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G = C132C16order 208 = 24·13

The semidirect product of C13 and C16 acting via C16/C8=C2

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C132C16, C26.2C8, C52.5C4, C8.2D13, C104.2C2, C4.2Dic13, C2.(C132C8), SmallGroup(208,1)

Series: Derived Chief Lower central Upper central

C1C13 — C132C16
C1C13C26C52C104 — C132C16
C13 — C132C16
C1C8

Generators and relations for C132C16
 G = < a,b | a13=b16=1, bab-1=a-1 >

13C16

Smallest permutation representation of C132C16
Regular action on 208 points
Generators in S208
(1 83 198 189 108 159 127 37 67 138 25 60 174)(2 175 61 26 139 68 38 128 160 109 190 199 84)(3 85 200 191 110 145 113 39 69 140 27 62 176)(4 161 63 28 141 70 40 114 146 111 192 201 86)(5 87 202 177 112 147 115 41 71 142 29 64 162)(6 163 49 30 143 72 42 116 148 97 178 203 88)(7 89 204 179 98 149 117 43 73 144 31 50 164)(8 165 51 32 129 74 44 118 150 99 180 205 90)(9 91 206 181 100 151 119 45 75 130 17 52 166)(10 167 53 18 131 76 46 120 152 101 182 207 92)(11 93 208 183 102 153 121 47 77 132 19 54 168)(12 169 55 20 133 78 48 122 154 103 184 193 94)(13 95 194 185 104 155 123 33 79 134 21 56 170)(14 171 57 22 135 80 34 124 156 105 186 195 96)(15 81 196 187 106 157 125 35 65 136 23 58 172)(16 173 59 24 137 66 36 126 158 107 188 197 82)
(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)

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

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

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

C132C16 is a maximal subgroup of
C13⋊C32  C16×D13  C208⋊C2  C52.4C8  C13⋊D16  D8.D13  C8.6D26  C13⋊Q32
C132C16 is a maximal quotient of
C132C32

64 conjugacy classes

class 1  2 4A4B8A8B8C8D13A···13F16A···16H26A···26F52A···52L104A···104X
order1244888813···1316···1626···2652···52104···104
size111111112···213···132···22···22···2

64 irreducible representations

dim111112222
type+++-
imageC1C2C4C8C16D13Dic13C132C8C132C16
kernelC132C16C104C52C26C13C8C4C2C1
# reps11248661224

Matrix representation of C132C16 in GL2(𝔽1249) generated by

01
1248417
,
641172
3821185
G:=sub<GL(2,GF(1249))| [0,1248,1,417],[64,382,1172,1185] >;

C132C16 in GAP, Magma, Sage, TeX

C_{13}\rtimes_2C_{16}
% in TeX

G:=Group("C13:2C16");
// GroupNames label

G:=SmallGroup(208,1);
// by ID

G=gap.SmallGroup(208,1);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-13,10,26,42,4804]);
// Polycyclic

G:=Group<a,b|a^13=b^16=1,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of C132C16 in TeX

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