direct product, abelian, monomial
Aliases: C2×C10×C20, SmallGroup(400,201)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C2×C10×C20 |
| C1 — C2×C10×C20 |
| C1 — C2×C10×C20 |
Generators and relations for C2×C10×C20
G = < a,b,c | a2=b10=c20=1, ab=ba, ac=ca, bc=cb >
Subgroups: 216, all normal (8 characteristic)
C1, C2, C2, C4, C22, C5, C2×C4, C23, C10, C22×C4, C20, C2×C10, C52, C2×C20, C22×C10, C5×C10, C5×C10, C22×C20, C5×C20, C102, C10×C20, C2×C102, C2×C10×C20
Quotients: C1, C2, C4, C22, C5, C2×C4, C23, C10, C22×C4, C20, C2×C10, C52, C2×C20, C22×C10, C5×C10, C22×C20, C5×C20, C102, C10×C20, C2×C102, C2×C10×C20
►Regular action on 400 points
Generators in S400
(1 322)(2 323)(3 324)(4 325)(5 326)(6 327)(7 328)(8 329)(9 330)(10 331)(11 332)(12 333)(13 334)(14 335)(15 336)(16 337)(17 338)(18 339)(19 340)(20 321)(21 78)(22 79)(23 80)(24 61)(25 62)(26 63)(27 64)(28 65)(29 66)(30 67)(31 68)(32 69)(33 70)(34 71)(35 72)(36 73)(37 74)(38 75)(39 76)(40 77)(41 383)(42 384)(43 385)(44 386)(45 387)(46 388)(47 389)(48 390)(49 391)(50 392)(51 393)(52 394)(53 395)(54 396)(55 397)(56 398)(57 399)(58 400)(59 381)(60 382)(81 168)(82 169)(83 170)(84 171)(85 172)(86 173)(87 174)(88 175)(89 176)(90 177)(91 178)(92 179)(93 180)(94 161)(95 162)(96 163)(97 164)(98 165)(99 166)(100 167)(101 138)(102 139)(103 140)(104 121)(105 122)(106 123)(107 124)(108 125)(109 126)(110 127)(111 128)(112 129)(113 130)(114 131)(115 132)(116 133)(117 134)(118 135)(119 136)(120 137)(141 358)(142 359)(143 360)(144 341)(145 342)(146 343)(147 344)(148 345)(149 346)(150 347)(151 348)(152 349)(153 350)(154 351)(155 352)(156 353)(157 354)(158 355)(159 356)(160 357)(181 231)(182 232)(183 233)(184 234)(185 235)(186 236)(187 237)(188 238)(189 239)(190 240)(191 221)(192 222)(193 223)(194 224)(195 225)(196 226)(197 227)(198 228)(199 229)(200 230)(201 276)(202 277)(203 278)(204 279)(205 280)(206 261)(207 262)(208 263)(209 264)(210 265)(211 266)(212 267)(213 268)(214 269)(215 270)(216 271)(217 272)(218 273)(219 274)(220 275)(241 316)(242 317)(243 318)(244 319)(245 320)(246 301)(247 302)(248 303)(249 304)(250 305)(251 306)(252 307)(253 308)(254 309)(255 310)(256 311)(257 312)(258 313)(259 314)(260 315)(281 374)(282 375)(283 376)(284 377)(285 378)(286 379)(287 380)(288 361)(289 362)(290 363)(291 364)(292 365)(293 366)(294 367)(295 368)(296 369)(297 370)(298 371)(299 372)(300 373)
(1 101 392 354 64 225 368 217 168 242)(2 102 393 355 65 226 369 218 169 243)(3 103 394 356 66 227 370 219 170 244)(4 104 395 357 67 228 371 220 171 245)(5 105 396 358 68 229 372 201 172 246)(6 106 397 359 69 230 373 202 173 247)(7 107 398 360 70 231 374 203 174 248)(8 108 399 341 71 232 375 204 175 249)(9 109 400 342 72 233 376 205 176 250)(10 110 381 343 73 234 377 206 177 251)(11 111 382 344 74 235 378 207 178 252)(12 112 383 345 75 236 379 208 179 253)(13 113 384 346 76 237 380 209 180 254)(14 114 385 347 77 238 361 210 161 255)(15 115 386 348 78 239 362 211 162 256)(16 116 387 349 79 240 363 212 163 257)(17 117 388 350 80 221 364 213 164 258)(18 118 389 351 61 222 365 214 165 259)(19 119 390 352 62 223 366 215 166 260)(20 120 391 353 63 224 367 216 167 241)(21 189 289 266 95 311 336 132 44 151)(22 190 290 267 96 312 337 133 45 152)(23 191 291 268 97 313 338 134 46 153)(24 192 292 269 98 314 339 135 47 154)(25 193 293 270 99 315 340 136 48 155)(26 194 294 271 100 316 321 137 49 156)(27 195 295 272 81 317 322 138 50 157)(28 196 296 273 82 318 323 139 51 158)(29 197 297 274 83 319 324 140 52 159)(30 198 298 275 84 320 325 121 53 160)(31 199 299 276 85 301 326 122 54 141)(32 200 300 277 86 302 327 123 55 142)(33 181 281 278 87 303 328 124 56 143)(34 182 282 279 88 304 329 125 57 144)(35 183 283 280 89 305 330 126 58 145)(36 184 284 261 90 306 331 127 59 146)(37 185 285 262 91 307 332 128 60 147)(38 186 286 263 92 308 333 129 41 148)(39 187 287 264 93 309 334 130 42 149)(40 188 288 265 94 310 335 131 43 150)
(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)| (1,322)(2,323)(3,324)(4,325)(5,326)(6,327)(7,328)(8,329)(9,330)(10,331)(11,332)(12,333)(13,334)(14,335)(15,336)(16,337)(17,338)(18,339)(19,340)(20,321)(21,78)(22,79)(23,80)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(39,76)(40,77)(41,383)(42,384)(43,385)(44,386)(45,387)(46,388)(47,389)(48,390)(49,391)(50,392)(51,393)(52,394)(53,395)(54,396)(55,397)(56,398)(57,399)(58,400)(59,381)(60,382)(81,168)(82,169)(83,170)(84,171)(85,172)(86,173)(87,174)(88,175)(89,176)(90,177)(91,178)(92,179)(93,180)(94,161)(95,162)(96,163)(97,164)(98,165)(99,166)(100,167)(101,138)(102,139)(103,140)(104,121)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,129)(113,130)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(120,137)(141,358)(142,359)(143,360)(144,341)(145,342)(146,343)(147,344)(148,345)(149,346)(150,347)(151,348)(152,349)(153,350)(154,351)(155,352)(156,353)(157,354)(158,355)(159,356)(160,357)(181,231)(182,232)(183,233)(184,234)(185,235)(186,236)(187,237)(188,238)(189,239)(190,240)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,276)(202,277)(203,278)(204,279)(205,280)(206,261)(207,262)(208,263)(209,264)(210,265)(211,266)(212,267)(213,268)(214,269)(215,270)(216,271)(217,272)(218,273)(219,274)(220,275)(241,316)(242,317)(243,318)(244,319)(245,320)(246,301)(247,302)(248,303)(249,304)(250,305)(251,306)(252,307)(253,308)(254,309)(255,310)(256,311)(257,312)(258,313)(259,314)(260,315)(281,374)(282,375)(283,376)(284,377)(285,378)(286,379)(287,380)(288,361)(289,362)(290,363)(291,364)(292,365)(293,366)(294,367)(295,368)(296,369)(297,370)(298,371)(299,372)(300,373), (1,101,392,354,64,225,368,217,168,242)(2,102,393,355,65,226,369,218,169,243)(3,103,394,356,66,227,370,219,170,244)(4,104,395,357,67,228,371,220,171,245)(5,105,396,358,68,229,372,201,172,246)(6,106,397,359,69,230,373,202,173,247)(7,107,398,360,70,231,374,203,174,248)(8,108,399,341,71,232,375,204,175,249)(9,109,400,342,72,233,376,205,176,250)(10,110,381,343,73,234,377,206,177,251)(11,111,382,344,74,235,378,207,178,252)(12,112,383,345,75,236,379,208,179,253)(13,113,384,346,76,237,380,209,180,254)(14,114,385,347,77,238,361,210,161,255)(15,115,386,348,78,239,362,211,162,256)(16,116,387,349,79,240,363,212,163,257)(17,117,388,350,80,221,364,213,164,258)(18,118,389,351,61,222,365,214,165,259)(19,119,390,352,62,223,366,215,166,260)(20,120,391,353,63,224,367,216,167,241)(21,189,289,266,95,311,336,132,44,151)(22,190,290,267,96,312,337,133,45,152)(23,191,291,268,97,313,338,134,46,153)(24,192,292,269,98,314,339,135,47,154)(25,193,293,270,99,315,340,136,48,155)(26,194,294,271,100,316,321,137,49,156)(27,195,295,272,81,317,322,138,50,157)(28,196,296,273,82,318,323,139,51,158)(29,197,297,274,83,319,324,140,52,159)(30,198,298,275,84,320,325,121,53,160)(31,199,299,276,85,301,326,122,54,141)(32,200,300,277,86,302,327,123,55,142)(33,181,281,278,87,303,328,124,56,143)(34,182,282,279,88,304,329,125,57,144)(35,183,283,280,89,305,330,126,58,145)(36,184,284,261,90,306,331,127,59,146)(37,185,285,262,91,307,332,128,60,147)(38,186,286,263,92,308,333,129,41,148)(39,187,287,264,93,309,334,130,42,149)(40,188,288,265,94,310,335,131,43,150), (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( (1,322)(2,323)(3,324)(4,325)(5,326)(6,327)(7,328)(8,329)(9,330)(10,331)(11,332)(12,333)(13,334)(14,335)(15,336)(16,337)(17,338)(18,339)(19,340)(20,321)(21,78)(22,79)(23,80)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(39,76)(40,77)(41,383)(42,384)(43,385)(44,386)(45,387)(46,388)(47,389)(48,390)(49,391)(50,392)(51,393)(52,394)(53,395)(54,396)(55,397)(56,398)(57,399)(58,400)(59,381)(60,382)(81,168)(82,169)(83,170)(84,171)(85,172)(86,173)(87,174)(88,175)(89,176)(90,177)(91,178)(92,179)(93,180)(94,161)(95,162)(96,163)(97,164)(98,165)(99,166)(100,167)(101,138)(102,139)(103,140)(104,121)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,129)(113,130)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(120,137)(141,358)(142,359)(143,360)(144,341)(145,342)(146,343)(147,344)(148,345)(149,346)(150,347)(151,348)(152,349)(153,350)(154,351)(155,352)(156,353)(157,354)(158,355)(159,356)(160,357)(181,231)(182,232)(183,233)(184,234)(185,235)(186,236)(187,237)(188,238)(189,239)(190,240)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,276)(202,277)(203,278)(204,279)(205,280)(206,261)(207,262)(208,263)(209,264)(210,265)(211,266)(212,267)(213,268)(214,269)(215,270)(216,271)(217,272)(218,273)(219,274)(220,275)(241,316)(242,317)(243,318)(244,319)(245,320)(246,301)(247,302)(248,303)(249,304)(250,305)(251,306)(252,307)(253,308)(254,309)(255,310)(256,311)(257,312)(258,313)(259,314)(260,315)(281,374)(282,375)(283,376)(284,377)(285,378)(286,379)(287,380)(288,361)(289,362)(290,363)(291,364)(292,365)(293,366)(294,367)(295,368)(296,369)(297,370)(298,371)(299,372)(300,373), (1,101,392,354,64,225,368,217,168,242)(2,102,393,355,65,226,369,218,169,243)(3,103,394,356,66,227,370,219,170,244)(4,104,395,357,67,228,371,220,171,245)(5,105,396,358,68,229,372,201,172,246)(6,106,397,359,69,230,373,202,173,247)(7,107,398,360,70,231,374,203,174,248)(8,108,399,341,71,232,375,204,175,249)(9,109,400,342,72,233,376,205,176,250)(10,110,381,343,73,234,377,206,177,251)(11,111,382,344,74,235,378,207,178,252)(12,112,383,345,75,236,379,208,179,253)(13,113,384,346,76,237,380,209,180,254)(14,114,385,347,77,238,361,210,161,255)(15,115,386,348,78,239,362,211,162,256)(16,116,387,349,79,240,363,212,163,257)(17,117,388,350,80,221,364,213,164,258)(18,118,389,351,61,222,365,214,165,259)(19,119,390,352,62,223,366,215,166,260)(20,120,391,353,63,224,367,216,167,241)(21,189,289,266,95,311,336,132,44,151)(22,190,290,267,96,312,337,133,45,152)(23,191,291,268,97,313,338,134,46,153)(24,192,292,269,98,314,339,135,47,154)(25,193,293,270,99,315,340,136,48,155)(26,194,294,271,100,316,321,137,49,156)(27,195,295,272,81,317,322,138,50,157)(28,196,296,273,82,318,323,139,51,158)(29,197,297,274,83,319,324,140,52,159)(30,198,298,275,84,320,325,121,53,160)(31,199,299,276,85,301,326,122,54,141)(32,200,300,277,86,302,327,123,55,142)(33,181,281,278,87,303,328,124,56,143)(34,182,282,279,88,304,329,125,57,144)(35,183,283,280,89,305,330,126,58,145)(36,184,284,261,90,306,331,127,59,146)(37,185,285,262,91,307,332,128,60,147)(38,186,286,263,92,308,333,129,41,148)(39,187,287,264,93,309,334,130,42,149)(40,188,288,265,94,310,335,131,43,150), (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([[(1,322),(2,323),(3,324),(4,325),(5,326),(6,327),(7,328),(8,329),(9,330),(10,331),(11,332),(12,333),(13,334),(14,335),(15,336),(16,337),(17,338),(18,339),(19,340),(20,321),(21,78),(22,79),(23,80),(24,61),(25,62),(26,63),(27,64),(28,65),(29,66),(30,67),(31,68),(32,69),(33,70),(34,71),(35,72),(36,73),(37,74),(38,75),(39,76),(40,77),(41,383),(42,384),(43,385),(44,386),(45,387),(46,388),(47,389),(48,390),(49,391),(50,392),(51,393),(52,394),(53,395),(54,396),(55,397),(56,398),(57,399),(58,400),(59,381),(60,382),(81,168),(82,169),(83,170),(84,171),(85,172),(86,173),(87,174),(88,175),(89,176),(90,177),(91,178),(92,179),(93,180),(94,161),(95,162),(96,163),(97,164),(98,165),(99,166),(100,167),(101,138),(102,139),(103,140),(104,121),(105,122),(106,123),(107,124),(108,125),(109,126),(110,127),(111,128),(112,129),(113,130),(114,131),(115,132),(116,133),(117,134),(118,135),(119,136),(120,137),(141,358),(142,359),(143,360),(144,341),(145,342),(146,343),(147,344),(148,345),(149,346),(150,347),(151,348),(152,349),(153,350),(154,351),(155,352),(156,353),(157,354),(158,355),(159,356),(160,357),(181,231),(182,232),(183,233),(184,234),(185,235),(186,236),(187,237),(188,238),(189,239),(190,240),(191,221),(192,222),(193,223),(194,224),(195,225),(196,226),(197,227),(198,228),(199,229),(200,230),(201,276),(202,277),(203,278),(204,279),(205,280),(206,261),(207,262),(208,263),(209,264),(210,265),(211,266),(212,267),(213,268),(214,269),(215,270),(216,271),(217,272),(218,273),(219,274),(220,275),(241,316),(242,317),(243,318),(244,319),(245,320),(246,301),(247,302),(248,303),(249,304),(250,305),(251,306),(252,307),(253,308),(254,309),(255,310),(256,311),(257,312),(258,313),(259,314),(260,315),(281,374),(282,375),(283,376),(284,377),(285,378),(286,379),(287,380),(288,361),(289,362),(290,363),(291,364),(292,365),(293,366),(294,367),(295,368),(296,369),(297,370),(298,371),(299,372),(300,373)], [(1,101,392,354,64,225,368,217,168,242),(2,102,393,355,65,226,369,218,169,243),(3,103,394,356,66,227,370,219,170,244),(4,104,395,357,67,228,371,220,171,245),(5,105,396,358,68,229,372,201,172,246),(6,106,397,359,69,230,373,202,173,247),(7,107,398,360,70,231,374,203,174,248),(8,108,399,341,71,232,375,204,175,249),(9,109,400,342,72,233,376,205,176,250),(10,110,381,343,73,234,377,206,177,251),(11,111,382,344,74,235,378,207,178,252),(12,112,383,345,75,236,379,208,179,253),(13,113,384,346,76,237,380,209,180,254),(14,114,385,347,77,238,361,210,161,255),(15,115,386,348,78,239,362,211,162,256),(16,116,387,349,79,240,363,212,163,257),(17,117,388,350,80,221,364,213,164,258),(18,118,389,351,61,222,365,214,165,259),(19,119,390,352,62,223,366,215,166,260),(20,120,391,353,63,224,367,216,167,241),(21,189,289,266,95,311,336,132,44,151),(22,190,290,267,96,312,337,133,45,152),(23,191,291,268,97,313,338,134,46,153),(24,192,292,269,98,314,339,135,47,154),(25,193,293,270,99,315,340,136,48,155),(26,194,294,271,100,316,321,137,49,156),(27,195,295,272,81,317,322,138,50,157),(28,196,296,273,82,318,323,139,51,158),(29,197,297,274,83,319,324,140,52,159),(30,198,298,275,84,320,325,121,53,160),(31,199,299,276,85,301,326,122,54,141),(32,200,300,277,86,302,327,123,55,142),(33,181,281,278,87,303,328,124,56,143),(34,182,282,279,88,304,329,125,57,144),(35,183,283,280,89,305,330,126,58,145),(36,184,284,261,90,306,331,127,59,146),(37,185,285,262,91,307,332,128,60,147),(38,186,286,263,92,308,333,129,41,148),(39,187,287,264,93,309,334,130,42,149),(40,188,288,265,94,310,335,131,43,150)], [(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 | ··· | 2G | 4A | ··· | 4H | 5A | ··· | 5X | 10A | ··· | 10FL | 20A | ··· | 20GJ |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 5 | ··· | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
400 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||
| image | C1 | C2 | C2 | C4 | C5 | C10 | C10 | C20 |
| kernel | C2×C10×C20 | C10×C20 | C2×C102 | C102 | C22×C20 | C2×C20 | C22×C10 | C2×C10 |
| # reps | 1 | 6 | 1 | 8 | 24 | 144 | 24 | 192 |
Matrix representation of C2×C10×C20 ►in GL3(𝔽41) generated by
| 40 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 23 | 0 | 0 |
| 0 | 23 | 0 |
| 0 | 0 | 4 |
| 4 | 0 | 0 |
| 0 | 4 | 0 |
| 0 | 0 | 5 |
G:=sub<GL(3,GF(41))| [40,0,0,0,1,0,0,0,1],[23,0,0,0,23,0,0,0,4],[4,0,0,0,4,0,0,0,5] >;
C2×C10×C20 in GAP, Magma, Sage, TeX
C_2\times C_{10}\times C_{20} % in TeX
G:=Group("C2xC10xC20"); // GroupNames label
G:=SmallGroup(400,201);
// by ID
G=gap.SmallGroup(400,201);
# by ID
G:=PCGroup([6,-2,-2,-2,-5,-5,-2,1200]);
// Polycyclic
G:=Group<a,b,c|a^2=b^10=c^20=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations