(208)| (1,66)(2,67)(3,68)(4,69)(5,70)(6,71)(7,72)(8,73)(9,74)(10,75)(11,76)(12,77)(13,78)(14,53)(15,54)(16,55)(17,56)(18,57)(19,58)(20,59)(21,60)(22,61)(23,62)(24,63)(25,64)(26,65)(27,92)(28,93)(29,94)(30,95)(31,96)(32,97)(33,98)(34,99)(35,100)(36,101)(37,102)(38,103)(39,104)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)(116,181)(117,182)(118,163)(119,164)(120,165)(121,166)(122,167)(123,168)(124,169)(125,157)(126,158)(127,159)(128,160)(129,161)(130,162)(131,208)(132,196)(133,197)(134,198)(135,199)(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,191)(145,192)(146,193)(147,194)(148,195)(149,183)(150,184)(151,185)(152,186)(153,187)(154,188)(155,189)(156,190), (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)(157,158,159,160,161,162,163,164,165,166,167,168,169)(170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195)(196,197,198,199,200,201,202,203,204,205,206,207,208), (1,155,44,128,14,134,32,110)(2,150,43,120,15,142,31,115)(3,145,42,125,16,137,30,107)(4,153,41,130,17,132,29,112)(5,148,40,122,18,140,28,117)(6,156,52,127,19,135,27,109)(7,151,51,119,20,143,39,114)(8,146,50,124,21,138,38,106)(9,154,49,129,22,133,37,111)(10,149,48,121,23,141,36,116)(11,144,47,126,24,136,35,108)(12,152,46,118,25,131,34,113)(13,147,45,123,26,139,33,105)(53,198,97,175,66,189,89,160)(54,206,96,180,67,184,88,165)(55,201,95,172,68,192,87,157)(56,196,94,177,69,187,86,162)(57,204,93,182,70,195,85,167)(58,199,92,174,71,190,84,159)(59,207,104,179,72,185,83,164)(60,202,103,171,73,193,82,169)(61,197,102,176,74,188,81,161)(62,205,101,181,75,183,80,166)(63,200,100,173,76,191,79,158)(64,208,99,178,77,186,91,163)(65,203,98,170,78,194,90,168)>;

G:=Group( (1,66)(2,67)(3,68)(4,69)(5,70)(6,71)(7,72)(8,73)(9,74)(10,75)(11,76)(12,77)(13,78)(14,53)(15,54)(16,55)(17,56)(18,57)(19,58)(20,59)(21,60)(22,61)(23,62)(24,63)(25,64)(26,65)(27,92)(28,93)(29,94)(30,95)(31,96)(32,97)(33,98)(34,99)(35,100)(36,101)(37,102)(38,103)(39,104)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)(116,181)(117,182)(118,163)(119,164)(120,165)(121,166)(122,167)(123,168)(124,169)(125,157)(126,158)(127,159)(128,160)(129,161)(130,162)(131,208)(132,196)(133,197)(134,198)(135,199)(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,191)(145,192)(146,193)(147,194)(148,195)(149,183)(150,184)(151,185)(152,186)(153,187)(154,188)(155,189)(156,190), (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)(157,158,159,160,161,162,163,164,165,166,167,168,169)(170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195)(196,197,198,199,200,201,202,203,204,205,206,207,208), (1,155,44,128,14,134,32,110)(2,150,43,120,15,142,31,115)(3,145,42,125,16,137,30,107)(4,153,41,130,17,132,29,112)(5,148,40,122,18,140,28,117)(6,156,52,127,19,135,27,109)(7,151,51,119,20,143,39,114)(8,146,50,124,21,138,38,106)(9,154,49,129,22,133,37,111)(10,149,48,121,23,141,36,116)(11,144,47,126,24,136,35,108)(12,152,46,118,25,131,34,113)(13,147,45,123,26,139,33,105)(53,198,97,175,66,189,89,160)(54,206,96,180,67,184,88,165)(55,201,95,172,68,192,87,157)(56,196,94,177,69,187,86,162)(57,204,93,182,70,195,85,167)(58,199,92,174,71,190,84,159)(59,207,104,179,72,185,83,164)(60,202,103,171,73,193,82,169)(61,197,102,176,74,188,81,161)(62,205,101,181,75,183,80,166)(63,200,100,173,76,191,79,158)(64,208,99,178,77,186,91,163)(65,203,98,170,78,194,90,168) );

G=PermutationGroup([[(1,66),(2,67),(3,68),(4,69),(5,70),(6,71),(7,72),(8,73),(9,74),(10,75),(11,76),(12,77),(13,78),(14,53),(15,54),(16,55),(17,56),(18,57),(19,58),(20,59),(21,60),(22,61),(23,62),(24,63),(25,64),(26,65),(27,92),(28,93),(29,94),(30,95),(31,96),(32,97),(33,98),(34,99),(35,100),(36,101),(37,102),(38,103),(39,104),(40,85),(41,86),(42,87),(43,88),(44,89),(45,90),(46,91),(47,79),(48,80),(49,81),(50,82),(51,83),(52,84),(105,170),(106,171),(107,172),(108,173),(109,174),(110,175),(111,176),(112,177),(113,178),(114,179),(115,180),(116,181),(117,182),(118,163),(119,164),(120,165),(121,166),(122,167),(123,168),(124,169),(125,157),(126,158),(127,159),(128,160),(129,161),(130,162),(131,208),(132,196),(133,197),(134,198),(135,199),(136,200),(137,201),(138,202),(139,203),(140,204),(141,205),(142,206),(143,207),(144,191),(145,192),(146,193),(147,194),(148,195),(149,183),(150,184),(151,185),(152,186),(153,187),(154,188),(155,189),(156,190)], [(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),(157,158,159,160,161,162,163,164,165,166,167,168,169),(170,171,172,173,174,175,176,177,178,179,180,181,182),(183,184,185,186,187,188,189,190,191,192,193,194,195),(196,197,198,199,200,201,202,203,204,205,206,207,208)], [(1,155,44,128,14,134,32,110),(2,150,43,120,15,142,31,115),(3,145,42,125,16,137,30,107),(4,153,41,130,17,132,29,112),(5,148,40,122,18,140,28,117),(6,156,52,127,19,135,27,109),(7,151,51,119,20,143,39,114),(8,146,50,124,21,138,38,106),(9,154,49,129,22,133,37,111),(10,149,48,121,23,141,36,116),(11,144,47,126,24,136,35,108),(12,152,46,118,25,131,34,113),(13,147,45,123,26,139,33,105),(53,198,97,175,66,189,89,160),(54,206,96,180,67,184,88,165),(55,201,95,172,68,192,87,157),(56,196,94,177,69,187,86,162),(57,204,93,182,70,195,85,167),(58,199,92,174,71,190,84,159),(59,207,104,179,72,185,83,164),(60,202,103,171,73,193,82,169),(61,197,102,176,74,188,81,161),(62,205,101,181,75,183,80,166),(63,200,100,173,76,191,79,158),(64,208,99,178,77,186,91,163),(65,203,98,170,78,194,90,168)]])

C2×C13⋊C8 is a maximal subgroup of   C52⋊C8  C26.C42  D26⋊C8  Dic13⋊C8  C26.M4(2)  Dic26.C4
C2×C13⋊C8 is a maximal quotient of   C52.C8  C52⋊C8  C26.M4(2)

Matrix representation of C2×C13⋊C8 in GL6(𝔽313)

 1 0 0 0 0 0 0 312 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 241 210 241 312 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
,
 125 0 0 0 0 0 0 312 0 0 0 0 0 0 44 82 216 127 0 0 270 77 171 235 0 0 114 164 131 285 0 0 164 100 280 61

G:=sub<GL(6,GF(313))| [1,0,0,0,0,0,0,312,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,241,1,0,0,0,0,210,0,1,0,0,0,241,0,0,1,0,0,312,0,0,0],[125,0,0,0,0,0,0,312,0,0,0,0,0,0,44,270,114,164,0,0,82,77,164,100,0,0,216,171,131,280,0,0,127,235,285,61] >;

C2×C13⋊C8 in GAP, Magma, Sage, TeX

C_2\times C_{13}\rtimes C_8
% in TeX

G:=Group("C2xC13:C8");
// GroupNames label

G:=SmallGroup(208,32);
// by ID

G=gap.SmallGroup(208,32);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-13,20,42,3204,1214]);
// Polycyclic

G:=Group<a,b,c|a^2=b^13=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^5>;
// generators/relations

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