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G = C22×C106order 424 = 23·53

Abelian group of type [2,2,106]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C106, SmallGroup(424,14)

Series: Derived Chief Lower central Upper central

C1 — C22×C106
C1C53C106C2×C106 — C22×C106
C1 — C22×C106
C1 — C22×C106

Generators and relations for C22×C106
 G = < a,b,c | a2=b2=c106=1, ab=ba, ac=ca, bc=cb >


Smallest permutation representation of C22×C106
Regular action on 424 points
Generators in S424
(1 310)(2 311)(3 312)(4 313)(5 314)(6 315)(7 316)(8 317)(9 318)(10 213)(11 214)(12 215)(13 216)(14 217)(15 218)(16 219)(17 220)(18 221)(19 222)(20 223)(21 224)(22 225)(23 226)(24 227)(25 228)(26 229)(27 230)(28 231)(29 232)(30 233)(31 234)(32 235)(33 236)(34 237)(35 238)(36 239)(37 240)(38 241)(39 242)(40 243)(41 244)(42 245)(43 246)(44 247)(45 248)(46 249)(47 250)(48 251)(49 252)(50 253)(51 254)(52 255)(53 256)(54 257)(55 258)(56 259)(57 260)(58 261)(59 262)(60 263)(61 264)(62 265)(63 266)(64 267)(65 268)(66 269)(67 270)(68 271)(69 272)(70 273)(71 274)(72 275)(73 276)(74 277)(75 278)(76 279)(77 280)(78 281)(79 282)(80 283)(81 284)(82 285)(83 286)(84 287)(85 288)(86 289)(87 290)(88 291)(89 292)(90 293)(91 294)(92 295)(93 296)(94 297)(95 298)(96 299)(97 300)(98 301)(99 302)(100 303)(101 304)(102 305)(103 306)(104 307)(105 308)(106 309)(107 403)(108 404)(109 405)(110 406)(111 407)(112 408)(113 409)(114 410)(115 411)(116 412)(117 413)(118 414)(119 415)(120 416)(121 417)(122 418)(123 419)(124 420)(125 421)(126 422)(127 423)(128 424)(129 319)(130 320)(131 321)(132 322)(133 323)(134 324)(135 325)(136 326)(137 327)(138 328)(139 329)(140 330)(141 331)(142 332)(143 333)(144 334)(145 335)(146 336)(147 337)(148 338)(149 339)(150 340)(151 341)(152 342)(153 343)(154 344)(155 345)(156 346)(157 347)(158 348)(159 349)(160 350)(161 351)(162 352)(163 353)(164 354)(165 355)(166 356)(167 357)(168 358)(169 359)(170 360)(171 361)(172 362)(173 363)(174 364)(175 365)(176 366)(177 367)(178 368)(179 369)(180 370)(181 371)(182 372)(183 373)(184 374)(185 375)(186 376)(187 377)(188 378)(189 379)(190 380)(191 381)(192 382)(193 383)(194 384)(195 385)(196 386)(197 387)(198 388)(199 389)(200 390)(201 391)(202 392)(203 393)(204 394)(205 395)(206 396)(207 397)(208 398)(209 399)(210 400)(211 401)(212 402)
(1 196)(2 197)(3 198)(4 199)(5 200)(6 201)(7 202)(8 203)(9 204)(10 205)(11 206)(12 207)(13 208)(14 209)(15 210)(16 211)(17 212)(18 107)(19 108)(20 109)(21 110)(22 111)(23 112)(24 113)(25 114)(26 115)(27 116)(28 117)(29 118)(30 119)(31 120)(32 121)(33 122)(34 123)(35 124)(36 125)(37 126)(38 127)(39 128)(40 129)(41 130)(42 131)(43 132)(44 133)(45 134)(46 135)(47 136)(48 137)(49 138)(50 139)(51 140)(52 141)(53 142)(54 143)(55 144)(56 145)(57 146)(58 147)(59 148)(60 149)(61 150)(62 151)(63 152)(64 153)(65 154)(66 155)(67 156)(68 157)(69 158)(70 159)(71 160)(72 161)(73 162)(74 163)(75 164)(76 165)(77 166)(78 167)(79 168)(80 169)(81 170)(82 171)(83 172)(84 173)(85 174)(86 175)(87 176)(88 177)(89 178)(90 179)(91 180)(92 181)(93 182)(94 183)(95 184)(96 185)(97 186)(98 187)(99 188)(100 189)(101 190)(102 191)(103 192)(104 193)(105 194)(106 195)(213 395)(214 396)(215 397)(216 398)(217 399)(218 400)(219 401)(220 402)(221 403)(222 404)(223 405)(224 406)(225 407)(226 408)(227 409)(228 410)(229 411)(230 412)(231 413)(232 414)(233 415)(234 416)(235 417)(236 418)(237 419)(238 420)(239 421)(240 422)(241 423)(242 424)(243 319)(244 320)(245 321)(246 322)(247 323)(248 324)(249 325)(250 326)(251 327)(252 328)(253 329)(254 330)(255 331)(256 332)(257 333)(258 334)(259 335)(260 336)(261 337)(262 338)(263 339)(264 340)(265 341)(266 342)(267 343)(268 344)(269 345)(270 346)(271 347)(272 348)(273 349)(274 350)(275 351)(276 352)(277 353)(278 354)(279 355)(280 356)(281 357)(282 358)(283 359)(284 360)(285 361)(286 362)(287 363)(288 364)(289 365)(290 366)(291 367)(292 368)(293 369)(294 370)(295 371)(296 372)(297 373)(298 374)(299 375)(300 376)(301 377)(302 378)(303 379)(304 380)(305 381)(306 382)(307 383)(308 384)(309 385)(310 386)(311 387)(312 388)(313 389)(314 390)(315 391)(316 392)(317 393)(318 394)
(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)(213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318)(319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424)

G:=sub<Sym(424)| (1,310)(2,311)(3,312)(4,313)(5,314)(6,315)(7,316)(8,317)(9,318)(10,213)(11,214)(12,215)(13,216)(14,217)(15,218)(16,219)(17,220)(18,221)(19,222)(20,223)(21,224)(22,225)(23,226)(24,227)(25,228)(26,229)(27,230)(28,231)(29,232)(30,233)(31,234)(32,235)(33,236)(34,237)(35,238)(36,239)(37,240)(38,241)(39,242)(40,243)(41,244)(42,245)(43,246)(44,247)(45,248)(46,249)(47,250)(48,251)(49,252)(50,253)(51,254)(52,255)(53,256)(54,257)(55,258)(56,259)(57,260)(58,261)(59,262)(60,263)(61,264)(62,265)(63,266)(64,267)(65,268)(66,269)(67,270)(68,271)(69,272)(70,273)(71,274)(72,275)(73,276)(74,277)(75,278)(76,279)(77,280)(78,281)(79,282)(80,283)(81,284)(82,285)(83,286)(84,287)(85,288)(86,289)(87,290)(88,291)(89,292)(90,293)(91,294)(92,295)(93,296)(94,297)(95,298)(96,299)(97,300)(98,301)(99,302)(100,303)(101,304)(102,305)(103,306)(104,307)(105,308)(106,309)(107,403)(108,404)(109,405)(110,406)(111,407)(112,408)(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)(120,416)(121,417)(122,418)(123,419)(124,420)(125,421)(126,422)(127,423)(128,424)(129,319)(130,320)(131,321)(132,322)(133,323)(134,324)(135,325)(136,326)(137,327)(138,328)(139,329)(140,330)(141,331)(142,332)(143,333)(144,334)(145,335)(146,336)(147,337)(148,338)(149,339)(150,340)(151,341)(152,342)(153,343)(154,344)(155,345)(156,346)(157,347)(158,348)(159,349)(160,350)(161,351)(162,352)(163,353)(164,354)(165,355)(166,356)(167,357)(168,358)(169,359)(170,360)(171,361)(172,362)(173,363)(174,364)(175,365)(176,366)(177,367)(178,368)(179,369)(180,370)(181,371)(182,372)(183,373)(184,374)(185,375)(186,376)(187,377)(188,378)(189,379)(190,380)(191,381)(192,382)(193,383)(194,384)(195,385)(196,386)(197,387)(198,388)(199,389)(200,390)(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)(208,398)(209,399)(210,400)(211,401)(212,402), (1,196)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,209)(15,210)(16,211)(17,212)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,113)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,120)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,127)(39,128)(40,129)(41,130)(42,131)(43,132)(44,133)(45,134)(46,135)(47,136)(48,137)(49,138)(50,139)(51,140)(52,141)(53,142)(54,143)(55,144)(56,145)(57,146)(58,147)(59,148)(60,149)(61,150)(62,151)(63,152)(64,153)(65,154)(66,155)(67,156)(68,157)(69,158)(70,159)(71,160)(72,161)(73,162)(74,163)(75,164)(76,165)(77,166)(78,167)(79,168)(80,169)(81,170)(82,171)(83,172)(84,173)(85,174)(86,175)(87,176)(88,177)(89,178)(90,179)(91,180)(92,181)(93,182)(94,183)(95,184)(96,185)(97,186)(98,187)(99,188)(100,189)(101,190)(102,191)(103,192)(104,193)(105,194)(106,195)(213,395)(214,396)(215,397)(216,398)(217,399)(218,400)(219,401)(220,402)(221,403)(222,404)(223,405)(224,406)(225,407)(226,408)(227,409)(228,410)(229,411)(230,412)(231,413)(232,414)(233,415)(234,416)(235,417)(236,418)(237,419)(238,420)(239,421)(240,422)(241,423)(242,424)(243,319)(244,320)(245,321)(246,322)(247,323)(248,324)(249,325)(250,326)(251,327)(252,328)(253,329)(254,330)(255,331)(256,332)(257,333)(258,334)(259,335)(260,336)(261,337)(262,338)(263,339)(264,340)(265,341)(266,342)(267,343)(268,344)(269,345)(270,346)(271,347)(272,348)(273,349)(274,350)(275,351)(276,352)(277,353)(278,354)(279,355)(280,356)(281,357)(282,358)(283,359)(284,360)(285,361)(286,362)(287,363)(288,364)(289,365)(290,366)(291,367)(292,368)(293,369)(294,370)(295,371)(296,372)(297,373)(298,374)(299,375)(300,376)(301,377)(302,378)(303,379)(304,380)(305,381)(306,382)(307,383)(308,384)(309,385)(310,386)(311,387)(312,388)(313,389)(314,390)(315,391)(316,392)(317,393)(318,394), (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)(213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318)(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424)>;

G:=Group( (1,310)(2,311)(3,312)(4,313)(5,314)(6,315)(7,316)(8,317)(9,318)(10,213)(11,214)(12,215)(13,216)(14,217)(15,218)(16,219)(17,220)(18,221)(19,222)(20,223)(21,224)(22,225)(23,226)(24,227)(25,228)(26,229)(27,230)(28,231)(29,232)(30,233)(31,234)(32,235)(33,236)(34,237)(35,238)(36,239)(37,240)(38,241)(39,242)(40,243)(41,244)(42,245)(43,246)(44,247)(45,248)(46,249)(47,250)(48,251)(49,252)(50,253)(51,254)(52,255)(53,256)(54,257)(55,258)(56,259)(57,260)(58,261)(59,262)(60,263)(61,264)(62,265)(63,266)(64,267)(65,268)(66,269)(67,270)(68,271)(69,272)(70,273)(71,274)(72,275)(73,276)(74,277)(75,278)(76,279)(77,280)(78,281)(79,282)(80,283)(81,284)(82,285)(83,286)(84,287)(85,288)(86,289)(87,290)(88,291)(89,292)(90,293)(91,294)(92,295)(93,296)(94,297)(95,298)(96,299)(97,300)(98,301)(99,302)(100,303)(101,304)(102,305)(103,306)(104,307)(105,308)(106,309)(107,403)(108,404)(109,405)(110,406)(111,407)(112,408)(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)(120,416)(121,417)(122,418)(123,419)(124,420)(125,421)(126,422)(127,423)(128,424)(129,319)(130,320)(131,321)(132,322)(133,323)(134,324)(135,325)(136,326)(137,327)(138,328)(139,329)(140,330)(141,331)(142,332)(143,333)(144,334)(145,335)(146,336)(147,337)(148,338)(149,339)(150,340)(151,341)(152,342)(153,343)(154,344)(155,345)(156,346)(157,347)(158,348)(159,349)(160,350)(161,351)(162,352)(163,353)(164,354)(165,355)(166,356)(167,357)(168,358)(169,359)(170,360)(171,361)(172,362)(173,363)(174,364)(175,365)(176,366)(177,367)(178,368)(179,369)(180,370)(181,371)(182,372)(183,373)(184,374)(185,375)(186,376)(187,377)(188,378)(189,379)(190,380)(191,381)(192,382)(193,383)(194,384)(195,385)(196,386)(197,387)(198,388)(199,389)(200,390)(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)(208,398)(209,399)(210,400)(211,401)(212,402), (1,196)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,209)(15,210)(16,211)(17,212)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,113)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,120)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,127)(39,128)(40,129)(41,130)(42,131)(43,132)(44,133)(45,134)(46,135)(47,136)(48,137)(49,138)(50,139)(51,140)(52,141)(53,142)(54,143)(55,144)(56,145)(57,146)(58,147)(59,148)(60,149)(61,150)(62,151)(63,152)(64,153)(65,154)(66,155)(67,156)(68,157)(69,158)(70,159)(71,160)(72,161)(73,162)(74,163)(75,164)(76,165)(77,166)(78,167)(79,168)(80,169)(81,170)(82,171)(83,172)(84,173)(85,174)(86,175)(87,176)(88,177)(89,178)(90,179)(91,180)(92,181)(93,182)(94,183)(95,184)(96,185)(97,186)(98,187)(99,188)(100,189)(101,190)(102,191)(103,192)(104,193)(105,194)(106,195)(213,395)(214,396)(215,397)(216,398)(217,399)(218,400)(219,401)(220,402)(221,403)(222,404)(223,405)(224,406)(225,407)(226,408)(227,409)(228,410)(229,411)(230,412)(231,413)(232,414)(233,415)(234,416)(235,417)(236,418)(237,419)(238,420)(239,421)(240,422)(241,423)(242,424)(243,319)(244,320)(245,321)(246,322)(247,323)(248,324)(249,325)(250,326)(251,327)(252,328)(253,329)(254,330)(255,331)(256,332)(257,333)(258,334)(259,335)(260,336)(261,337)(262,338)(263,339)(264,340)(265,341)(266,342)(267,343)(268,344)(269,345)(270,346)(271,347)(272,348)(273,349)(274,350)(275,351)(276,352)(277,353)(278,354)(279,355)(280,356)(281,357)(282,358)(283,359)(284,360)(285,361)(286,362)(287,363)(288,364)(289,365)(290,366)(291,367)(292,368)(293,369)(294,370)(295,371)(296,372)(297,373)(298,374)(299,375)(300,376)(301,377)(302,378)(303,379)(304,380)(305,381)(306,382)(307,383)(308,384)(309,385)(310,386)(311,387)(312,388)(313,389)(314,390)(315,391)(316,392)(317,393)(318,394), (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)(213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318)(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424) );

G=PermutationGroup([(1,310),(2,311),(3,312),(4,313),(5,314),(6,315),(7,316),(8,317),(9,318),(10,213),(11,214),(12,215),(13,216),(14,217),(15,218),(16,219),(17,220),(18,221),(19,222),(20,223),(21,224),(22,225),(23,226),(24,227),(25,228),(26,229),(27,230),(28,231),(29,232),(30,233),(31,234),(32,235),(33,236),(34,237),(35,238),(36,239),(37,240),(38,241),(39,242),(40,243),(41,244),(42,245),(43,246),(44,247),(45,248),(46,249),(47,250),(48,251),(49,252),(50,253),(51,254),(52,255),(53,256),(54,257),(55,258),(56,259),(57,260),(58,261),(59,262),(60,263),(61,264),(62,265),(63,266),(64,267),(65,268),(66,269),(67,270),(68,271),(69,272),(70,273),(71,274),(72,275),(73,276),(74,277),(75,278),(76,279),(77,280),(78,281),(79,282),(80,283),(81,284),(82,285),(83,286),(84,287),(85,288),(86,289),(87,290),(88,291),(89,292),(90,293),(91,294),(92,295),(93,296),(94,297),(95,298),(96,299),(97,300),(98,301),(99,302),(100,303),(101,304),(102,305),(103,306),(104,307),(105,308),(106,309),(107,403),(108,404),(109,405),(110,406),(111,407),(112,408),(113,409),(114,410),(115,411),(116,412),(117,413),(118,414),(119,415),(120,416),(121,417),(122,418),(123,419),(124,420),(125,421),(126,422),(127,423),(128,424),(129,319),(130,320),(131,321),(132,322),(133,323),(134,324),(135,325),(136,326),(137,327),(138,328),(139,329),(140,330),(141,331),(142,332),(143,333),(144,334),(145,335),(146,336),(147,337),(148,338),(149,339),(150,340),(151,341),(152,342),(153,343),(154,344),(155,345),(156,346),(157,347),(158,348),(159,349),(160,350),(161,351),(162,352),(163,353),(164,354),(165,355),(166,356),(167,357),(168,358),(169,359),(170,360),(171,361),(172,362),(173,363),(174,364),(175,365),(176,366),(177,367),(178,368),(179,369),(180,370),(181,371),(182,372),(183,373),(184,374),(185,375),(186,376),(187,377),(188,378),(189,379),(190,380),(191,381),(192,382),(193,383),(194,384),(195,385),(196,386),(197,387),(198,388),(199,389),(200,390),(201,391),(202,392),(203,393),(204,394),(205,395),(206,396),(207,397),(208,398),(209,399),(210,400),(211,401),(212,402)], [(1,196),(2,197),(3,198),(4,199),(5,200),(6,201),(7,202),(8,203),(9,204),(10,205),(11,206),(12,207),(13,208),(14,209),(15,210),(16,211),(17,212),(18,107),(19,108),(20,109),(21,110),(22,111),(23,112),(24,113),(25,114),(26,115),(27,116),(28,117),(29,118),(30,119),(31,120),(32,121),(33,122),(34,123),(35,124),(36,125),(37,126),(38,127),(39,128),(40,129),(41,130),(42,131),(43,132),(44,133),(45,134),(46,135),(47,136),(48,137),(49,138),(50,139),(51,140),(52,141),(53,142),(54,143),(55,144),(56,145),(57,146),(58,147),(59,148),(60,149),(61,150),(62,151),(63,152),(64,153),(65,154),(66,155),(67,156),(68,157),(69,158),(70,159),(71,160),(72,161),(73,162),(74,163),(75,164),(76,165),(77,166),(78,167),(79,168),(80,169),(81,170),(82,171),(83,172),(84,173),(85,174),(86,175),(87,176),(88,177),(89,178),(90,179),(91,180),(92,181),(93,182),(94,183),(95,184),(96,185),(97,186),(98,187),(99,188),(100,189),(101,190),(102,191),(103,192),(104,193),(105,194),(106,195),(213,395),(214,396),(215,397),(216,398),(217,399),(218,400),(219,401),(220,402),(221,403),(222,404),(223,405),(224,406),(225,407),(226,408),(227,409),(228,410),(229,411),(230,412),(231,413),(232,414),(233,415),(234,416),(235,417),(236,418),(237,419),(238,420),(239,421),(240,422),(241,423),(242,424),(243,319),(244,320),(245,321),(246,322),(247,323),(248,324),(249,325),(250,326),(251,327),(252,328),(253,329),(254,330),(255,331),(256,332),(257,333),(258,334),(259,335),(260,336),(261,337),(262,338),(263,339),(264,340),(265,341),(266,342),(267,343),(268,344),(269,345),(270,346),(271,347),(272,348),(273,349),(274,350),(275,351),(276,352),(277,353),(278,354),(279,355),(280,356),(281,357),(282,358),(283,359),(284,360),(285,361),(286,362),(287,363),(288,364),(289,365),(290,366),(291,367),(292,368),(293,369),(294,370),(295,371),(296,372),(297,373),(298,374),(299,375),(300,376),(301,377),(302,378),(303,379),(304,380),(305,381),(306,382),(307,383),(308,384),(309,385),(310,386),(311,387),(312,388),(313,389),(314,390),(315,391),(316,392),(317,393),(318,394)], [(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),(213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318),(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424)])

424 conjugacy classes

class 1 2A···2G53A···53AZ106A···106MZ
order12···253···53106···106
size11···11···11···1

424 irreducible representations

dim1111
type++
imageC1C2C53C106
kernelC22×C106C2×C106C23C22
# reps1752364

Matrix representation of C22×C106 in GL3(𝔽107) generated by

100
01060
00106
,
100
010
00106
,
6700
0220
0052
G:=sub<GL(3,GF(107))| [1,0,0,0,106,0,0,0,106],[1,0,0,0,1,0,0,0,106],[67,0,0,0,22,0,0,0,52] >;

C22×C106 in GAP, Magma, Sage, TeX

C_2^2\times C_{106}
% in TeX

G:=Group("C2^2xC106");
// GroupNames label

G:=SmallGroup(424,14);
// by ID

G=gap.SmallGroup(424,14);
# by ID

G:=PCGroup([4,-2,-2,-2,-53]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^106=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

Export

Subgroup lattice of C22×C106 in TeX

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