direct product, abelian, monomial, 2-elementary
Aliases: C23×C50, SmallGroup(400,55)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C23×C50 |
| C1 — C23×C50 |
| C1 — C23×C50 |
Generators and relations for C23×C50
G = < a,b,c,d | a2=b2=c2=d50=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >
Subgroups: 201, all normal (6 characteristic)
C1, C2, C22, C5, C23, C10, C24, C2×C10, C25, C22×C10, C50, C23×C10, C2×C50, C22×C50, C23×C50
Quotients: C1, C2, C22, C5, C23, C10, C24, C2×C10, C25, C22×C10, C50, C23×C10, C2×C50, C22×C50, C23×C50
►Regular action on 400 points
Generators in S400
(1 221)(2 222)(3 223)(4 224)(5 225)(6 226)(7 227)(8 228)(9 229)(10 230)(11 231)(12 232)(13 233)(14 234)(15 235)(16 236)(17 237)(18 238)(19 239)(20 240)(21 241)(22 242)(23 243)(24 244)(25 245)(26 246)(27 247)(28 248)(29 249)(30 250)(31 201)(32 202)(33 203)(34 204)(35 205)(36 206)(37 207)(38 208)(39 209)(40 210)(41 211)(42 212)(43 213)(44 214)(45 215)(46 216)(47 217)(48 218)(49 219)(50 220)(51 280)(52 281)(53 282)(54 283)(55 284)(56 285)(57 286)(58 287)(59 288)(60 289)(61 290)(62 291)(63 292)(64 293)(65 294)(66 295)(67 296)(68 297)(69 298)(70 299)(71 300)(72 251)(73 252)(74 253)(75 254)(76 255)(77 256)(78 257)(79 258)(80 259)(81 260)(82 261)(83 262)(84 263)(85 264)(86 265)(87 266)(88 267)(89 268)(90 269)(91 270)(92 271)(93 272)(94 273)(95 274)(96 275)(97 276)(98 277)(99 278)(100 279)(101 322)(102 323)(103 324)(104 325)(105 326)(106 327)(107 328)(108 329)(109 330)(110 331)(111 332)(112 333)(113 334)(114 335)(115 336)(116 337)(117 338)(118 339)(119 340)(120 341)(121 342)(122 343)(123 344)(124 345)(125 346)(126 347)(127 348)(128 349)(129 350)(130 301)(131 302)(132 303)(133 304)(134 305)(135 306)(136 307)(137 308)(138 309)(139 310)(140 311)(141 312)(142 313)(143 314)(144 315)(145 316)(146 317)(147 318)(148 319)(149 320)(150 321)(151 364)(152 365)(153 366)(154 367)(155 368)(156 369)(157 370)(158 371)(159 372)(160 373)(161 374)(162 375)(163 376)(164 377)(165 378)(166 379)(167 380)(168 381)(169 382)(170 383)(171 384)(172 385)(173 386)(174 387)(175 388)(176 389)(177 390)(178 391)(179 392)(180 393)(181 394)(182 395)(183 396)(184 397)(185 398)(186 399)(187 400)(188 351)(189 352)(190 353)(191 354)(192 355)(193 356)(194 357)(195 358)(196 359)(197 360)(198 361)(199 362)(200 363)
(1 121)(2 122)(3 123)(4 124)(5 125)(6 126)(7 127)(8 128)(9 129)(10 130)(11 131)(12 132)(13 133)(14 134)(15 135)(16 136)(17 137)(18 138)(19 139)(20 140)(21 141)(22 142)(23 143)(24 144)(25 145)(26 146)(27 147)(28 148)(29 149)(30 150)(31 101)(32 102)(33 103)(34 104)(35 105)(36 106)(37 107)(38 108)(39 109)(40 110)(41 111)(42 112)(43 113)(44 114)(45 115)(46 116)(47 117)(48 118)(49 119)(50 120)(51 151)(52 152)(53 153)(54 154)(55 155)(56 156)(57 157)(58 158)(59 159)(60 160)(61 161)(62 162)(63 163)(64 164)(65 165)(66 166)(67 167)(68 168)(69 169)(70 170)(71 171)(72 172)(73 173)(74 174)(75 175)(76 176)(77 177)(78 178)(79 179)(80 180)(81 181)(82 182)(83 183)(84 184)(85 185)(86 186)(87 187)(88 188)(89 189)(90 190)(91 191)(92 192)(93 193)(94 194)(95 195)(96 196)(97 197)(98 198)(99 199)(100 200)(201 322)(202 323)(203 324)(204 325)(205 326)(206 327)(207 328)(208 329)(209 330)(210 331)(211 332)(212 333)(213 334)(214 335)(215 336)(216 337)(217 338)(218 339)(219 340)(220 341)(221 342)(222 343)(223 344)(224 345)(225 346)(226 347)(227 348)(228 349)(229 350)(230 301)(231 302)(232 303)(233 304)(234 305)(235 306)(236 307)(237 308)(238 309)(239 310)(240 311)(241 312)(242 313)(243 314)(244 315)(245 316)(246 317)(247 318)(248 319)(249 320)(250 321)(251 385)(252 386)(253 387)(254 388)(255 389)(256 390)(257 391)(258 392)(259 393)(260 394)(261 395)(262 396)(263 397)(264 398)(265 399)(266 400)(267 351)(268 352)(269 353)(270 354)(271 355)(272 356)(273 357)(274 358)(275 359)(276 360)(277 361)(278 362)(279 363)(280 364)(281 365)(282 366)(283 367)(284 368)(285 369)(286 370)(287 371)(288 372)(289 373)(290 374)(291 375)(292 376)(293 377)(294 378)(295 379)(296 380)(297 381)(298 382)(299 383)(300 384)
(1 51)(2 52)(3 53)(4 54)(5 55)(6 56)(7 57)(8 58)(9 59)(10 60)(11 61)(12 62)(13 63)(14 64)(15 65)(16 66)(17 67)(18 68)(19 69)(20 70)(21 71)(22 72)(23 73)(24 74)(25 75)(26 76)(27 77)(28 78)(29 79)(30 80)(31 81)(32 82)(33 83)(34 84)(35 85)(36 86)(37 87)(38 88)(39 89)(40 90)(41 91)(42 92)(43 93)(44 94)(45 95)(46 96)(47 97)(48 98)(49 99)(50 100)(101 181)(102 182)(103 183)(104 184)(105 185)(106 186)(107 187)(108 188)(109 189)(110 190)(111 191)(112 192)(113 193)(114 194)(115 195)(116 196)(117 197)(118 198)(119 199)(120 200)(121 151)(122 152)(123 153)(124 154)(125 155)(126 156)(127 157)(128 158)(129 159)(130 160)(131 161)(132 162)(133 163)(134 164)(135 165)(136 166)(137 167)(138 168)(139 169)(140 170)(141 171)(142 172)(143 173)(144 174)(145 175)(146 176)(147 177)(148 178)(149 179)(150 180)(201 260)(202 261)(203 262)(204 263)(205 264)(206 265)(207 266)(208 267)(209 268)(210 269)(211 270)(212 271)(213 272)(214 273)(215 274)(216 275)(217 276)(218 277)(219 278)(220 279)(221 280)(222 281)(223 282)(224 283)(225 284)(226 285)(227 286)(228 287)(229 288)(230 289)(231 290)(232 291)(233 292)(234 293)(235 294)(236 295)(237 296)(238 297)(239 298)(240 299)(241 300)(242 251)(243 252)(244 253)(245 254)(246 255)(247 256)(248 257)(249 258)(250 259)(301 373)(302 374)(303 375)(304 376)(305 377)(306 378)(307 379)(308 380)(309 381)(310 382)(311 383)(312 384)(313 385)(314 386)(315 387)(316 388)(317 389)(318 390)(319 391)(320 392)(321 393)(322 394)(323 395)(324 396)(325 397)(326 398)(327 399)(328 400)(329 351)(330 352)(331 353)(332 354)(333 355)(334 356)(335 357)(336 358)(337 359)(338 360)(339 361)(340 362)(341 363)(342 364)(343 365)(344 366)(345 367)(346 368)(347 369)(348 370)(349 371)(350 372)
(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)
G:=sub<Sym(400)| (1,221)(2,222)(3,223)(4,224)(5,225)(6,226)(7,227)(8,228)(9,229)(10,230)(11,231)(12,232)(13,233)(14,234)(15,235)(16,236)(17,237)(18,238)(19,239)(20,240)(21,241)(22,242)(23,243)(24,244)(25,245)(26,246)(27,247)(28,248)(29,249)(30,250)(31,201)(32,202)(33,203)(34,204)(35,205)(36,206)(37,207)(38,208)(39,209)(40,210)(41,211)(42,212)(43,213)(44,214)(45,215)(46,216)(47,217)(48,218)(49,219)(50,220)(51,280)(52,281)(53,282)(54,283)(55,284)(56,285)(57,286)(58,287)(59,288)(60,289)(61,290)(62,291)(63,292)(64,293)(65,294)(66,295)(67,296)(68,297)(69,298)(70,299)(71,300)(72,251)(73,252)(74,253)(75,254)(76,255)(77,256)(78,257)(79,258)(80,259)(81,260)(82,261)(83,262)(84,263)(85,264)(86,265)(87,266)(88,267)(89,268)(90,269)(91,270)(92,271)(93,272)(94,273)(95,274)(96,275)(97,276)(98,277)(99,278)(100,279)(101,322)(102,323)(103,324)(104,325)(105,326)(106,327)(107,328)(108,329)(109,330)(110,331)(111,332)(112,333)(113,334)(114,335)(115,336)(116,337)(117,338)(118,339)(119,340)(120,341)(121,342)(122,343)(123,344)(124,345)(125,346)(126,347)(127,348)(128,349)(129,350)(130,301)(131,302)(132,303)(133,304)(134,305)(135,306)(136,307)(137,308)(138,309)(139,310)(140,311)(141,312)(142,313)(143,314)(144,315)(145,316)(146,317)(147,318)(148,319)(149,320)(150,321)(151,364)(152,365)(153,366)(154,367)(155,368)(156,369)(157,370)(158,371)(159,372)(160,373)(161,374)(162,375)(163,376)(164,377)(165,378)(166,379)(167,380)(168,381)(169,382)(170,383)(171,384)(172,385)(173,386)(174,387)(175,388)(176,389)(177,390)(178,391)(179,392)(180,393)(181,394)(182,395)(183,396)(184,397)(185,398)(186,399)(187,400)(188,351)(189,352)(190,353)(191,354)(192,355)(193,356)(194,357)(195,358)(196,359)(197,360)(198,361)(199,362)(200,363), (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,127)(8,128)(9,129)(10,130)(11,131)(12,132)(13,133)(14,134)(15,135)(16,136)(17,137)(18,138)(19,139)(20,140)(21,141)(22,142)(23,143)(24,144)(25,145)(26,146)(27,147)(28,148)(29,149)(30,150)(31,101)(32,102)(33,103)(34,104)(35,105)(36,106)(37,107)(38,108)(39,109)(40,110)(41,111)(42,112)(43,113)(44,114)(45,115)(46,116)(47,117)(48,118)(49,119)(50,120)(51,151)(52,152)(53,153)(54,154)(55,155)(56,156)(57,157)(58,158)(59,159)(60,160)(61,161)(62,162)(63,163)(64,164)(65,165)(66,166)(67,167)(68,168)(69,169)(70,170)(71,171)(72,172)(73,173)(74,174)(75,175)(76,176)(77,177)(78,178)(79,179)(80,180)(81,181)(82,182)(83,183)(84,184)(85,185)(86,186)(87,187)(88,188)(89,189)(90,190)(91,191)(92,192)(93,193)(94,194)(95,195)(96,196)(97,197)(98,198)(99,199)(100,200)(201,322)(202,323)(203,324)(204,325)(205,326)(206,327)(207,328)(208,329)(209,330)(210,331)(211,332)(212,333)(213,334)(214,335)(215,336)(216,337)(217,338)(218,339)(219,340)(220,341)(221,342)(222,343)(223,344)(224,345)(225,346)(226,347)(227,348)(228,349)(229,350)(230,301)(231,302)(232,303)(233,304)(234,305)(235,306)(236,307)(237,308)(238,309)(239,310)(240,311)(241,312)(242,313)(243,314)(244,315)(245,316)(246,317)(247,318)(248,319)(249,320)(250,321)(251,385)(252,386)(253,387)(254,388)(255,389)(256,390)(257,391)(258,392)(259,393)(260,394)(261,395)(262,396)(263,397)(264,398)(265,399)(266,400)(267,351)(268,352)(269,353)(270,354)(271,355)(272,356)(273,357)(274,358)(275,359)(276,360)(277,361)(278,362)(279,363)(280,364)(281,365)(282,366)(283,367)(284,368)(285,369)(286,370)(287,371)(288,372)(289,373)(290,374)(291,375)(292,376)(293,377)(294,378)(295,379)(296,380)(297,381)(298,382)(299,383)(300,384), (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,57)(8,58)(9,59)(10,60)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,85)(36,86)(37,87)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(101,181)(102,182)(103,183)(104,184)(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)(112,192)(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)(120,200)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(201,260)(202,261)(203,262)(204,263)(205,264)(206,265)(207,266)(208,267)(209,268)(210,269)(211,270)(212,271)(213,272)(214,273)(215,274)(216,275)(217,276)(218,277)(219,278)(220,279)(221,280)(222,281)(223,282)(224,283)(225,284)(226,285)(227,286)(228,287)(229,288)(230,289)(231,290)(232,291)(233,292)(234,293)(235,294)(236,295)(237,296)(238,297)(239,298)(240,299)(241,300)(242,251)(243,252)(244,253)(245,254)(246,255)(247,256)(248,257)(249,258)(250,259)(301,373)(302,374)(303,375)(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)(329,351)(330,352)(331,353)(332,354)(333,355)(334,356)(335,357)(336,358)(337,359)(338,360)(339,361)(340,362)(341,363)(342,364)(343,365)(344,366)(345,367)(346,368)(347,369)(348,370)(349,371)(350,372), (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)>;
G:=Group( (1,221)(2,222)(3,223)(4,224)(5,225)(6,226)(7,227)(8,228)(9,229)(10,230)(11,231)(12,232)(13,233)(14,234)(15,235)(16,236)(17,237)(18,238)(19,239)(20,240)(21,241)(22,242)(23,243)(24,244)(25,245)(26,246)(27,247)(28,248)(29,249)(30,250)(31,201)(32,202)(33,203)(34,204)(35,205)(36,206)(37,207)(38,208)(39,209)(40,210)(41,211)(42,212)(43,213)(44,214)(45,215)(46,216)(47,217)(48,218)(49,219)(50,220)(51,280)(52,281)(53,282)(54,283)(55,284)(56,285)(57,286)(58,287)(59,288)(60,289)(61,290)(62,291)(63,292)(64,293)(65,294)(66,295)(67,296)(68,297)(69,298)(70,299)(71,300)(72,251)(73,252)(74,253)(75,254)(76,255)(77,256)(78,257)(79,258)(80,259)(81,260)(82,261)(83,262)(84,263)(85,264)(86,265)(87,266)(88,267)(89,268)(90,269)(91,270)(92,271)(93,272)(94,273)(95,274)(96,275)(97,276)(98,277)(99,278)(100,279)(101,322)(102,323)(103,324)(104,325)(105,326)(106,327)(107,328)(108,329)(109,330)(110,331)(111,332)(112,333)(113,334)(114,335)(115,336)(116,337)(117,338)(118,339)(119,340)(120,341)(121,342)(122,343)(123,344)(124,345)(125,346)(126,347)(127,348)(128,349)(129,350)(130,301)(131,302)(132,303)(133,304)(134,305)(135,306)(136,307)(137,308)(138,309)(139,310)(140,311)(141,312)(142,313)(143,314)(144,315)(145,316)(146,317)(147,318)(148,319)(149,320)(150,321)(151,364)(152,365)(153,366)(154,367)(155,368)(156,369)(157,370)(158,371)(159,372)(160,373)(161,374)(162,375)(163,376)(164,377)(165,378)(166,379)(167,380)(168,381)(169,382)(170,383)(171,384)(172,385)(173,386)(174,387)(175,388)(176,389)(177,390)(178,391)(179,392)(180,393)(181,394)(182,395)(183,396)(184,397)(185,398)(186,399)(187,400)(188,351)(189,352)(190,353)(191,354)(192,355)(193,356)(194,357)(195,358)(196,359)(197,360)(198,361)(199,362)(200,363), (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,127)(8,128)(9,129)(10,130)(11,131)(12,132)(13,133)(14,134)(15,135)(16,136)(17,137)(18,138)(19,139)(20,140)(21,141)(22,142)(23,143)(24,144)(25,145)(26,146)(27,147)(28,148)(29,149)(30,150)(31,101)(32,102)(33,103)(34,104)(35,105)(36,106)(37,107)(38,108)(39,109)(40,110)(41,111)(42,112)(43,113)(44,114)(45,115)(46,116)(47,117)(48,118)(49,119)(50,120)(51,151)(52,152)(53,153)(54,154)(55,155)(56,156)(57,157)(58,158)(59,159)(60,160)(61,161)(62,162)(63,163)(64,164)(65,165)(66,166)(67,167)(68,168)(69,169)(70,170)(71,171)(72,172)(73,173)(74,174)(75,175)(76,176)(77,177)(78,178)(79,179)(80,180)(81,181)(82,182)(83,183)(84,184)(85,185)(86,186)(87,187)(88,188)(89,189)(90,190)(91,191)(92,192)(93,193)(94,194)(95,195)(96,196)(97,197)(98,198)(99,199)(100,200)(201,322)(202,323)(203,324)(204,325)(205,326)(206,327)(207,328)(208,329)(209,330)(210,331)(211,332)(212,333)(213,334)(214,335)(215,336)(216,337)(217,338)(218,339)(219,340)(220,341)(221,342)(222,343)(223,344)(224,345)(225,346)(226,347)(227,348)(228,349)(229,350)(230,301)(231,302)(232,303)(233,304)(234,305)(235,306)(236,307)(237,308)(238,309)(239,310)(240,311)(241,312)(242,313)(243,314)(244,315)(245,316)(246,317)(247,318)(248,319)(249,320)(250,321)(251,385)(252,386)(253,387)(254,388)(255,389)(256,390)(257,391)(258,392)(259,393)(260,394)(261,395)(262,396)(263,397)(264,398)(265,399)(266,400)(267,351)(268,352)(269,353)(270,354)(271,355)(272,356)(273,357)(274,358)(275,359)(276,360)(277,361)(278,362)(279,363)(280,364)(281,365)(282,366)(283,367)(284,368)(285,369)(286,370)(287,371)(288,372)(289,373)(290,374)(291,375)(292,376)(293,377)(294,378)(295,379)(296,380)(297,381)(298,382)(299,383)(300,384), (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,57)(8,58)(9,59)(10,60)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,85)(36,86)(37,87)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(101,181)(102,182)(103,183)(104,184)(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)(112,192)(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)(120,200)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(201,260)(202,261)(203,262)(204,263)(205,264)(206,265)(207,266)(208,267)(209,268)(210,269)(211,270)(212,271)(213,272)(214,273)(215,274)(216,275)(217,276)(218,277)(219,278)(220,279)(221,280)(222,281)(223,282)(224,283)(225,284)(226,285)(227,286)(228,287)(229,288)(230,289)(231,290)(232,291)(233,292)(234,293)(235,294)(236,295)(237,296)(238,297)(239,298)(240,299)(241,300)(242,251)(243,252)(244,253)(245,254)(246,255)(247,256)(248,257)(249,258)(250,259)(301,373)(302,374)(303,375)(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)(329,351)(330,352)(331,353)(332,354)(333,355)(334,356)(335,357)(336,358)(337,359)(338,360)(339,361)(340,362)(341,363)(342,364)(343,365)(344,366)(345,367)(346,368)(347,369)(348,370)(349,371)(350,372), (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) );
G=PermutationGroup([[(1,221),(2,222),(3,223),(4,224),(5,225),(6,226),(7,227),(8,228),(9,229),(10,230),(11,231),(12,232),(13,233),(14,234),(15,235),(16,236),(17,237),(18,238),(19,239),(20,240),(21,241),(22,242),(23,243),(24,244),(25,245),(26,246),(27,247),(28,248),(29,249),(30,250),(31,201),(32,202),(33,203),(34,204),(35,205),(36,206),(37,207),(38,208),(39,209),(40,210),(41,211),(42,212),(43,213),(44,214),(45,215),(46,216),(47,217),(48,218),(49,219),(50,220),(51,280),(52,281),(53,282),(54,283),(55,284),(56,285),(57,286),(58,287),(59,288),(60,289),(61,290),(62,291),(63,292),(64,293),(65,294),(66,295),(67,296),(68,297),(69,298),(70,299),(71,300),(72,251),(73,252),(74,253),(75,254),(76,255),(77,256),(78,257),(79,258),(80,259),(81,260),(82,261),(83,262),(84,263),(85,264),(86,265),(87,266),(88,267),(89,268),(90,269),(91,270),(92,271),(93,272),(94,273),(95,274),(96,275),(97,276),(98,277),(99,278),(100,279),(101,322),(102,323),(103,324),(104,325),(105,326),(106,327),(107,328),(108,329),(109,330),(110,331),(111,332),(112,333),(113,334),(114,335),(115,336),(116,337),(117,338),(118,339),(119,340),(120,341),(121,342),(122,343),(123,344),(124,345),(125,346),(126,347),(127,348),(128,349),(129,350),(130,301),(131,302),(132,303),(133,304),(134,305),(135,306),(136,307),(137,308),(138,309),(139,310),(140,311),(141,312),(142,313),(143,314),(144,315),(145,316),(146,317),(147,318),(148,319),(149,320),(150,321),(151,364),(152,365),(153,366),(154,367),(155,368),(156,369),(157,370),(158,371),(159,372),(160,373),(161,374),(162,375),(163,376),(164,377),(165,378),(166,379),(167,380),(168,381),(169,382),(170,383),(171,384),(172,385),(173,386),(174,387),(175,388),(176,389),(177,390),(178,391),(179,392),(180,393),(181,394),(182,395),(183,396),(184,397),(185,398),(186,399),(187,400),(188,351),(189,352),(190,353),(191,354),(192,355),(193,356),(194,357),(195,358),(196,359),(197,360),(198,361),(199,362),(200,363)], [(1,121),(2,122),(3,123),(4,124),(5,125),(6,126),(7,127),(8,128),(9,129),(10,130),(11,131),(12,132),(13,133),(14,134),(15,135),(16,136),(17,137),(18,138),(19,139),(20,140),(21,141),(22,142),(23,143),(24,144),(25,145),(26,146),(27,147),(28,148),(29,149),(30,150),(31,101),(32,102),(33,103),(34,104),(35,105),(36,106),(37,107),(38,108),(39,109),(40,110),(41,111),(42,112),(43,113),(44,114),(45,115),(46,116),(47,117),(48,118),(49,119),(50,120),(51,151),(52,152),(53,153),(54,154),(55,155),(56,156),(57,157),(58,158),(59,159),(60,160),(61,161),(62,162),(63,163),(64,164),(65,165),(66,166),(67,167),(68,168),(69,169),(70,170),(71,171),(72,172),(73,173),(74,174),(75,175),(76,176),(77,177),(78,178),(79,179),(80,180),(81,181),(82,182),(83,183),(84,184),(85,185),(86,186),(87,187),(88,188),(89,189),(90,190),(91,191),(92,192),(93,193),(94,194),(95,195),(96,196),(97,197),(98,198),(99,199),(100,200),(201,322),(202,323),(203,324),(204,325),(205,326),(206,327),(207,328),(208,329),(209,330),(210,331),(211,332),(212,333),(213,334),(214,335),(215,336),(216,337),(217,338),(218,339),(219,340),(220,341),(221,342),(222,343),(223,344),(224,345),(225,346),(226,347),(227,348),(228,349),(229,350),(230,301),(231,302),(232,303),(233,304),(234,305),(235,306),(236,307),(237,308),(238,309),(239,310),(240,311),(241,312),(242,313),(243,314),(244,315),(245,316),(246,317),(247,318),(248,319),(249,320),(250,321),(251,385),(252,386),(253,387),(254,388),(255,389),(256,390),(257,391),(258,392),(259,393),(260,394),(261,395),(262,396),(263,397),(264,398),(265,399),(266,400),(267,351),(268,352),(269,353),(270,354),(271,355),(272,356),(273,357),(274,358),(275,359),(276,360),(277,361),(278,362),(279,363),(280,364),(281,365),(282,366),(283,367),(284,368),(285,369),(286,370),(287,371),(288,372),(289,373),(290,374),(291,375),(292,376),(293,377),(294,378),(295,379),(296,380),(297,381),(298,382),(299,383),(300,384)], [(1,51),(2,52),(3,53),(4,54),(5,55),(6,56),(7,57),(8,58),(9,59),(10,60),(11,61),(12,62),(13,63),(14,64),(15,65),(16,66),(17,67),(18,68),(19,69),(20,70),(21,71),(22,72),(23,73),(24,74),(25,75),(26,76),(27,77),(28,78),(29,79),(30,80),(31,81),(32,82),(33,83),(34,84),(35,85),(36,86),(37,87),(38,88),(39,89),(40,90),(41,91),(42,92),(43,93),(44,94),(45,95),(46,96),(47,97),(48,98),(49,99),(50,100),(101,181),(102,182),(103,183),(104,184),(105,185),(106,186),(107,187),(108,188),(109,189),(110,190),(111,191),(112,192),(113,193),(114,194),(115,195),(116,196),(117,197),(118,198),(119,199),(120,200),(121,151),(122,152),(123,153),(124,154),(125,155),(126,156),(127,157),(128,158),(129,159),(130,160),(131,161),(132,162),(133,163),(134,164),(135,165),(136,166),(137,167),(138,168),(139,169),(140,170),(141,171),(142,172),(143,173),(144,174),(145,175),(146,176),(147,177),(148,178),(149,179),(150,180),(201,260),(202,261),(203,262),(204,263),(205,264),(206,265),(207,266),(208,267),(209,268),(210,269),(211,270),(212,271),(213,272),(214,273),(215,274),(216,275),(217,276),(218,277),(219,278),(220,279),(221,280),(222,281),(223,282),(224,283),(225,284),(226,285),(227,286),(228,287),(229,288),(230,289),(231,290),(232,291),(233,292),(234,293),(235,294),(236,295),(237,296),(238,297),(239,298),(240,299),(241,300),(242,251),(243,252),(244,253),(245,254),(246,255),(247,256),(248,257),(249,258),(250,259),(301,373),(302,374),(303,375),(304,376),(305,377),(306,378),(307,379),(308,380),(309,381),(310,382),(311,383),(312,384),(313,385),(314,386),(315,387),(316,388),(317,389),(318,390),(319,391),(320,392),(321,393),(322,394),(323,395),(324,396),(325,397),(326,398),(327,399),(328,400),(329,351),(330,352),(331,353),(332,354),(333,355),(334,356),(335,357),(336,358),(337,359),(338,360),(339,361),(340,362),(341,363),(342,364),(343,365),(344,366),(345,367),(346,368),(347,369),(348,370),(349,371),(350,372)], [(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)]])
400 conjugacy classes
| class | 1 | 2A | ··· | 2O | 5A | 5B | 5C | 5D | 10A | ··· | 10BH | 25A | ··· | 25T | 50A | ··· | 50KN |
| order | 1 | 2 | ··· | 2 | 5 | 5 | 5 | 5 | 10 | ··· | 10 | 25 | ··· | 25 | 50 | ··· | 50 |
| size | 1 | 1 | ··· | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
400 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||
| image | C1 | C2 | C5 | C10 | C25 | C50 |
| kernel | C23×C50 | C22×C50 | C23×C10 | C22×C10 | C24 | C23 |
| # reps | 1 | 15 | 4 | 60 | 20 | 300 |
Matrix representation of C23×C50 ►in GL4(𝔽101) generated by
| 1 | 0 | 0 | 0 |
| 0 | 100 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 100 |
| 100 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 100 | 0 |
| 0 | 0 | 0 | 1 |
| 100 | 0 | 0 | 0 |
| 0 | 100 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 13 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 87 | 0 |
| 0 | 0 | 0 | 100 |
G:=sub<GL(4,GF(101))| [1,0,0,0,0,100,0,0,0,0,1,0,0,0,0,100],[100,0,0,0,0,1,0,0,0,0,100,0,0,0,0,1],[100,0,0,0,0,100,0,0,0,0,1,0,0,0,0,1],[13,0,0,0,0,17,0,0,0,0,87,0,0,0,0,100] >;
C23×C50 in GAP, Magma, Sage, TeX
C_2^3\times C_{50} % in TeX
G:=Group("C2^3xC50"); // GroupNames label
G:=SmallGroup(400,55);
// by ID
G=gap.SmallGroup(400,55);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-5,-5,178]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^2=d^50=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,c*d=d*c>;
// generators/relations