direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C25⋊C8, C50⋊C8, Dic25.2C4, Dic25.7C22, C25⋊2(C2×C8), C10.2(C5⋊C8), C50.5(C2×C4), (C2×C50).1C4, (C2×C10).1F5, C10.10(C2×F5), C22.2(C25⋊C4), (C2×Dic25).4C2, C5.(C2×C5⋊C8), C2.3(C2×C25⋊C4), SmallGroup(400,32)
Series: Derived ►Chief ►Lower central ►Upper central
| C25 — C2×C25⋊C8 |
Generators and relations for C2×C25⋊C8
G = < a,b,c | a2=b25=c8=1, ab=ba, ac=ca, cbc-1=b18 >
Smallest permutation representation of C2×C25⋊C8
►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)(26 130)(27 131)(28 132)(29 133)(30 134)(31 135)(32 136)(33 137)(34 138)(35 139)(36 140)(37 141)(38 142)(39 143)(40 144)(41 145)(42 146)(43 147)(44 148)(45 149)(46 150)(47 126)(48 127)(49 128)(50 129)(51 163)(52 164)(53 165)(54 166)(55 167)(56 168)(57 169)(58 170)(59 171)(60 172)(61 173)(62 174)(63 175)(64 151)(65 152)(66 153)(67 154)(68 155)(69 156)(70 157)(71 158)(72 159)(73 160)(74 161)(75 162)(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)(201 321)(202 322)(203 323)(204 324)(205 325)(206 301)(207 302)(208 303)(209 304)(210 305)(211 306)(212 307)(213 308)(214 309)(215 310)(216 311)(217 312)(218 313)(219 314)(220 315)(221 316)(222 317)(223 318)(224 319)(225 320)(226 340)(227 341)(228 342)(229 343)(230 344)(231 345)(232 346)(233 347)(234 348)(235 349)(236 350)(237 326)(238 327)(239 328)(240 329)(241 330)(242 331)(243 332)(244 333)(245 334)(246 335)(247 336)(248 337)(249 338)(250 339)(251 368)(252 369)(253 370)(254 371)(255 372)(256 373)(257 374)(258 375)(259 351)(260 352)(261 353)(262 354)(263 355)(264 356)(265 357)(266 358)(267 359)(268 360)(269 361)(270 362)(271 363)(272 364)(273 365)(274 366)(275 367)(276 387)(277 388)(278 389)(279 390)(280 391)(281 392)(282 393)(283 394)(284 395)(285 396)(286 397)(287 398)(288 399)(289 400)(290 376)(291 377)(292 378)(293 379)(294 380)(295 381)(296 382)(297 383)(298 384)(299 385)(300 386)
(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)
(1 379 94 335 30 351 56 307)(2 386 93 328 31 358 55 325)(3 393 92 346 32 365 54 318)(4 400 91 339 33 372 53 311)(5 382 90 332 34 354 52 304)(6 389 89 350 35 361 51 322)(7 396 88 343 36 368 75 315)(8 378 87 336 37 375 74 308)(9 385 86 329 38 357 73 301)(10 392 85 347 39 364 72 319)(11 399 84 340 40 371 71 312)(12 381 83 333 41 353 70 305)(13 388 82 326 42 360 69 323)(14 395 81 344 43 367 68 316)(15 377 80 337 44 374 67 309)(16 384 79 330 45 356 66 302)(17 391 78 348 46 363 65 320)(18 398 77 341 47 370 64 313)(19 380 76 334 48 352 63 306)(20 387 100 327 49 359 62 324)(21 394 99 345 50 366 61 317)(22 376 98 338 26 373 60 310)(23 383 97 331 27 355 59 303)(24 390 96 349 28 362 58 321)(25 397 95 342 29 369 57 314)(101 287 177 227 126 253 151 218)(102 294 176 245 127 260 175 211)(103 276 200 238 128 267 174 204)(104 283 199 231 129 274 173 222)(105 290 198 249 130 256 172 215)(106 297 197 242 131 263 171 208)(107 279 196 235 132 270 170 201)(108 286 195 228 133 252 169 219)(109 293 194 246 134 259 168 212)(110 300 193 239 135 266 167 205)(111 282 192 232 136 273 166 223)(112 289 191 250 137 255 165 216)(113 296 190 243 138 262 164 209)(114 278 189 236 139 269 163 202)(115 285 188 229 140 251 162 220)(116 292 187 247 141 258 161 213)(117 299 186 240 142 265 160 206)(118 281 185 233 143 272 159 224)(119 288 184 226 144 254 158 217)(120 295 183 244 145 261 157 210)(121 277 182 237 146 268 156 203)(122 284 181 230 147 275 155 221)(123 291 180 248 148 257 154 214)(124 298 179 241 149 264 153 207)(125 280 178 234 150 271 152 225)
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)(26,130)(27,131)(28,132)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,126)(48,127)(49,128)(50,129)(51,163)(52,164)(53,165)(54,166)(55,167)(56,168)(57,169)(58,170)(59,171)(60,172)(61,173)(62,174)(63,175)(64,151)(65,152)(66,153)(67,154)(68,155)(69,156)(70,157)(71,158)(72,159)(73,160)(74,161)(75,162)(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)(201,321)(202,322)(203,323)(204,324)(205,325)(206,301)(207,302)(208,303)(209,304)(210,305)(211,306)(212,307)(213,308)(214,309)(215,310)(216,311)(217,312)(218,313)(219,314)(220,315)(221,316)(222,317)(223,318)(224,319)(225,320)(226,340)(227,341)(228,342)(229,343)(230,344)(231,345)(232,346)(233,347)(234,348)(235,349)(236,350)(237,326)(238,327)(239,328)(240,329)(241,330)(242,331)(243,332)(244,333)(245,334)(246,335)(247,336)(248,337)(249,338)(250,339)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,351)(260,352)(261,353)(262,354)(263,355)(264,356)(265,357)(266,358)(267,359)(268,360)(269,361)(270,362)(271,363)(272,364)(273,365)(274,366)(275,367)(276,387)(277,388)(278,389)(279,390)(280,391)(281,392)(282,393)(283,394)(284,395)(285,396)(286,397)(287,398)(288,399)(289,400)(290,376)(291,377)(292,378)(293,379)(294,380)(295,381)(296,382)(297,383)(298,384)(299,385)(300,386), (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), (1,379,94,335,30,351,56,307)(2,386,93,328,31,358,55,325)(3,393,92,346,32,365,54,318)(4,400,91,339,33,372,53,311)(5,382,90,332,34,354,52,304)(6,389,89,350,35,361,51,322)(7,396,88,343,36,368,75,315)(8,378,87,336,37,375,74,308)(9,385,86,329,38,357,73,301)(10,392,85,347,39,364,72,319)(11,399,84,340,40,371,71,312)(12,381,83,333,41,353,70,305)(13,388,82,326,42,360,69,323)(14,395,81,344,43,367,68,316)(15,377,80,337,44,374,67,309)(16,384,79,330,45,356,66,302)(17,391,78,348,46,363,65,320)(18,398,77,341,47,370,64,313)(19,380,76,334,48,352,63,306)(20,387,100,327,49,359,62,324)(21,394,99,345,50,366,61,317)(22,376,98,338,26,373,60,310)(23,383,97,331,27,355,59,303)(24,390,96,349,28,362,58,321)(25,397,95,342,29,369,57,314)(101,287,177,227,126,253,151,218)(102,294,176,245,127,260,175,211)(103,276,200,238,128,267,174,204)(104,283,199,231,129,274,173,222)(105,290,198,249,130,256,172,215)(106,297,197,242,131,263,171,208)(107,279,196,235,132,270,170,201)(108,286,195,228,133,252,169,219)(109,293,194,246,134,259,168,212)(110,300,193,239,135,266,167,205)(111,282,192,232,136,273,166,223)(112,289,191,250,137,255,165,216)(113,296,190,243,138,262,164,209)(114,278,189,236,139,269,163,202)(115,285,188,229,140,251,162,220)(116,292,187,247,141,258,161,213)(117,299,186,240,142,265,160,206)(118,281,185,233,143,272,159,224)(119,288,184,226,144,254,158,217)(120,295,183,244,145,261,157,210)(121,277,182,237,146,268,156,203)(122,284,181,230,147,275,155,221)(123,291,180,248,148,257,154,214)(124,298,179,241,149,264,153,207)(125,280,178,234,150,271,152,225)>;
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)(26,130)(27,131)(28,132)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,126)(48,127)(49,128)(50,129)(51,163)(52,164)(53,165)(54,166)(55,167)(56,168)(57,169)(58,170)(59,171)(60,172)(61,173)(62,174)(63,175)(64,151)(65,152)(66,153)(67,154)(68,155)(69,156)(70,157)(71,158)(72,159)(73,160)(74,161)(75,162)(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)(201,321)(202,322)(203,323)(204,324)(205,325)(206,301)(207,302)(208,303)(209,304)(210,305)(211,306)(212,307)(213,308)(214,309)(215,310)(216,311)(217,312)(218,313)(219,314)(220,315)(221,316)(222,317)(223,318)(224,319)(225,320)(226,340)(227,341)(228,342)(229,343)(230,344)(231,345)(232,346)(233,347)(234,348)(235,349)(236,350)(237,326)(238,327)(239,328)(240,329)(241,330)(242,331)(243,332)(244,333)(245,334)(246,335)(247,336)(248,337)(249,338)(250,339)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,351)(260,352)(261,353)(262,354)(263,355)(264,356)(265,357)(266,358)(267,359)(268,360)(269,361)(270,362)(271,363)(272,364)(273,365)(274,366)(275,367)(276,387)(277,388)(278,389)(279,390)(280,391)(281,392)(282,393)(283,394)(284,395)(285,396)(286,397)(287,398)(288,399)(289,400)(290,376)(291,377)(292,378)(293,379)(294,380)(295,381)(296,382)(297,383)(298,384)(299,385)(300,386), (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), (1,379,94,335,30,351,56,307)(2,386,93,328,31,358,55,325)(3,393,92,346,32,365,54,318)(4,400,91,339,33,372,53,311)(5,382,90,332,34,354,52,304)(6,389,89,350,35,361,51,322)(7,396,88,343,36,368,75,315)(8,378,87,336,37,375,74,308)(9,385,86,329,38,357,73,301)(10,392,85,347,39,364,72,319)(11,399,84,340,40,371,71,312)(12,381,83,333,41,353,70,305)(13,388,82,326,42,360,69,323)(14,395,81,344,43,367,68,316)(15,377,80,337,44,374,67,309)(16,384,79,330,45,356,66,302)(17,391,78,348,46,363,65,320)(18,398,77,341,47,370,64,313)(19,380,76,334,48,352,63,306)(20,387,100,327,49,359,62,324)(21,394,99,345,50,366,61,317)(22,376,98,338,26,373,60,310)(23,383,97,331,27,355,59,303)(24,390,96,349,28,362,58,321)(25,397,95,342,29,369,57,314)(101,287,177,227,126,253,151,218)(102,294,176,245,127,260,175,211)(103,276,200,238,128,267,174,204)(104,283,199,231,129,274,173,222)(105,290,198,249,130,256,172,215)(106,297,197,242,131,263,171,208)(107,279,196,235,132,270,170,201)(108,286,195,228,133,252,169,219)(109,293,194,246,134,259,168,212)(110,300,193,239,135,266,167,205)(111,282,192,232,136,273,166,223)(112,289,191,250,137,255,165,216)(113,296,190,243,138,262,164,209)(114,278,189,236,139,269,163,202)(115,285,188,229,140,251,162,220)(116,292,187,247,141,258,161,213)(117,299,186,240,142,265,160,206)(118,281,185,233,143,272,159,224)(119,288,184,226,144,254,158,217)(120,295,183,244,145,261,157,210)(121,277,182,237,146,268,156,203)(122,284,181,230,147,275,155,221)(123,291,180,248,148,257,154,214)(124,298,179,241,149,264,153,207)(125,280,178,234,150,271,152,225) );
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),(26,130),(27,131),(28,132),(29,133),(30,134),(31,135),(32,136),(33,137),(34,138),(35,139),(36,140),(37,141),(38,142),(39,143),(40,144),(41,145),(42,146),(43,147),(44,148),(45,149),(46,150),(47,126),(48,127),(49,128),(50,129),(51,163),(52,164),(53,165),(54,166),(55,167),(56,168),(57,169),(58,170),(59,171),(60,172),(61,173),(62,174),(63,175),(64,151),(65,152),(66,153),(67,154),(68,155),(69,156),(70,157),(71,158),(72,159),(73,160),(74,161),(75,162),(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),(201,321),(202,322),(203,323),(204,324),(205,325),(206,301),(207,302),(208,303),(209,304),(210,305),(211,306),(212,307),(213,308),(214,309),(215,310),(216,311),(217,312),(218,313),(219,314),(220,315),(221,316),(222,317),(223,318),(224,319),(225,320),(226,340),(227,341),(228,342),(229,343),(230,344),(231,345),(232,346),(233,347),(234,348),(235,349),(236,350),(237,326),(238,327),(239,328),(240,329),(241,330),(242,331),(243,332),(244,333),(245,334),(246,335),(247,336),(248,337),(249,338),(250,339),(251,368),(252,369),(253,370),(254,371),(255,372),(256,373),(257,374),(258,375),(259,351),(260,352),(261,353),(262,354),(263,355),(264,356),(265,357),(266,358),(267,359),(268,360),(269,361),(270,362),(271,363),(272,364),(273,365),(274,366),(275,367),(276,387),(277,388),(278,389),(279,390),(280,391),(281,392),(282,393),(283,394),(284,395),(285,396),(286,397),(287,398),(288,399),(289,400),(290,376),(291,377),(292,378),(293,379),(294,380),(295,381),(296,382),(297,383),(298,384),(299,385),(300,386)], [(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)], [(1,379,94,335,30,351,56,307),(2,386,93,328,31,358,55,325),(3,393,92,346,32,365,54,318),(4,400,91,339,33,372,53,311),(5,382,90,332,34,354,52,304),(6,389,89,350,35,361,51,322),(7,396,88,343,36,368,75,315),(8,378,87,336,37,375,74,308),(9,385,86,329,38,357,73,301),(10,392,85,347,39,364,72,319),(11,399,84,340,40,371,71,312),(12,381,83,333,41,353,70,305),(13,388,82,326,42,360,69,323),(14,395,81,344,43,367,68,316),(15,377,80,337,44,374,67,309),(16,384,79,330,45,356,66,302),(17,391,78,348,46,363,65,320),(18,398,77,341,47,370,64,313),(19,380,76,334,48,352,63,306),(20,387,100,327,49,359,62,324),(21,394,99,345,50,366,61,317),(22,376,98,338,26,373,60,310),(23,383,97,331,27,355,59,303),(24,390,96,349,28,362,58,321),(25,397,95,342,29,369,57,314),(101,287,177,227,126,253,151,218),(102,294,176,245,127,260,175,211),(103,276,200,238,128,267,174,204),(104,283,199,231,129,274,173,222),(105,290,198,249,130,256,172,215),(106,297,197,242,131,263,171,208),(107,279,196,235,132,270,170,201),(108,286,195,228,133,252,169,219),(109,293,194,246,134,259,168,212),(110,300,193,239,135,266,167,205),(111,282,192,232,136,273,166,223),(112,289,191,250,137,255,165,216),(113,296,190,243,138,262,164,209),(114,278,189,236,139,269,163,202),(115,285,188,229,140,251,162,220),(116,292,187,247,141,258,161,213),(117,299,186,240,142,265,160,206),(118,281,185,233,143,272,159,224),(119,288,184,226,144,254,158,217),(120,295,183,244,145,261,157,210),(121,277,182,237,146,268,156,203),(122,284,181,230,147,275,155,221),(123,291,180,248,148,257,154,214),(124,298,179,241,149,264,153,207),(125,280,178,234,150,271,152,225)]])
40 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 5 | 8A | ··· | 8H | 10A | 10B | 10C | 25A | ··· | 25E | 50A | ··· | 50O |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 5 | 8 | ··· | 8 | 10 | 10 | 10 | 25 | ··· | 25 | 50 | ··· | 50 |
| size | 1 | 1 | 1 | 1 | 25 | 25 | 25 | 25 | 4 | 25 | ··· | 25 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
40 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | + | |||
| image | C1 | C2 | C2 | C4 | C4 | C8 | F5 | C5⋊C8 | C2×F5 | C25⋊C4 | C25⋊C8 | C2×C25⋊C4 |
| kernel | C2×C25⋊C8 | C25⋊C8 | C2×Dic25 | Dic25 | C2×C50 | C50 | C2×C10 | C10 | C10 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 1 | 2 | 1 | 5 | 10 | 5 |
Matrix representation of C2×C25⋊C8 ►in GL6(𝔽401)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 400 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 227 | 140 | 272 | 39 |
| 0 | 0 | 362 | 188 | 101 | 233 |
| 0 | 0 | 168 | 129 | 356 | 269 |
| 0 | 0 | 132 | 300 | 261 | 87 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 400 | 0 | 0 | 0 | 0 |
| 0 | 0 | 264 | 218 | 146 | 215 |
| 0 | 0 | 329 | 398 | 183 | 46 |
| 0 | 0 | 186 | 49 | 3 | 332 |
| 0 | 0 | 355 | 283 | 352 | 137 |
G:=sub<GL(6,GF(401))| [1,0,0,0,0,0,0,400,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,227,362,168,132,0,0,140,188,129,300,0,0,272,101,356,261,0,0,39,233,269,87],[98,0,0,0,0,0,0,400,0,0,0,0,0,0,264,329,186,355,0,0,218,398,49,283,0,0,146,183,3,352,0,0,215,46,332,137] >;
C2×C25⋊C8 in GAP, Magma, Sage, TeX
C_2\times C_{25}\rtimes C_8 % in TeX
G:=Group("C2xC25:C8"); // GroupNames label
G:=SmallGroup(400,32);
// by ID
G=gap.SmallGroup(400,32);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-5,-5,24,50,3364,2896,178,5765,2897]);
// 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^18>;
// generators/relations
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