direct product, abelian, monomial, 2-elementary
Aliases: C2×C148, SmallGroup(296,9)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C2×C148 |
| C1 — C2×C148 |
| C1 — C2×C148 |
Generators and relations for C2×C148
G = < a,b | a2=b148=1, ab=ba >
Smallest permutation representation of C2×C148
►Regular action on 296 points
Generators in S296
(1 253)(2 254)(3 255)(4 256)(5 257)(6 258)(7 259)(8 260)(9 261)(10 262)(11 263)(12 264)(13 265)(14 266)(15 267)(16 268)(17 269)(18 270)(19 271)(20 272)(21 273)(22 274)(23 275)(24 276)(25 277)(26 278)(27 279)(28 280)(29 281)(30 282)(31 283)(32 284)(33 285)(34 286)(35 287)(36 288)(37 289)(38 290)(39 291)(40 292)(41 293)(42 294)(43 295)(44 296)(45 149)(46 150)(47 151)(48 152)(49 153)(50 154)(51 155)(52 156)(53 157)(54 158)(55 159)(56 160)(57 161)(58 162)(59 163)(60 164)(61 165)(62 166)(63 167)(64 168)(65 169)(66 170)(67 171)(68 172)(69 173)(70 174)(71 175)(72 176)(73 177)(74 178)(75 179)(76 180)(77 181)(78 182)(79 183)(80 184)(81 185)(82 186)(83 187)(84 188)(85 189)(86 190)(87 191)(88 192)(89 193)(90 194)(91 195)(92 196)(93 197)(94 198)(95 199)(96 200)(97 201)(98 202)(99 203)(100 204)(101 205)(102 206)(103 207)(104 208)(105 209)(106 210)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)(113 217)(114 218)(115 219)(116 220)(117 221)(118 222)(119 223)(120 224)(121 225)(122 226)(123 227)(124 228)(125 229)(126 230)(127 231)(128 232)(129 233)(130 234)(131 235)(132 236)(133 237)(134 238)(135 239)(136 240)(137 241)(138 242)(139 243)(140 244)(141 245)(142 246)(143 247)(144 248)(145 249)(146 250)(147 251)(148 252)
(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)(149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296)
G:=sub<Sym(296)| (1,253)(2,254)(3,255)(4,256)(5,257)(6,258)(7,259)(8,260)(9,261)(10,262)(11,263)(12,264)(13,265)(14,266)(15,267)(16,268)(17,269)(18,270)(19,271)(20,272)(21,273)(22,274)(23,275)(24,276)(25,277)(26,278)(27,279)(28,280)(29,281)(30,282)(31,283)(32,284)(33,285)(34,286)(35,287)(36,288)(37,289)(38,290)(39,291)(40,292)(41,293)(42,294)(43,295)(44,296)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,169)(66,170)(67,171)(68,172)(69,173)(70,174)(71,175)(72,176)(73,177)(74,178)(75,179)(76,180)(77,181)(78,182)(79,183)(80,184)(81,185)(82,186)(83,187)(84,188)(85,189)(86,190)(87,191)(88,192)(89,193)(90,194)(91,195)(92,196)(93,197)(94,198)(95,199)(96,200)(97,201)(98,202)(99,203)(100,204)(101,205)(102,206)(103,207)(104,208)(105,209)(106,210)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(121,225)(122,226)(123,227)(124,228)(125,229)(126,230)(127,231)(128,232)(129,233)(130,234)(131,235)(132,236)(133,237)(134,238)(135,239)(136,240)(137,241)(138,242)(139,243)(140,244)(141,245)(142,246)(143,247)(144,248)(145,249)(146,250)(147,251)(148,252), (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)(149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296)>;
G:=Group( (1,253)(2,254)(3,255)(4,256)(5,257)(6,258)(7,259)(8,260)(9,261)(10,262)(11,263)(12,264)(13,265)(14,266)(15,267)(16,268)(17,269)(18,270)(19,271)(20,272)(21,273)(22,274)(23,275)(24,276)(25,277)(26,278)(27,279)(28,280)(29,281)(30,282)(31,283)(32,284)(33,285)(34,286)(35,287)(36,288)(37,289)(38,290)(39,291)(40,292)(41,293)(42,294)(43,295)(44,296)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,169)(66,170)(67,171)(68,172)(69,173)(70,174)(71,175)(72,176)(73,177)(74,178)(75,179)(76,180)(77,181)(78,182)(79,183)(80,184)(81,185)(82,186)(83,187)(84,188)(85,189)(86,190)(87,191)(88,192)(89,193)(90,194)(91,195)(92,196)(93,197)(94,198)(95,199)(96,200)(97,201)(98,202)(99,203)(100,204)(101,205)(102,206)(103,207)(104,208)(105,209)(106,210)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(121,225)(122,226)(123,227)(124,228)(125,229)(126,230)(127,231)(128,232)(129,233)(130,234)(131,235)(132,236)(133,237)(134,238)(135,239)(136,240)(137,241)(138,242)(139,243)(140,244)(141,245)(142,246)(143,247)(144,248)(145,249)(146,250)(147,251)(148,252), (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)(149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296) );
G=PermutationGroup([[(1,253),(2,254),(3,255),(4,256),(5,257),(6,258),(7,259),(8,260),(9,261),(10,262),(11,263),(12,264),(13,265),(14,266),(15,267),(16,268),(17,269),(18,270),(19,271),(20,272),(21,273),(22,274),(23,275),(24,276),(25,277),(26,278),(27,279),(28,280),(29,281),(30,282),(31,283),(32,284),(33,285),(34,286),(35,287),(36,288),(37,289),(38,290),(39,291),(40,292),(41,293),(42,294),(43,295),(44,296),(45,149),(46,150),(47,151),(48,152),(49,153),(50,154),(51,155),(52,156),(53,157),(54,158),(55,159),(56,160),(57,161),(58,162),(59,163),(60,164),(61,165),(62,166),(63,167),(64,168),(65,169),(66,170),(67,171),(68,172),(69,173),(70,174),(71,175),(72,176),(73,177),(74,178),(75,179),(76,180),(77,181),(78,182),(79,183),(80,184),(81,185),(82,186),(83,187),(84,188),(85,189),(86,190),(87,191),(88,192),(89,193),(90,194),(91,195),(92,196),(93,197),(94,198),(95,199),(96,200),(97,201),(98,202),(99,203),(100,204),(101,205),(102,206),(103,207),(104,208),(105,209),(106,210),(107,211),(108,212),(109,213),(110,214),(111,215),(112,216),(113,217),(114,218),(115,219),(116,220),(117,221),(118,222),(119,223),(120,224),(121,225),(122,226),(123,227),(124,228),(125,229),(126,230),(127,231),(128,232),(129,233),(130,234),(131,235),(132,236),(133,237),(134,238),(135,239),(136,240),(137,241),(138,242),(139,243),(140,244),(141,245),(142,246),(143,247),(144,248),(145,249),(146,250),(147,251),(148,252)], [(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),(149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296)]])
296 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 37A | ··· | 37AJ | 74A | ··· | 74DD | 148A | ··· | 148EN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 37 | ··· | 37 | 74 | ··· | 74 | 148 | ··· | 148 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
296 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||
| image | C1 | C2 | C2 | C4 | C37 | C74 | C74 | C148 |
| kernel | C2×C148 | C148 | C2×C74 | C74 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 4 | 36 | 72 | 36 | 144 |
Matrix representation of C2×C148 ►in GL2(𝔽149) generated by
| 148 | 0 |
| 0 | 148 |
| 66 | 0 |
| 0 | 86 |
G:=sub<GL(2,GF(149))| [148,0,0,148],[66,0,0,86] >;
C2×C148 in GAP, Magma, Sage, TeX
C_2\times C_{148} % in TeX
G:=Group("C2xC148"); // GroupNames label
G:=SmallGroup(296,9);
// by ID
G=gap.SmallGroup(296,9);
# by ID
G:=PCGroup([4,-2,-2,-37,-2,592]);
// Polycyclic
G:=Group<a,b|a^2=b^148=1,a*b=b*a>;
// generators/relations
Export