direct product, abelian, monomial, 3-elementary
Aliases: C3×C93, SmallGroup(279,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C3×C93 |
| C1 — C3×C93 |
| C1 — C3×C93 |
Generators and relations for C3×C93
G = < a,b | a3=b93=1, ab=ba >
Smallest permutation representation of C3×C93
►Regular action on 279 points
Generators in S279
(1 213 174)(2 214 175)(3 215 176)(4 216 177)(5 217 178)(6 218 179)(7 219 180)(8 220 181)(9 221 182)(10 222 183)(11 223 184)(12 224 185)(13 225 186)(14 226 94)(15 227 95)(16 228 96)(17 229 97)(18 230 98)(19 231 99)(20 232 100)(21 233 101)(22 234 102)(23 235 103)(24 236 104)(25 237 105)(26 238 106)(27 239 107)(28 240 108)(29 241 109)(30 242 110)(31 243 111)(32 244 112)(33 245 113)(34 246 114)(35 247 115)(36 248 116)(37 249 117)(38 250 118)(39 251 119)(40 252 120)(41 253 121)(42 254 122)(43 255 123)(44 256 124)(45 257 125)(46 258 126)(47 259 127)(48 260 128)(49 261 129)(50 262 130)(51 263 131)(52 264 132)(53 265 133)(54 266 134)(55 267 135)(56 268 136)(57 269 137)(58 270 138)(59 271 139)(60 272 140)(61 273 141)(62 274 142)(63 275 143)(64 276 144)(65 277 145)(66 278 146)(67 279 147)(68 187 148)(69 188 149)(70 189 150)(71 190 151)(72 191 152)(73 192 153)(74 193 154)(75 194 155)(76 195 156)(77 196 157)(78 197 158)(79 198 159)(80 199 160)(81 200 161)(82 201 162)(83 202 163)(84 203 164)(85 204 165)(86 205 166)(87 206 167)(88 207 168)(89 208 169)(90 209 170)(91 210 171)(92 211 172)(93 212 173)
(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)(187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279)
G:=sub<Sym(279)| (1,213,174)(2,214,175)(3,215,176)(4,216,177)(5,217,178)(6,218,179)(7,219,180)(8,220,181)(9,221,182)(10,222,183)(11,223,184)(12,224,185)(13,225,186)(14,226,94)(15,227,95)(16,228,96)(17,229,97)(18,230,98)(19,231,99)(20,232,100)(21,233,101)(22,234,102)(23,235,103)(24,236,104)(25,237,105)(26,238,106)(27,239,107)(28,240,108)(29,241,109)(30,242,110)(31,243,111)(32,244,112)(33,245,113)(34,246,114)(35,247,115)(36,248,116)(37,249,117)(38,250,118)(39,251,119)(40,252,120)(41,253,121)(42,254,122)(43,255,123)(44,256,124)(45,257,125)(46,258,126)(47,259,127)(48,260,128)(49,261,129)(50,262,130)(51,263,131)(52,264,132)(53,265,133)(54,266,134)(55,267,135)(56,268,136)(57,269,137)(58,270,138)(59,271,139)(60,272,140)(61,273,141)(62,274,142)(63,275,143)(64,276,144)(65,277,145)(66,278,146)(67,279,147)(68,187,148)(69,188,149)(70,189,150)(71,190,151)(72,191,152)(73,192,153)(74,193,154)(75,194,155)(76,195,156)(77,196,157)(78,197,158)(79,198,159)(80,199,160)(81,200,161)(82,201,162)(83,202,163)(84,203,164)(85,204,165)(86,205,166)(87,206,167)(88,207,168)(89,208,169)(90,209,170)(91,210,171)(92,211,172)(93,212,173), (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)(187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279)>;
G:=Group( (1,213,174)(2,214,175)(3,215,176)(4,216,177)(5,217,178)(6,218,179)(7,219,180)(8,220,181)(9,221,182)(10,222,183)(11,223,184)(12,224,185)(13,225,186)(14,226,94)(15,227,95)(16,228,96)(17,229,97)(18,230,98)(19,231,99)(20,232,100)(21,233,101)(22,234,102)(23,235,103)(24,236,104)(25,237,105)(26,238,106)(27,239,107)(28,240,108)(29,241,109)(30,242,110)(31,243,111)(32,244,112)(33,245,113)(34,246,114)(35,247,115)(36,248,116)(37,249,117)(38,250,118)(39,251,119)(40,252,120)(41,253,121)(42,254,122)(43,255,123)(44,256,124)(45,257,125)(46,258,126)(47,259,127)(48,260,128)(49,261,129)(50,262,130)(51,263,131)(52,264,132)(53,265,133)(54,266,134)(55,267,135)(56,268,136)(57,269,137)(58,270,138)(59,271,139)(60,272,140)(61,273,141)(62,274,142)(63,275,143)(64,276,144)(65,277,145)(66,278,146)(67,279,147)(68,187,148)(69,188,149)(70,189,150)(71,190,151)(72,191,152)(73,192,153)(74,193,154)(75,194,155)(76,195,156)(77,196,157)(78,197,158)(79,198,159)(80,199,160)(81,200,161)(82,201,162)(83,202,163)(84,203,164)(85,204,165)(86,205,166)(87,206,167)(88,207,168)(89,208,169)(90,209,170)(91,210,171)(92,211,172)(93,212,173), (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)(187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279) );
G=PermutationGroup([[(1,213,174),(2,214,175),(3,215,176),(4,216,177),(5,217,178),(6,218,179),(7,219,180),(8,220,181),(9,221,182),(10,222,183),(11,223,184),(12,224,185),(13,225,186),(14,226,94),(15,227,95),(16,228,96),(17,229,97),(18,230,98),(19,231,99),(20,232,100),(21,233,101),(22,234,102),(23,235,103),(24,236,104),(25,237,105),(26,238,106),(27,239,107),(28,240,108),(29,241,109),(30,242,110),(31,243,111),(32,244,112),(33,245,113),(34,246,114),(35,247,115),(36,248,116),(37,249,117),(38,250,118),(39,251,119),(40,252,120),(41,253,121),(42,254,122),(43,255,123),(44,256,124),(45,257,125),(46,258,126),(47,259,127),(48,260,128),(49,261,129),(50,262,130),(51,263,131),(52,264,132),(53,265,133),(54,266,134),(55,267,135),(56,268,136),(57,269,137),(58,270,138),(59,271,139),(60,272,140),(61,273,141),(62,274,142),(63,275,143),(64,276,144),(65,277,145),(66,278,146),(67,279,147),(68,187,148),(69,188,149),(70,189,150),(71,190,151),(72,191,152),(73,192,153),(74,193,154),(75,194,155),(76,195,156),(77,196,157),(78,197,158),(79,198,159),(80,199,160),(81,200,161),(82,201,162),(83,202,163),(84,203,164),(85,204,165),(86,205,166),(87,206,167),(88,207,168),(89,208,169),(90,209,170),(91,210,171),(92,211,172),(93,212,173)], [(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),(187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279)]])
279 conjugacy classes
| class | 1 | 3A | ··· | 3H | 31A | ··· | 31AD | 93A | ··· | 93IF |
| order | 1 | 3 | ··· | 3 | 31 | ··· | 31 | 93 | ··· | 93 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
279 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C31 | C93 |
| kernel | C3×C93 | C93 | C32 | C3 |
| # reps | 1 | 8 | 30 | 240 |
Matrix representation of C3×C93 ►in GL2(𝔽373) generated by
| 284 | 0 |
| 0 | 1 |
| 283 | 0 |
| 0 | 16 |
G:=sub<GL(2,GF(373))| [284,0,0,1],[283,0,0,16] >;
C3×C93 in GAP, Magma, Sage, TeX
C_3\times C_{93} % in TeX
G:=Group("C3xC93"); // GroupNames label
G:=SmallGroup(279,4);
// by ID
G=gap.SmallGroup(279,4);
# by ID
G:=PCGroup([3,-3,-3,-31]);
// Polycyclic
G:=Group<a,b|a^3=b^93=1,a*b=b*a>;
// generators/relations
Export