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## G = C20⋊3Dic5order 400 = 24·52

### 1st semidirect product of C20 and Dic5 acting via Dic5/C10=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C5×C10 — C20⋊3Dic5
 Chief series C1 — C5 — C52 — C5×C10 — C102 — C2×C52⋊6C4 — C20⋊3Dic5
 Lower central C52 — C5×C10 — C20⋊3Dic5
 Upper central C1 — C22 — C2×C4

Generators and relations for C203Dic5
G = < a,b,c | a20=b10=1, c2=b5, ab=ba, cac-1=a-1, cbc-1=b-1 >

Subgroups: 456 in 104 conjugacy classes, 67 normal (13 characteristic)
C1, C2, C4, C4, C22, C5, C2×C4, C2×C4, C10, C4⋊C4, Dic5, C20, C2×C10, C52, C2×Dic5, C2×C20, C5×C10, C4⋊Dic5, C526C4, C5×C20, C102, C2×C526C4, C10×C20, C203Dic5
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, D5, C4⋊C4, Dic5, D10, Dic10, D20, C2×Dic5, C5⋊D5, C4⋊Dic5, C526C4, C2×C5⋊D5, C524Q8, C20⋊D5, C2×C526C4, C203Dic5

Smallest permutation representation of C203Dic5
Regular action on 400 points
Generators in S400
(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)
(1 355 368 302 96 129 385 24 225 163)(2 356 369 303 97 130 386 25 226 164)(3 357 370 304 98 131 387 26 227 165)(4 358 371 305 99 132 388 27 228 166)(5 359 372 306 100 133 389 28 229 167)(6 360 373 307 81 134 390 29 230 168)(7 341 374 308 82 135 391 30 231 169)(8 342 375 309 83 136 392 31 232 170)(9 343 376 310 84 137 393 32 233 171)(10 344 377 311 85 138 394 33 234 172)(11 345 378 312 86 139 395 34 235 173)(12 346 379 313 87 140 396 35 236 174)(13 347 380 314 88 121 397 36 237 175)(14 348 361 315 89 122 398 37 238 176)(15 349 362 316 90 123 399 38 239 177)(16 350 363 317 91 124 400 39 240 178)(17 351 364 318 92 125 381 40 221 179)(18 352 365 319 93 126 382 21 222 180)(19 353 366 320 94 127 383 22 223 161)(20 354 367 301 95 128 384 23 224 162)(41 63 326 285 148 115 271 241 220 200)(42 64 327 286 149 116 272 242 201 181)(43 65 328 287 150 117 273 243 202 182)(44 66 329 288 151 118 274 244 203 183)(45 67 330 289 152 119 275 245 204 184)(46 68 331 290 153 120 276 246 205 185)(47 69 332 291 154 101 277 247 206 186)(48 70 333 292 155 102 278 248 207 187)(49 71 334 293 156 103 279 249 208 188)(50 72 335 294 157 104 280 250 209 189)(51 73 336 295 158 105 261 251 210 190)(52 74 337 296 159 106 262 252 211 191)(53 75 338 297 160 107 263 253 212 192)(54 76 339 298 141 108 264 254 213 193)(55 77 340 299 142 109 265 255 214 194)(56 78 321 300 143 110 266 256 215 195)(57 79 322 281 144 111 267 257 216 196)(58 80 323 282 145 112 268 258 217 197)(59 61 324 283 146 113 269 259 218 198)(60 62 325 284 147 114 270 260 219 199)
(1 209 129 294)(2 208 130 293)(3 207 131 292)(4 206 132 291)(5 205 133 290)(6 204 134 289)(7 203 135 288)(8 202 136 287)(9 201 137 286)(10 220 138 285)(11 219 139 284)(12 218 140 283)(13 217 121 282)(14 216 122 281)(15 215 123 300)(16 214 124 299)(17 213 125 298)(18 212 126 297)(19 211 127 296)(20 210 128 295)(21 75 365 263)(22 74 366 262)(23 73 367 261)(24 72 368 280)(25 71 369 279)(26 70 370 278)(27 69 371 277)(28 68 372 276)(29 67 373 275)(30 66 374 274)(31 65 375 273)(32 64 376 272)(33 63 377 271)(34 62 378 270)(35 61 379 269)(36 80 380 268)(37 79 361 267)(38 78 362 266)(39 77 363 265)(40 76 364 264)(41 311 115 234)(42 310 116 233)(43 309 117 232)(44 308 118 231)(45 307 119 230)(46 306 120 229)(47 305 101 228)(48 304 102 227)(49 303 103 226)(50 302 104 225)(51 301 105 224)(52 320 106 223)(53 319 107 222)(54 318 108 221)(55 317 109 240)(56 316 110 239)(57 315 111 238)(58 314 112 237)(59 313 113 236)(60 312 114 235)(81 152 168 184)(82 151 169 183)(83 150 170 182)(84 149 171 181)(85 148 172 200)(86 147 173 199)(87 146 174 198)(88 145 175 197)(89 144 176 196)(90 143 177 195)(91 142 178 194)(92 141 179 193)(93 160 180 192)(94 159 161 191)(95 158 162 190)(96 157 163 189)(97 156 164 188)(98 155 165 187)(99 154 166 186)(100 153 167 185)(241 394 326 344)(242 393 327 343)(243 392 328 342)(244 391 329 341)(245 390 330 360)(246 389 331 359)(247 388 332 358)(248 387 333 357)(249 386 334 356)(250 385 335 355)(251 384 336 354)(252 383 337 353)(253 382 338 352)(254 381 339 351)(255 400 340 350)(256 399 321 349)(257 398 322 348)(258 397 323 347)(259 396 324 346)(260 395 325 345)

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

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

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

106 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 5A ··· 5L 10A ··· 10AJ 20A ··· 20AV order 1 2 2 2 4 4 4 4 4 4 5 ··· 5 10 ··· 10 20 ··· 20 size 1 1 1 1 2 2 50 50 50 50 2 ··· 2 2 ··· 2 2 ··· 2

106 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 2 2 type + + + + - + - + - + image C1 C2 C2 C4 D4 Q8 D5 Dic5 D10 Dic10 D20 kernel C20⋊3Dic5 C2×C52⋊6C4 C10×C20 C5×C20 C5×C10 C5×C10 C2×C20 C20 C2×C10 C10 C10 # reps 1 2 1 4 1 1 12 24 12 24 24

Matrix representation of C203Dic5 in GL4(𝔽41) generated by

 2 32 0 0 37 39 0 0 0 0 7 40 0 0 8 40
,
 35 1 0 0 5 40 0 0 0 0 40 0 0 0 0 40
,
 1 1 0 0 0 40 0 0 0 0 0 13 0 0 22 0
G:=sub<GL(4,GF(41))| [2,37,0,0,32,39,0,0,0,0,7,8,0,0,40,40],[35,5,0,0,1,40,0,0,0,0,40,0,0,0,0,40],[1,0,0,0,1,40,0,0,0,0,0,22,0,0,13,0] >;

C203Dic5 in GAP, Magma, Sage, TeX

C_{20}\rtimes_3{\rm Dic}_5
% in TeX

G:=Group("C20:3Dic5");
// GroupNames label

G:=SmallGroup(400,101);
// by ID

G=gap.SmallGroup(400,101);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-5,-5,24,121,55,1924,11525]);
// Polycyclic

G:=Group<a,b,c|a^20=b^10=1,c^2=b^5,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations

׿
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