direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C25⋊2C8, C50⋊2C8, C100.6C4, C4.14D50, C20.53D10, C20.8Dic5, C4.3Dic25, C100.14C22, C22.2Dic25, C25⋊4(C2×C8), (C2×C50).4C4, (C2×C4).5D25, (C2×C100).5C2, C50.13(C2×C4), (C2×C20).13D5, C10.3(C5⋊2C8), (C2×C10).4Dic5, C2.1(C2×Dic25), C10.13(C2×Dic5), C5.(C2×C5⋊2C8), SmallGroup(400,9)
Series: Derived ►Chief ►Lower central ►Upper central
| C25 — C2×C25⋊2C8 |
Generators and relations for C2×C25⋊2C8
G = < a,b,c | a2=b25=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C25⋊2C8
►Regular action on 400 points
Generators in S400
(1 109)(2 110)(3 111)(4 112)(5 113)(6 114)(7 115)(8 116)(9 117)(10 118)(11 119)(12 120)(13 121)(14 122)(15 123)(16 124)(17 125)(18 101)(19 102)(20 103)(21 104)(22 105)(23 106)(24 107)(25 108)(26 131)(27 132)(28 133)(29 134)(30 135)(31 136)(32 137)(33 138)(34 139)(35 140)(36 141)(37 142)(38 143)(39 144)(40 145)(41 146)(42 147)(43 148)(44 149)(45 150)(46 126)(47 127)(48 128)(49 129)(50 130)(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)(201 324)(202 325)(203 301)(204 302)(205 303)(206 304)(207 305)(208 306)(209 307)(210 308)(211 309)(212 310)(213 311)(214 312)(215 313)(216 314)(217 315)(218 316)(219 317)(220 318)(221 319)(222 320)(223 321)(224 322)(225 323)(226 336)(227 337)(228 338)(229 339)(230 340)(231 341)(232 342)(233 343)(234 344)(235 345)(236 346)(237 347)(238 348)(239 349)(240 350)(241 326)(242 327)(243 328)(244 329)(245 330)(246 331)(247 332)(248 333)(249 334)(250 335)(251 356)(252 357)(253 358)(254 359)(255 360)(256 361)(257 362)(258 363)(259 364)(260 365)(261 366)(262 367)(263 368)(264 369)(265 370)(266 371)(267 372)(268 373)(269 374)(270 375)(271 351)(272 352)(273 353)(274 354)(275 355)(276 397)(277 398)(278 399)(279 400)(280 376)(281 377)(282 378)(283 379)(284 380)(285 381)(286 382)(287 383)(288 384)(289 385)(290 386)(291 387)(292 388)(293 389)(294 390)(295 391)(296 392)(297 393)(298 394)(299 395)(300 396)
(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)
(1 300 86 229 49 268 72 222)(2 299 87 228 50 267 73 221)(3 298 88 227 26 266 74 220)(4 297 89 226 27 265 75 219)(5 296 90 250 28 264 51 218)(6 295 91 249 29 263 52 217)(7 294 92 248 30 262 53 216)(8 293 93 247 31 261 54 215)(9 292 94 246 32 260 55 214)(10 291 95 245 33 259 56 213)(11 290 96 244 34 258 57 212)(12 289 97 243 35 257 58 211)(13 288 98 242 36 256 59 210)(14 287 99 241 37 255 60 209)(15 286 100 240 38 254 61 208)(16 285 76 239 39 253 62 207)(17 284 77 238 40 252 63 206)(18 283 78 237 41 251 64 205)(19 282 79 236 42 275 65 204)(20 281 80 235 43 274 66 203)(21 280 81 234 44 273 67 202)(22 279 82 233 45 272 68 201)(23 278 83 232 46 271 69 225)(24 277 84 231 47 270 70 224)(25 276 85 230 48 269 71 223)(101 379 178 347 146 356 164 303)(102 378 179 346 147 355 165 302)(103 377 180 345 148 354 166 301)(104 376 181 344 149 353 167 325)(105 400 182 343 150 352 168 324)(106 399 183 342 126 351 169 323)(107 398 184 341 127 375 170 322)(108 397 185 340 128 374 171 321)(109 396 186 339 129 373 172 320)(110 395 187 338 130 372 173 319)(111 394 188 337 131 371 174 318)(112 393 189 336 132 370 175 317)(113 392 190 335 133 369 151 316)(114 391 191 334 134 368 152 315)(115 390 192 333 135 367 153 314)(116 389 193 332 136 366 154 313)(117 388 194 331 137 365 155 312)(118 387 195 330 138 364 156 311)(119 386 196 329 139 363 157 310)(120 385 197 328 140 362 158 309)(121 384 198 327 141 361 159 308)(122 383 199 326 142 360 160 307)(123 382 200 350 143 359 161 306)(124 381 176 349 144 358 162 305)(125 380 177 348 145 357 163 304)
G:=sub<Sym(400)| (1,109)(2,110)(3,111)(4,112)(5,113)(6,114)(7,115)(8,116)(9,117)(10,118)(11,119)(12,120)(13,121)(14,122)(15,123)(16,124)(17,125)(18,101)(19,102)(20,103)(21,104)(22,105)(23,106)(24,107)(25,108)(26,131)(27,132)(28,133)(29,134)(30,135)(31,136)(32,137)(33,138)(34,139)(35,140)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,148)(44,149)(45,150)(46,126)(47,127)(48,128)(49,129)(50,130)(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)(201,324)(202,325)(203,301)(204,302)(205,303)(206,304)(207,305)(208,306)(209,307)(210,308)(211,309)(212,310)(213,311)(214,312)(215,313)(216,314)(217,315)(218,316)(219,317)(220,318)(221,319)(222,320)(223,321)(224,322)(225,323)(226,336)(227,337)(228,338)(229,339)(230,340)(231,341)(232,342)(233,343)(234,344)(235,345)(236,346)(237,347)(238,348)(239,349)(240,350)(241,326)(242,327)(243,328)(244,329)(245,330)(246,331)(247,332)(248,333)(249,334)(250,335)(251,356)(252,357)(253,358)(254,359)(255,360)(256,361)(257,362)(258,363)(259,364)(260,365)(261,366)(262,367)(263,368)(264,369)(265,370)(266,371)(267,372)(268,373)(269,374)(270,375)(271,351)(272,352)(273,353)(274,354)(275,355)(276,397)(277,398)(278,399)(279,400)(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)(289,385)(290,386)(291,387)(292,388)(293,389)(294,390)(295,391)(296,392)(297,393)(298,394)(299,395)(300,396), (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), (1,300,86,229,49,268,72,222)(2,299,87,228,50,267,73,221)(3,298,88,227,26,266,74,220)(4,297,89,226,27,265,75,219)(5,296,90,250,28,264,51,218)(6,295,91,249,29,263,52,217)(7,294,92,248,30,262,53,216)(8,293,93,247,31,261,54,215)(9,292,94,246,32,260,55,214)(10,291,95,245,33,259,56,213)(11,290,96,244,34,258,57,212)(12,289,97,243,35,257,58,211)(13,288,98,242,36,256,59,210)(14,287,99,241,37,255,60,209)(15,286,100,240,38,254,61,208)(16,285,76,239,39,253,62,207)(17,284,77,238,40,252,63,206)(18,283,78,237,41,251,64,205)(19,282,79,236,42,275,65,204)(20,281,80,235,43,274,66,203)(21,280,81,234,44,273,67,202)(22,279,82,233,45,272,68,201)(23,278,83,232,46,271,69,225)(24,277,84,231,47,270,70,224)(25,276,85,230,48,269,71,223)(101,379,178,347,146,356,164,303)(102,378,179,346,147,355,165,302)(103,377,180,345,148,354,166,301)(104,376,181,344,149,353,167,325)(105,400,182,343,150,352,168,324)(106,399,183,342,126,351,169,323)(107,398,184,341,127,375,170,322)(108,397,185,340,128,374,171,321)(109,396,186,339,129,373,172,320)(110,395,187,338,130,372,173,319)(111,394,188,337,131,371,174,318)(112,393,189,336,132,370,175,317)(113,392,190,335,133,369,151,316)(114,391,191,334,134,368,152,315)(115,390,192,333,135,367,153,314)(116,389,193,332,136,366,154,313)(117,388,194,331,137,365,155,312)(118,387,195,330,138,364,156,311)(119,386,196,329,139,363,157,310)(120,385,197,328,140,362,158,309)(121,384,198,327,141,361,159,308)(122,383,199,326,142,360,160,307)(123,382,200,350,143,359,161,306)(124,381,176,349,144,358,162,305)(125,380,177,348,145,357,163,304)>;
G:=Group( (1,109)(2,110)(3,111)(4,112)(5,113)(6,114)(7,115)(8,116)(9,117)(10,118)(11,119)(12,120)(13,121)(14,122)(15,123)(16,124)(17,125)(18,101)(19,102)(20,103)(21,104)(22,105)(23,106)(24,107)(25,108)(26,131)(27,132)(28,133)(29,134)(30,135)(31,136)(32,137)(33,138)(34,139)(35,140)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,148)(44,149)(45,150)(46,126)(47,127)(48,128)(49,129)(50,130)(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)(201,324)(202,325)(203,301)(204,302)(205,303)(206,304)(207,305)(208,306)(209,307)(210,308)(211,309)(212,310)(213,311)(214,312)(215,313)(216,314)(217,315)(218,316)(219,317)(220,318)(221,319)(222,320)(223,321)(224,322)(225,323)(226,336)(227,337)(228,338)(229,339)(230,340)(231,341)(232,342)(233,343)(234,344)(235,345)(236,346)(237,347)(238,348)(239,349)(240,350)(241,326)(242,327)(243,328)(244,329)(245,330)(246,331)(247,332)(248,333)(249,334)(250,335)(251,356)(252,357)(253,358)(254,359)(255,360)(256,361)(257,362)(258,363)(259,364)(260,365)(261,366)(262,367)(263,368)(264,369)(265,370)(266,371)(267,372)(268,373)(269,374)(270,375)(271,351)(272,352)(273,353)(274,354)(275,355)(276,397)(277,398)(278,399)(279,400)(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)(289,385)(290,386)(291,387)(292,388)(293,389)(294,390)(295,391)(296,392)(297,393)(298,394)(299,395)(300,396), (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), (1,300,86,229,49,268,72,222)(2,299,87,228,50,267,73,221)(3,298,88,227,26,266,74,220)(4,297,89,226,27,265,75,219)(5,296,90,250,28,264,51,218)(6,295,91,249,29,263,52,217)(7,294,92,248,30,262,53,216)(8,293,93,247,31,261,54,215)(9,292,94,246,32,260,55,214)(10,291,95,245,33,259,56,213)(11,290,96,244,34,258,57,212)(12,289,97,243,35,257,58,211)(13,288,98,242,36,256,59,210)(14,287,99,241,37,255,60,209)(15,286,100,240,38,254,61,208)(16,285,76,239,39,253,62,207)(17,284,77,238,40,252,63,206)(18,283,78,237,41,251,64,205)(19,282,79,236,42,275,65,204)(20,281,80,235,43,274,66,203)(21,280,81,234,44,273,67,202)(22,279,82,233,45,272,68,201)(23,278,83,232,46,271,69,225)(24,277,84,231,47,270,70,224)(25,276,85,230,48,269,71,223)(101,379,178,347,146,356,164,303)(102,378,179,346,147,355,165,302)(103,377,180,345,148,354,166,301)(104,376,181,344,149,353,167,325)(105,400,182,343,150,352,168,324)(106,399,183,342,126,351,169,323)(107,398,184,341,127,375,170,322)(108,397,185,340,128,374,171,321)(109,396,186,339,129,373,172,320)(110,395,187,338,130,372,173,319)(111,394,188,337,131,371,174,318)(112,393,189,336,132,370,175,317)(113,392,190,335,133,369,151,316)(114,391,191,334,134,368,152,315)(115,390,192,333,135,367,153,314)(116,389,193,332,136,366,154,313)(117,388,194,331,137,365,155,312)(118,387,195,330,138,364,156,311)(119,386,196,329,139,363,157,310)(120,385,197,328,140,362,158,309)(121,384,198,327,141,361,159,308)(122,383,199,326,142,360,160,307)(123,382,200,350,143,359,161,306)(124,381,176,349,144,358,162,305)(125,380,177,348,145,357,163,304) );
G=PermutationGroup([[(1,109),(2,110),(3,111),(4,112),(5,113),(6,114),(7,115),(8,116),(9,117),(10,118),(11,119),(12,120),(13,121),(14,122),(15,123),(16,124),(17,125),(18,101),(19,102),(20,103),(21,104),(22,105),(23,106),(24,107),(25,108),(26,131),(27,132),(28,133),(29,134),(30,135),(31,136),(32,137),(33,138),(34,139),(35,140),(36,141),(37,142),(38,143),(39,144),(40,145),(41,146),(42,147),(43,148),(44,149),(45,150),(46,126),(47,127),(48,128),(49,129),(50,130),(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),(201,324),(202,325),(203,301),(204,302),(205,303),(206,304),(207,305),(208,306),(209,307),(210,308),(211,309),(212,310),(213,311),(214,312),(215,313),(216,314),(217,315),(218,316),(219,317),(220,318),(221,319),(222,320),(223,321),(224,322),(225,323),(226,336),(227,337),(228,338),(229,339),(230,340),(231,341),(232,342),(233,343),(234,344),(235,345),(236,346),(237,347),(238,348),(239,349),(240,350),(241,326),(242,327),(243,328),(244,329),(245,330),(246,331),(247,332),(248,333),(249,334),(250,335),(251,356),(252,357),(253,358),(254,359),(255,360),(256,361),(257,362),(258,363),(259,364),(260,365),(261,366),(262,367),(263,368),(264,369),(265,370),(266,371),(267,372),(268,373),(269,374),(270,375),(271,351),(272,352),(273,353),(274,354),(275,355),(276,397),(277,398),(278,399),(279,400),(280,376),(281,377),(282,378),(283,379),(284,380),(285,381),(286,382),(287,383),(288,384),(289,385),(290,386),(291,387),(292,388),(293,389),(294,390),(295,391),(296,392),(297,393),(298,394),(299,395),(300,396)], [(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)], [(1,300,86,229,49,268,72,222),(2,299,87,228,50,267,73,221),(3,298,88,227,26,266,74,220),(4,297,89,226,27,265,75,219),(5,296,90,250,28,264,51,218),(6,295,91,249,29,263,52,217),(7,294,92,248,30,262,53,216),(8,293,93,247,31,261,54,215),(9,292,94,246,32,260,55,214),(10,291,95,245,33,259,56,213),(11,290,96,244,34,258,57,212),(12,289,97,243,35,257,58,211),(13,288,98,242,36,256,59,210),(14,287,99,241,37,255,60,209),(15,286,100,240,38,254,61,208),(16,285,76,239,39,253,62,207),(17,284,77,238,40,252,63,206),(18,283,78,237,41,251,64,205),(19,282,79,236,42,275,65,204),(20,281,80,235,43,274,66,203),(21,280,81,234,44,273,67,202),(22,279,82,233,45,272,68,201),(23,278,83,232,46,271,69,225),(24,277,84,231,47,270,70,224),(25,276,85,230,48,269,71,223),(101,379,178,347,146,356,164,303),(102,378,179,346,147,355,165,302),(103,377,180,345,148,354,166,301),(104,376,181,344,149,353,167,325),(105,400,182,343,150,352,168,324),(106,399,183,342,126,351,169,323),(107,398,184,341,127,375,170,322),(108,397,185,340,128,374,171,321),(109,396,186,339,129,373,172,320),(110,395,187,338,130,372,173,319),(111,394,188,337,131,371,174,318),(112,393,189,336,132,370,175,317),(113,392,190,335,133,369,151,316),(114,391,191,334,134,368,152,315),(115,390,192,333,135,367,153,314),(116,389,193,332,136,366,154,313),(117,388,194,331,137,365,155,312),(118,387,195,330,138,364,156,311),(119,386,196,329,139,363,157,310),(120,385,197,328,140,362,158,309),(121,384,198,327,141,361,159,308),(122,383,199,326,142,360,160,307),(123,382,200,350,143,359,161,306),(124,381,176,349,144,358,162,305),(125,380,177,348,145,357,163,304)]])
112 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10F | 20A | ··· | 20H | 25A | ··· | 25J | 50A | ··· | 50AD | 100A | ··· | 100AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 25 | ··· | 25 | 50 | ··· | 50 | 100 | ··· | 100 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 25 | ··· | 25 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | + | - | + | - | |||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D5 | Dic5 | D10 | Dic5 | C5⋊2C8 | D25 | Dic25 | D50 | Dic25 | C25⋊2C8 |
| kernel | C2×C25⋊2C8 | C25⋊2C8 | C2×C100 | C100 | C2×C50 | C50 | C2×C20 | C20 | C20 | C2×C10 | C10 | C2×C4 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 8 | 10 | 10 | 10 | 10 | 40 |
Matrix representation of C2×C25⋊2C8 ►in GL3(𝔽401) generated by
| 400 | 0 | 0 |
| 0 | 400 | 0 |
| 0 | 0 | 400 |
| 1 | 0 | 0 |
| 0 | 302 | 37 |
| 0 | 230 | 72 |
| 381 | 0 | 0 |
| 0 | 101 | 63 |
| 0 | 86 | 300 |
G:=sub<GL(3,GF(401))| [400,0,0,0,400,0,0,0,400],[1,0,0,0,302,230,0,37,72],[381,0,0,0,101,86,0,63,300] >;
C2×C25⋊2C8 in GAP, Magma, Sage, TeX
C_2\times C_{25}\rtimes_2C_8 % in TeX
G:=Group("C2xC25:2C8"); // GroupNames label
G:=SmallGroup(400,9);
// by ID
G=gap.SmallGroup(400,9);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-5,-5,24,50,4324,628,11525]);
// Polycyclic
G:=Group<a,b,c|a^2=b^25=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export