metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C29⋊C8, C58.C4, Dic29.2C2, C2.(C29⋊C4), SmallGroup(232,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C29⋊C8 |
Generators and relations for C29⋊C8
G = < a,b | a29=b8=1, bab-1=a17 >
Character table of C29⋊C8
| class | 1 | 2 | 4A | 4B | 8A | 8B | 8C | 8D | 29A | 29B | 29C | 29D | 29E | 29F | 29G | 58A | 58B | 58C | 58D | 58E | 58F | 58G | |
| size | 1 | 1 | 29 | 29 | 29 | 29 | 29 | 29 | 4 | 4 | 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 | trivial |
| ρ2 | 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 | i | -i | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ4 | 1 | 1 | -1 | -1 | -i | i | -i | i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ5 | 1 | -1 | -i | i | ζ8 | ζ83 | ζ85 | ζ87 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ6 | 1 | -1 | i | -i | ζ83 | ζ8 | ζ87 | ζ85 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ7 | 1 | -1 | i | -i | ζ87 | ζ85 | ζ83 | ζ8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ8 | 1 | -1 | -i | i | ζ85 | ζ87 | ζ8 | ζ83 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ9 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | ζ2927+ζ2924+ζ295+ζ292 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | orthogonal lifted from C29⋊C4 |
| ρ10 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | orthogonal lifted from C29⋊C4 |
| ρ11 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | ζ2921+ζ2920+ζ299+ζ298 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | orthogonal lifted from C29⋊C4 |
| ρ12 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | orthogonal lifted from C29⋊C4 |
| ρ13 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | orthogonal lifted from C29⋊C4 |
| ρ14 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | ζ2926+ζ2922+ζ297+ζ293 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | orthogonal lifted from C29⋊C4 |
| ρ15 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | orthogonal lifted from C29⋊C4 |
| ρ16 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | -ζ2918-ζ2916-ζ2913-ζ2911 | -ζ2928-ζ2917-ζ2912-ζ29 | -ζ2927-ζ2924-ζ295-ζ292 | -ζ2926-ζ2922-ζ297-ζ293 | -ζ2925-ζ2919-ζ2910-ζ294 | -ζ2923-ζ2915-ζ2914-ζ296 | -ζ2921-ζ2920-ζ299-ζ298 | symplectic faithful, Schur index 2 |
| ρ17 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | -ζ2927-ζ2924-ζ295-ζ292 | -ζ2918-ζ2916-ζ2913-ζ2911 | -ζ2926-ζ2922-ζ297-ζ293 | -ζ2925-ζ2919-ζ2910-ζ294 | -ζ2923-ζ2915-ζ2914-ζ296 | -ζ2921-ζ2920-ζ299-ζ298 | -ζ2928-ζ2917-ζ2912-ζ29 | symplectic faithful, Schur index 2 |
| ρ18 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | -ζ2923-ζ2915-ζ2914-ζ296 | -ζ2925-ζ2919-ζ2910-ζ294 | -ζ2921-ζ2920-ζ299-ζ298 | -ζ2928-ζ2917-ζ2912-ζ29 | -ζ2918-ζ2916-ζ2913-ζ2911 | -ζ2927-ζ2924-ζ295-ζ292 | -ζ2926-ζ2922-ζ297-ζ293 | symplectic faithful, Schur index 2 |
| ρ19 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | -ζ2928-ζ2917-ζ2912-ζ29 | -ζ2921-ζ2920-ζ299-ζ298 | -ζ2918-ζ2916-ζ2913-ζ2911 | -ζ2927-ζ2924-ζ295-ζ292 | -ζ2926-ζ2922-ζ297-ζ293 | -ζ2925-ζ2919-ζ2910-ζ294 | -ζ2923-ζ2915-ζ2914-ζ296 | symplectic faithful, Schur index 2 |
| ρ20 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | -ζ2926-ζ2922-ζ297-ζ293 | -ζ2927-ζ2924-ζ295-ζ292 | -ζ2925-ζ2919-ζ2910-ζ294 | -ζ2923-ζ2915-ζ2914-ζ296 | -ζ2921-ζ2920-ζ299-ζ298 | -ζ2928-ζ2917-ζ2912-ζ29 | -ζ2918-ζ2916-ζ2913-ζ2911 | symplectic faithful, Schur index 2 |
| ρ21 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | -ζ2921-ζ2920-ζ299-ζ298 | -ζ2923-ζ2915-ζ2914-ζ296 | -ζ2928-ζ2917-ζ2912-ζ29 | -ζ2918-ζ2916-ζ2913-ζ2911 | -ζ2927-ζ2924-ζ295-ζ292 | -ζ2926-ζ2922-ζ297-ζ293 | -ζ2925-ζ2919-ζ2910-ζ294 | symplectic faithful, Schur index 2 |
| ρ22 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | -ζ2925-ζ2919-ζ2910-ζ294 | -ζ2926-ζ2922-ζ297-ζ293 | -ζ2923-ζ2915-ζ2914-ζ296 | -ζ2921-ζ2920-ζ299-ζ298 | -ζ2928-ζ2917-ζ2912-ζ29 | -ζ2918-ζ2916-ζ2913-ζ2911 | -ζ2927-ζ2924-ζ295-ζ292 | symplectic faithful, Schur index 2 |
►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)
(1 231 88 154 58 199 59 141)(2 214 116 171 30 182 87 129)(3 226 115 159 31 194 86 117)(4 209 114 147 32 177 85 134)(5 221 113 164 33 189 84 122)(6 204 112 152 34 201 83 139)(7 216 111 169 35 184 82 127)(8 228 110 157 36 196 81 144)(9 211 109 174 37 179 80 132)(10 223 108 162 38 191 79 120)(11 206 107 150 39 203 78 137)(12 218 106 167 40 186 77 125)(13 230 105 155 41 198 76 142)(14 213 104 172 42 181 75 130)(15 225 103 160 43 193 74 118)(16 208 102 148 44 176 73 135)(17 220 101 165 45 188 72 123)(18 232 100 153 46 200 71 140)(19 215 99 170 47 183 70 128)(20 227 98 158 48 195 69 145)(21 210 97 146 49 178 68 133)(22 222 96 163 50 190 67 121)(23 205 95 151 51 202 66 138)(24 217 94 168 52 185 65 126)(25 229 93 156 53 197 64 143)(26 212 92 173 54 180 63 131)(27 224 91 161 55 192 62 119)(28 207 90 149 56 175 61 136)(29 219 89 166 57 187 60 124)
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), (1,231,88,154,58,199,59,141)(2,214,116,171,30,182,87,129)(3,226,115,159,31,194,86,117)(4,209,114,147,32,177,85,134)(5,221,113,164,33,189,84,122)(6,204,112,152,34,201,83,139)(7,216,111,169,35,184,82,127)(8,228,110,157,36,196,81,144)(9,211,109,174,37,179,80,132)(10,223,108,162,38,191,79,120)(11,206,107,150,39,203,78,137)(12,218,106,167,40,186,77,125)(13,230,105,155,41,198,76,142)(14,213,104,172,42,181,75,130)(15,225,103,160,43,193,74,118)(16,208,102,148,44,176,73,135)(17,220,101,165,45,188,72,123)(18,232,100,153,46,200,71,140)(19,215,99,170,47,183,70,128)(20,227,98,158,48,195,69,145)(21,210,97,146,49,178,68,133)(22,222,96,163,50,190,67,121)(23,205,95,151,51,202,66,138)(24,217,94,168,52,185,65,126)(25,229,93,156,53,197,64,143)(26,212,92,173,54,180,63,131)(27,224,91,161,55,192,62,119)(28,207,90,149,56,175,61,136)(29,219,89,166,57,187,60,124)>;
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), (1,231,88,154,58,199,59,141)(2,214,116,171,30,182,87,129)(3,226,115,159,31,194,86,117)(4,209,114,147,32,177,85,134)(5,221,113,164,33,189,84,122)(6,204,112,152,34,201,83,139)(7,216,111,169,35,184,82,127)(8,228,110,157,36,196,81,144)(9,211,109,174,37,179,80,132)(10,223,108,162,38,191,79,120)(11,206,107,150,39,203,78,137)(12,218,106,167,40,186,77,125)(13,230,105,155,41,198,76,142)(14,213,104,172,42,181,75,130)(15,225,103,160,43,193,74,118)(16,208,102,148,44,176,73,135)(17,220,101,165,45,188,72,123)(18,232,100,153,46,200,71,140)(19,215,99,170,47,183,70,128)(20,227,98,158,48,195,69,145)(21,210,97,146,49,178,68,133)(22,222,96,163,50,190,67,121)(23,205,95,151,51,202,66,138)(24,217,94,168,52,185,65,126)(25,229,93,156,53,197,64,143)(26,212,92,173,54,180,63,131)(27,224,91,161,55,192,62,119)(28,207,90,149,56,175,61,136)(29,219,89,166,57,187,60,124) );
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)], [(1,231,88,154,58,199,59,141),(2,214,116,171,30,182,87,129),(3,226,115,159,31,194,86,117),(4,209,114,147,32,177,85,134),(5,221,113,164,33,189,84,122),(6,204,112,152,34,201,83,139),(7,216,111,169,35,184,82,127),(8,228,110,157,36,196,81,144),(9,211,109,174,37,179,80,132),(10,223,108,162,38,191,79,120),(11,206,107,150,39,203,78,137),(12,218,106,167,40,186,77,125),(13,230,105,155,41,198,76,142),(14,213,104,172,42,181,75,130),(15,225,103,160,43,193,74,118),(16,208,102,148,44,176,73,135),(17,220,101,165,45,188,72,123),(18,232,100,153,46,200,71,140),(19,215,99,170,47,183,70,128),(20,227,98,158,48,195,69,145),(21,210,97,146,49,178,68,133),(22,222,96,163,50,190,67,121),(23,205,95,151,51,202,66,138),(24,217,94,168,52,185,65,126),(25,229,93,156,53,197,64,143),(26,212,92,173,54,180,63,131),(27,224,91,161,55,192,62,119),(28,207,90,149,56,175,61,136),(29,219,89,166,57,187,60,124)]])
C29⋊C8 is a maximal subgroup of
D29⋊C8 C116.C4 C29⋊M4(2)
C29⋊C8 is a maximal quotient of C29⋊C16
Matrix representation of C29⋊C8 ►in GL5(𝔽233)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 232 | 1 | 0 | 0 |
| 0 | 232 | 0 | 1 | 0 |
| 0 | 232 | 0 | 0 | 1 |
| 0 | 84 | 219 | 14 | 148 |
| 136 | 0 | 0 | 0 | 0 |
| 0 | 196 | 149 | 169 | 81 |
| 0 | 110 | 205 | 10 | 2 |
| 0 | 163 | 228 | 19 | 124 |
| 0 | 53 | 204 | 1 | 46 |
G:=sub<GL(5,GF(233))| [1,0,0,0,0,0,232,232,232,84,0,1,0,0,219,0,0,1,0,14,0,0,0,1,148],[136,0,0,0,0,0,196,110,163,53,0,149,205,228,204,0,169,10,19,1,0,81,2,124,46] >;
C29⋊C8 in GAP, Magma, Sage, TeX
C_{29}\rtimes C_8 % in TeX
G:=Group("C29:C8"); // GroupNames label
G:=SmallGroup(232,3);
// by ID
G=gap.SmallGroup(232,3);
# by ID
G:=PCGroup([4,-2,-2,-2,-29,8,21,1539,1799]);
// Polycyclic
G:=Group<a,b|a^29=b^8=1,b*a*b^-1=a^17>;
// generators/relations
Export
Subgroup lattice of C29⋊C8 in TeX
Character table of C29⋊C8 in TeX