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## G = C4⋊Dic25order 400 = 24·52

### The semidirect product of C4 and Dic25 acting via Dic25/C50=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C50 — C4⋊Dic25
 Chief series C1 — C5 — C25 — C50 — C2×C50 — C2×Dic25 — C4⋊Dic25
 Lower central C25 — C50 — C4⋊Dic25
 Upper central C1 — C22 — C2×C4

Generators and relations for C4⋊Dic25
G = < a,b,c | a4=b50=1, c2=b25, ab=ba, cac-1=a-1, cbc-1=b-1 >

Smallest permutation representation of C4⋊Dic25
Regular action on 400 points
Generators in S400
(1 52 140 190)(2 53 141 191)(3 54 142 192)(4 55 143 193)(5 56 144 194)(6 57 145 195)(7 58 146 196)(8 59 147 197)(9 60 148 198)(10 61 149 199)(11 62 150 200)(12 63 101 151)(13 64 102 152)(14 65 103 153)(15 66 104 154)(16 67 105 155)(17 68 106 156)(18 69 107 157)(19 70 108 158)(20 71 109 159)(21 72 110 160)(22 73 111 161)(23 74 112 162)(24 75 113 163)(25 76 114 164)(26 77 115 165)(27 78 116 166)(28 79 117 167)(29 80 118 168)(30 81 119 169)(31 82 120 170)(32 83 121 171)(33 84 122 172)(34 85 123 173)(35 86 124 174)(36 87 125 175)(37 88 126 176)(38 89 127 177)(39 90 128 178)(40 91 129 179)(41 92 130 180)(42 93 131 181)(43 94 132 182)(44 95 133 183)(45 96 134 184)(46 97 135 185)(47 98 136 186)(48 99 137 187)(49 100 138 188)(50 51 139 189)(201 276 313 377)(202 277 314 378)(203 278 315 379)(204 279 316 380)(205 280 317 381)(206 281 318 382)(207 282 319 383)(208 283 320 384)(209 284 321 385)(210 285 322 386)(211 286 323 387)(212 287 324 388)(213 288 325 389)(214 289 326 390)(215 290 327 391)(216 291 328 392)(217 292 329 393)(218 293 330 394)(219 294 331 395)(220 295 332 396)(221 296 333 397)(222 297 334 398)(223 298 335 399)(224 299 336 400)(225 300 337 351)(226 251 338 352)(227 252 339 353)(228 253 340 354)(229 254 341 355)(230 255 342 356)(231 256 343 357)(232 257 344 358)(233 258 345 359)(234 259 346 360)(235 260 347 361)(236 261 348 362)(237 262 349 363)(238 263 350 364)(239 264 301 365)(240 265 302 366)(241 266 303 367)(242 267 304 368)(243 268 305 369)(244 269 306 370)(245 270 307 371)(246 271 308 372)(247 272 309 373)(248 273 310 374)(249 274 311 375)(250 275 312 376)
(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)
(1 359 26 384)(2 358 27 383)(3 357 28 382)(4 356 29 381)(5 355 30 380)(6 354 31 379)(7 353 32 378)(8 352 33 377)(9 351 34 376)(10 400 35 375)(11 399 36 374)(12 398 37 373)(13 397 38 372)(14 396 39 371)(15 395 40 370)(16 394 41 369)(17 393 42 368)(18 392 43 367)(19 391 44 366)(20 390 45 365)(21 389 46 364)(22 388 47 363)(23 387 48 362)(24 386 49 361)(25 385 50 360)(51 346 76 321)(52 345 77 320)(53 344 78 319)(54 343 79 318)(55 342 80 317)(56 341 81 316)(57 340 82 315)(58 339 83 314)(59 338 84 313)(60 337 85 312)(61 336 86 311)(62 335 87 310)(63 334 88 309)(64 333 89 308)(65 332 90 307)(66 331 91 306)(67 330 92 305)(68 329 93 304)(69 328 94 303)(70 327 95 302)(71 326 96 301)(72 325 97 350)(73 324 98 349)(74 323 99 348)(75 322 100 347)(101 297 126 272)(102 296 127 271)(103 295 128 270)(104 294 129 269)(105 293 130 268)(106 292 131 267)(107 291 132 266)(108 290 133 265)(109 289 134 264)(110 288 135 263)(111 287 136 262)(112 286 137 261)(113 285 138 260)(114 284 139 259)(115 283 140 258)(116 282 141 257)(117 281 142 256)(118 280 143 255)(119 279 144 254)(120 278 145 253)(121 277 146 252)(122 276 147 251)(123 275 148 300)(124 274 149 299)(125 273 150 298)(151 222 176 247)(152 221 177 246)(153 220 178 245)(154 219 179 244)(155 218 180 243)(156 217 181 242)(157 216 182 241)(158 215 183 240)(159 214 184 239)(160 213 185 238)(161 212 186 237)(162 211 187 236)(163 210 188 235)(164 209 189 234)(165 208 190 233)(166 207 191 232)(167 206 192 231)(168 205 193 230)(169 204 194 229)(170 203 195 228)(171 202 196 227)(172 201 197 226)(173 250 198 225)(174 249 199 224)(175 248 200 223)

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

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

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

106 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 5A 5B 10A ··· 10F 20A ··· 20H 25A ··· 25J 50A ··· 50AD 100A ··· 100AN order 1 2 2 2 4 4 4 4 4 4 5 5 10 ··· 10 20 ··· 20 25 ··· 25 50 ··· 50 100 ··· 100 size 1 1 1 1 2 2 50 50 50 50 2 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2

106 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + - + - + - + + - + - + image C1 C2 C2 C4 D4 Q8 D5 Dic5 D10 Dic10 D20 D25 Dic25 D50 Dic50 D100 kernel C4⋊Dic25 C2×Dic25 C2×C100 C100 C50 C50 C2×C20 C20 C2×C10 C10 C10 C2×C4 C4 C22 C2 C2 # reps 1 2 1 4 1 1 2 4 2 4 4 10 20 10 20 20

Matrix representation of C4⋊Dic25 in GL3(𝔽101) generated by

 100 0 0 0 25 61 0 51 76
,
 100 0 0 0 72 29 0 11 83
,
 10 0 0 0 56 27 0 11 45
G:=sub<GL(3,GF(101))| [100,0,0,0,25,51,0,61,76],[100,0,0,0,72,11,0,29,83],[10,0,0,0,56,11,0,27,45] >;

C4⋊Dic25 in GAP, Magma, Sage, TeX

C_4\rtimes {\rm Dic}_{25}
% in TeX

G:=Group("C4:Dic25");
// GroupNames label

G:=SmallGroup(400,13);
// by ID

G=gap.SmallGroup(400,13);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-5,-5,24,121,55,4324,628,11525]);
// Polycyclic

G:=Group<a,b,c|a^4=b^50=1,c^2=b^25,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations

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