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G = C292C8order 232 = 23·29

The semidirect product of C29 and C8 acting via C8/C4=C2

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

Aliases: C292C8, C58.2C4, C4.2D29, C2.Dic29, C116.2C2, SmallGroup(232,1)

Series: Derived Chief Lower central Upper central

C1C29 — C292C8
C1C29C58C116 — C292C8
C29 — C292C8
C1C4

Generators and relations for C292C8
 G = < a,b | a29=b8=1, bab-1=a-1 >

29C8

Smallest permutation representation of C292C8
Regular action on 232 points
Generators in S232
(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)(204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232)
(1 204 112 146 53 175 81 117)(2 232 113 174 54 203 82 145)(3 231 114 173 55 202 83 144)(4 230 115 172 56 201 84 143)(5 229 116 171 57 200 85 142)(6 228 88 170 58 199 86 141)(7 227 89 169 30 198 87 140)(8 226 90 168 31 197 59 139)(9 225 91 167 32 196 60 138)(10 224 92 166 33 195 61 137)(11 223 93 165 34 194 62 136)(12 222 94 164 35 193 63 135)(13 221 95 163 36 192 64 134)(14 220 96 162 37 191 65 133)(15 219 97 161 38 190 66 132)(16 218 98 160 39 189 67 131)(17 217 99 159 40 188 68 130)(18 216 100 158 41 187 69 129)(19 215 101 157 42 186 70 128)(20 214 102 156 43 185 71 127)(21 213 103 155 44 184 72 126)(22 212 104 154 45 183 73 125)(23 211 105 153 46 182 74 124)(24 210 106 152 47 181 75 123)(25 209 107 151 48 180 76 122)(26 208 108 150 49 179 77 121)(27 207 109 149 50 178 78 120)(28 206 110 148 51 177 79 119)(29 205 111 147 52 176 80 118)

G:=sub<Sym(232)| (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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,204,112,146,53,175,81,117)(2,232,113,174,54,203,82,145)(3,231,114,173,55,202,83,144)(4,230,115,172,56,201,84,143)(5,229,116,171,57,200,85,142)(6,228,88,170,58,199,86,141)(7,227,89,169,30,198,87,140)(8,226,90,168,31,197,59,139)(9,225,91,167,32,196,60,138)(10,224,92,166,33,195,61,137)(11,223,93,165,34,194,62,136)(12,222,94,164,35,193,63,135)(13,221,95,163,36,192,64,134)(14,220,96,162,37,191,65,133)(15,219,97,161,38,190,66,132)(16,218,98,160,39,189,67,131)(17,217,99,159,40,188,68,130)(18,216,100,158,41,187,69,129)(19,215,101,157,42,186,70,128)(20,214,102,156,43,185,71,127)(21,213,103,155,44,184,72,126)(22,212,104,154,45,183,73,125)(23,211,105,153,46,182,74,124)(24,210,106,152,47,181,75,123)(25,209,107,151,48,180,76,122)(26,208,108,150,49,179,77,121)(27,207,109,149,50,178,78,120)(28,206,110,148,51,177,79,119)(29,205,111,147,52,176,80,118)>;

G:=Group( (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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,204,112,146,53,175,81,117)(2,232,113,174,54,203,82,145)(3,231,114,173,55,202,83,144)(4,230,115,172,56,201,84,143)(5,229,116,171,57,200,85,142)(6,228,88,170,58,199,86,141)(7,227,89,169,30,198,87,140)(8,226,90,168,31,197,59,139)(9,225,91,167,32,196,60,138)(10,224,92,166,33,195,61,137)(11,223,93,165,34,194,62,136)(12,222,94,164,35,193,63,135)(13,221,95,163,36,192,64,134)(14,220,96,162,37,191,65,133)(15,219,97,161,38,190,66,132)(16,218,98,160,39,189,67,131)(17,217,99,159,40,188,68,130)(18,216,100,158,41,187,69,129)(19,215,101,157,42,186,70,128)(20,214,102,156,43,185,71,127)(21,213,103,155,44,184,72,126)(22,212,104,154,45,183,73,125)(23,211,105,153,46,182,74,124)(24,210,106,152,47,181,75,123)(25,209,107,151,48,180,76,122)(26,208,108,150,49,179,77,121)(27,207,109,149,50,178,78,120)(28,206,110,148,51,177,79,119)(29,205,111,147,52,176,80,118) );

G=PermutationGroup([(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),(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)], [(1,204,112,146,53,175,81,117),(2,232,113,174,54,203,82,145),(3,231,114,173,55,202,83,144),(4,230,115,172,56,201,84,143),(5,229,116,171,57,200,85,142),(6,228,88,170,58,199,86,141),(7,227,89,169,30,198,87,140),(8,226,90,168,31,197,59,139),(9,225,91,167,32,196,60,138),(10,224,92,166,33,195,61,137),(11,223,93,165,34,194,62,136),(12,222,94,164,35,193,63,135),(13,221,95,163,36,192,64,134),(14,220,96,162,37,191,65,133),(15,219,97,161,38,190,66,132),(16,218,98,160,39,189,67,131),(17,217,99,159,40,188,68,130),(18,216,100,158,41,187,69,129),(19,215,101,157,42,186,70,128),(20,214,102,156,43,185,71,127),(21,213,103,155,44,184,72,126),(22,212,104,154,45,183,73,125),(23,211,105,153,46,182,74,124),(24,210,106,152,47,181,75,123),(25,209,107,151,48,180,76,122),(26,208,108,150,49,179,77,121),(27,207,109,149,50,178,78,120),(28,206,110,148,51,177,79,119),(29,205,111,147,52,176,80,118)])

C292C8 is a maximal subgroup of
C29⋊C16  C8×D29  C8⋊D29  C4.Dic29  D4⋊D29  D4.D29  Q8⋊D29  C29⋊Q16
C292C8 is a maximal quotient of
C292C16

64 conjugacy classes

class 1  2 4A4B8A8B8C8D29A···29N58A···58N116A···116AB
order1244888829···2958···58116···116
size1111292929292···22···22···2

64 irreducible representations

dim1111222
type+++-
imageC1C2C4C8D29Dic29C292C8
kernelC292C8C116C58C29C4C2C1
# reps1124141428

Matrix representation of C292C8 in GL3(𝔽233) generated by

100
02321
0112120
,
1200
0184106
014049
G:=sub<GL(3,GF(233))| [1,0,0,0,232,112,0,1,120],[12,0,0,0,184,140,0,106,49] >;

C292C8 in GAP, Magma, Sage, TeX

C_{29}\rtimes_2C_8
% in TeX

G:=Group("C29:2C8");
// GroupNames label

G:=SmallGroup(232,1);
// by ID

G=gap.SmallGroup(232,1);
# by ID

G:=PCGroup([4,-2,-2,-2,-29,8,21,3587]);
// Polycyclic

G:=Group<a,b|a^29=b^8=1,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of C292C8 in TeX

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