metabelian, supersoluble, monomial, A-group
Aliases: C52⋊7C16, C40.8D5, C20.10Dic5, (C5×C10).7C8, (C5×C40).4C2, C8.2(C5⋊D5), C5⋊2(C5⋊2C16), (C5×C20).16C4, C2.(C52⋊7C8), C10.4(C5⋊2C8), C4.2(C52⋊6C4), SmallGroup(400,50)
Series: Derived ►Chief ►Lower central ►Upper central
| C52 — C52⋊7C16 |
Generators and relations for C52⋊7C16
G = < a,b,c | a5=b5=c16=1, ab=ba, cac-1=a-1, cbc-1=b-1 >
25C16
Smallest permutation representation of C52⋊7C16
►Regular action on 400 points
Generators in S400
(1 160 97 22 186)(2 187 23 98 145)(3 146 99 24 188)(4 189 25 100 147)(5 148 101 26 190)(6 191 27 102 149)(7 150 103 28 192)(8 177 29 104 151)(9 152 105 30 178)(10 179 31 106 153)(11 154 107 32 180)(12 181 17 108 155)(13 156 109 18 182)(14 183 19 110 157)(15 158 111 20 184)(16 185 21 112 159)(33 73 340 326 136)(34 137 327 341 74)(35 75 342 328 138)(36 139 329 343 76)(37 77 344 330 140)(38 141 331 345 78)(39 79 346 332 142)(40 143 333 347 80)(41 65 348 334 144)(42 129 335 349 66)(43 67 350 336 130)(44 131 321 351 68)(45 69 352 322 132)(46 133 323 337 70)(47 71 338 324 134)(48 135 325 339 72)(49 374 193 232 362)(50 363 233 194 375)(51 376 195 234 364)(52 365 235 196 377)(53 378 197 236 366)(54 367 237 198 379)(55 380 199 238 368)(56 353 239 200 381)(57 382 201 240 354)(58 355 225 202 383)(59 384 203 226 356)(60 357 227 204 369)(61 370 205 228 358)(62 359 229 206 371)(63 372 207 230 360)(64 361 231 208 373)(81 287 293 221 394)(82 395 222 294 288)(83 273 295 223 396)(84 397 224 296 274)(85 275 297 209 398)(86 399 210 298 276)(87 277 299 211 400)(88 385 212 300 278)(89 279 301 213 386)(90 387 214 302 280)(91 281 303 215 388)(92 389 216 304 282)(93 283 289 217 390)(94 391 218 290 284)(95 285 291 219 392)(96 393 220 292 286)(113 319 252 271 163)(114 164 272 253 320)(115 305 254 257 165)(116 166 258 255 306)(117 307 256 259 167)(118 168 260 241 308)(119 309 242 261 169)(120 170 262 243 310)(121 311 244 263 171)(122 172 264 245 312)(123 313 246 265 173)(124 174 266 247 314)(125 315 248 267 175)(126 176 268 249 316)(127 317 250 269 161)(128 162 270 251 318)
(1 265 70 217 225)(2 226 218 71 266)(3 267 72 219 227)(4 228 220 73 268)(5 269 74 221 229)(6 230 222 75 270)(7 271 76 223 231)(8 232 224 77 272)(9 257 78 209 233)(10 234 210 79 258)(11 259 80 211 235)(12 236 212 65 260)(13 261 66 213 237)(14 238 214 67 262)(15 263 68 215 239)(16 240 216 69 264)(17 53 278 334 308)(18 309 335 279 54)(19 55 280 336 310)(20 311 321 281 56)(21 57 282 322 312)(22 313 323 283 58)(23 59 284 324 314)(24 315 325 285 60)(25 61 286 326 316)(26 317 327 287 62)(27 63 288 328 318)(28 319 329 273 64)(29 49 274 330 320)(30 305 331 275 50)(31 51 276 332 306)(32 307 333 277 52)(33 176 147 205 393)(34 394 206 148 161)(35 162 149 207 395)(36 396 208 150 163)(37 164 151 193 397)(38 398 194 152 165)(39 166 153 195 399)(40 400 196 154 167)(41 168 155 197 385)(42 386 198 156 169)(43 170 157 199 387)(44 388 200 158 171)(45 172 159 201 389)(46 390 202 160 173)(47 174 145 203 391)(48 392 204 146 175)(81 371 101 127 137)(82 138 128 102 372)(83 373 103 113 139)(84 140 114 104 374)(85 375 105 115 141)(86 142 116 106 376)(87 377 107 117 143)(88 144 118 108 378)(89 379 109 119 129)(90 130 120 110 380)(91 381 111 121 131)(92 132 122 112 382)(93 383 97 123 133)(94 134 124 98 384)(95 369 99 125 135)(96 136 126 100 370)(177 362 296 344 253)(178 254 345 297 363)(179 364 298 346 255)(180 256 347 299 365)(181 366 300 348 241)(182 242 349 301 367)(183 368 302 350 243)(184 244 351 303 353)(185 354 304 352 245)(186 246 337 289 355)(187 356 290 338 247)(188 248 339 291 357)(189 358 292 340 249)(190 250 341 293 359)(191 360 294 342 251)(192 252 343 295 361)
(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)| (1,160,97,22,186)(2,187,23,98,145)(3,146,99,24,188)(4,189,25,100,147)(5,148,101,26,190)(6,191,27,102,149)(7,150,103,28,192)(8,177,29,104,151)(9,152,105,30,178)(10,179,31,106,153)(11,154,107,32,180)(12,181,17,108,155)(13,156,109,18,182)(14,183,19,110,157)(15,158,111,20,184)(16,185,21,112,159)(33,73,340,326,136)(34,137,327,341,74)(35,75,342,328,138)(36,139,329,343,76)(37,77,344,330,140)(38,141,331,345,78)(39,79,346,332,142)(40,143,333,347,80)(41,65,348,334,144)(42,129,335,349,66)(43,67,350,336,130)(44,131,321,351,68)(45,69,352,322,132)(46,133,323,337,70)(47,71,338,324,134)(48,135,325,339,72)(49,374,193,232,362)(50,363,233,194,375)(51,376,195,234,364)(52,365,235,196,377)(53,378,197,236,366)(54,367,237,198,379)(55,380,199,238,368)(56,353,239,200,381)(57,382,201,240,354)(58,355,225,202,383)(59,384,203,226,356)(60,357,227,204,369)(61,370,205,228,358)(62,359,229,206,371)(63,372,207,230,360)(64,361,231,208,373)(81,287,293,221,394)(82,395,222,294,288)(83,273,295,223,396)(84,397,224,296,274)(85,275,297,209,398)(86,399,210,298,276)(87,277,299,211,400)(88,385,212,300,278)(89,279,301,213,386)(90,387,214,302,280)(91,281,303,215,388)(92,389,216,304,282)(93,283,289,217,390)(94,391,218,290,284)(95,285,291,219,392)(96,393,220,292,286)(113,319,252,271,163)(114,164,272,253,320)(115,305,254,257,165)(116,166,258,255,306)(117,307,256,259,167)(118,168,260,241,308)(119,309,242,261,169)(120,170,262,243,310)(121,311,244,263,171)(122,172,264,245,312)(123,313,246,265,173)(124,174,266,247,314)(125,315,248,267,175)(126,176,268,249,316)(127,317,250,269,161)(128,162,270,251,318), (1,265,70,217,225)(2,226,218,71,266)(3,267,72,219,227)(4,228,220,73,268)(5,269,74,221,229)(6,230,222,75,270)(7,271,76,223,231)(8,232,224,77,272)(9,257,78,209,233)(10,234,210,79,258)(11,259,80,211,235)(12,236,212,65,260)(13,261,66,213,237)(14,238,214,67,262)(15,263,68,215,239)(16,240,216,69,264)(17,53,278,334,308)(18,309,335,279,54)(19,55,280,336,310)(20,311,321,281,56)(21,57,282,322,312)(22,313,323,283,58)(23,59,284,324,314)(24,315,325,285,60)(25,61,286,326,316)(26,317,327,287,62)(27,63,288,328,318)(28,319,329,273,64)(29,49,274,330,320)(30,305,331,275,50)(31,51,276,332,306)(32,307,333,277,52)(33,176,147,205,393)(34,394,206,148,161)(35,162,149,207,395)(36,396,208,150,163)(37,164,151,193,397)(38,398,194,152,165)(39,166,153,195,399)(40,400,196,154,167)(41,168,155,197,385)(42,386,198,156,169)(43,170,157,199,387)(44,388,200,158,171)(45,172,159,201,389)(46,390,202,160,173)(47,174,145,203,391)(48,392,204,146,175)(81,371,101,127,137)(82,138,128,102,372)(83,373,103,113,139)(84,140,114,104,374)(85,375,105,115,141)(86,142,116,106,376)(87,377,107,117,143)(88,144,118,108,378)(89,379,109,119,129)(90,130,120,110,380)(91,381,111,121,131)(92,132,122,112,382)(93,383,97,123,133)(94,134,124,98,384)(95,369,99,125,135)(96,136,126,100,370)(177,362,296,344,253)(178,254,345,297,363)(179,364,298,346,255)(180,256,347,299,365)(181,366,300,348,241)(182,242,349,301,367)(183,368,302,350,243)(184,244,351,303,353)(185,354,304,352,245)(186,246,337,289,355)(187,356,290,338,247)(188,248,339,291,357)(189,358,292,340,249)(190,250,341,293,359)(191,360,294,342,251)(192,252,343,295,361), (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( (1,160,97,22,186)(2,187,23,98,145)(3,146,99,24,188)(4,189,25,100,147)(5,148,101,26,190)(6,191,27,102,149)(7,150,103,28,192)(8,177,29,104,151)(9,152,105,30,178)(10,179,31,106,153)(11,154,107,32,180)(12,181,17,108,155)(13,156,109,18,182)(14,183,19,110,157)(15,158,111,20,184)(16,185,21,112,159)(33,73,340,326,136)(34,137,327,341,74)(35,75,342,328,138)(36,139,329,343,76)(37,77,344,330,140)(38,141,331,345,78)(39,79,346,332,142)(40,143,333,347,80)(41,65,348,334,144)(42,129,335,349,66)(43,67,350,336,130)(44,131,321,351,68)(45,69,352,322,132)(46,133,323,337,70)(47,71,338,324,134)(48,135,325,339,72)(49,374,193,232,362)(50,363,233,194,375)(51,376,195,234,364)(52,365,235,196,377)(53,378,197,236,366)(54,367,237,198,379)(55,380,199,238,368)(56,353,239,200,381)(57,382,201,240,354)(58,355,225,202,383)(59,384,203,226,356)(60,357,227,204,369)(61,370,205,228,358)(62,359,229,206,371)(63,372,207,230,360)(64,361,231,208,373)(81,287,293,221,394)(82,395,222,294,288)(83,273,295,223,396)(84,397,224,296,274)(85,275,297,209,398)(86,399,210,298,276)(87,277,299,211,400)(88,385,212,300,278)(89,279,301,213,386)(90,387,214,302,280)(91,281,303,215,388)(92,389,216,304,282)(93,283,289,217,390)(94,391,218,290,284)(95,285,291,219,392)(96,393,220,292,286)(113,319,252,271,163)(114,164,272,253,320)(115,305,254,257,165)(116,166,258,255,306)(117,307,256,259,167)(118,168,260,241,308)(119,309,242,261,169)(120,170,262,243,310)(121,311,244,263,171)(122,172,264,245,312)(123,313,246,265,173)(124,174,266,247,314)(125,315,248,267,175)(126,176,268,249,316)(127,317,250,269,161)(128,162,270,251,318), (1,265,70,217,225)(2,226,218,71,266)(3,267,72,219,227)(4,228,220,73,268)(5,269,74,221,229)(6,230,222,75,270)(7,271,76,223,231)(8,232,224,77,272)(9,257,78,209,233)(10,234,210,79,258)(11,259,80,211,235)(12,236,212,65,260)(13,261,66,213,237)(14,238,214,67,262)(15,263,68,215,239)(16,240,216,69,264)(17,53,278,334,308)(18,309,335,279,54)(19,55,280,336,310)(20,311,321,281,56)(21,57,282,322,312)(22,313,323,283,58)(23,59,284,324,314)(24,315,325,285,60)(25,61,286,326,316)(26,317,327,287,62)(27,63,288,328,318)(28,319,329,273,64)(29,49,274,330,320)(30,305,331,275,50)(31,51,276,332,306)(32,307,333,277,52)(33,176,147,205,393)(34,394,206,148,161)(35,162,149,207,395)(36,396,208,150,163)(37,164,151,193,397)(38,398,194,152,165)(39,166,153,195,399)(40,400,196,154,167)(41,168,155,197,385)(42,386,198,156,169)(43,170,157,199,387)(44,388,200,158,171)(45,172,159,201,389)(46,390,202,160,173)(47,174,145,203,391)(48,392,204,146,175)(81,371,101,127,137)(82,138,128,102,372)(83,373,103,113,139)(84,140,114,104,374)(85,375,105,115,141)(86,142,116,106,376)(87,377,107,117,143)(88,144,118,108,378)(89,379,109,119,129)(90,130,120,110,380)(91,381,111,121,131)(92,132,122,112,382)(93,383,97,123,133)(94,134,124,98,384)(95,369,99,125,135)(96,136,126,100,370)(177,362,296,344,253)(178,254,345,297,363)(179,364,298,346,255)(180,256,347,299,365)(181,366,300,348,241)(182,242,349,301,367)(183,368,302,350,243)(184,244,351,303,353)(185,354,304,352,245)(186,246,337,289,355)(187,356,290,338,247)(188,248,339,291,357)(189,358,292,340,249)(190,250,341,293,359)(191,360,294,342,251)(192,252,343,295,361), (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([[(1,160,97,22,186),(2,187,23,98,145),(3,146,99,24,188),(4,189,25,100,147),(5,148,101,26,190),(6,191,27,102,149),(7,150,103,28,192),(8,177,29,104,151),(9,152,105,30,178),(10,179,31,106,153),(11,154,107,32,180),(12,181,17,108,155),(13,156,109,18,182),(14,183,19,110,157),(15,158,111,20,184),(16,185,21,112,159),(33,73,340,326,136),(34,137,327,341,74),(35,75,342,328,138),(36,139,329,343,76),(37,77,344,330,140),(38,141,331,345,78),(39,79,346,332,142),(40,143,333,347,80),(41,65,348,334,144),(42,129,335,349,66),(43,67,350,336,130),(44,131,321,351,68),(45,69,352,322,132),(46,133,323,337,70),(47,71,338,324,134),(48,135,325,339,72),(49,374,193,232,362),(50,363,233,194,375),(51,376,195,234,364),(52,365,235,196,377),(53,378,197,236,366),(54,367,237,198,379),(55,380,199,238,368),(56,353,239,200,381),(57,382,201,240,354),(58,355,225,202,383),(59,384,203,226,356),(60,357,227,204,369),(61,370,205,228,358),(62,359,229,206,371),(63,372,207,230,360),(64,361,231,208,373),(81,287,293,221,394),(82,395,222,294,288),(83,273,295,223,396),(84,397,224,296,274),(85,275,297,209,398),(86,399,210,298,276),(87,277,299,211,400),(88,385,212,300,278),(89,279,301,213,386),(90,387,214,302,280),(91,281,303,215,388),(92,389,216,304,282),(93,283,289,217,390),(94,391,218,290,284),(95,285,291,219,392),(96,393,220,292,286),(113,319,252,271,163),(114,164,272,253,320),(115,305,254,257,165),(116,166,258,255,306),(117,307,256,259,167),(118,168,260,241,308),(119,309,242,261,169),(120,170,262,243,310),(121,311,244,263,171),(122,172,264,245,312),(123,313,246,265,173),(124,174,266,247,314),(125,315,248,267,175),(126,176,268,249,316),(127,317,250,269,161),(128,162,270,251,318)], [(1,265,70,217,225),(2,226,218,71,266),(3,267,72,219,227),(4,228,220,73,268),(5,269,74,221,229),(6,230,222,75,270),(7,271,76,223,231),(8,232,224,77,272),(9,257,78,209,233),(10,234,210,79,258),(11,259,80,211,235),(12,236,212,65,260),(13,261,66,213,237),(14,238,214,67,262),(15,263,68,215,239),(16,240,216,69,264),(17,53,278,334,308),(18,309,335,279,54),(19,55,280,336,310),(20,311,321,281,56),(21,57,282,322,312),(22,313,323,283,58),(23,59,284,324,314),(24,315,325,285,60),(25,61,286,326,316),(26,317,327,287,62),(27,63,288,328,318),(28,319,329,273,64),(29,49,274,330,320),(30,305,331,275,50),(31,51,276,332,306),(32,307,333,277,52),(33,176,147,205,393),(34,394,206,148,161),(35,162,149,207,395),(36,396,208,150,163),(37,164,151,193,397),(38,398,194,152,165),(39,166,153,195,399),(40,400,196,154,167),(41,168,155,197,385),(42,386,198,156,169),(43,170,157,199,387),(44,388,200,158,171),(45,172,159,201,389),(46,390,202,160,173),(47,174,145,203,391),(48,392,204,146,175),(81,371,101,127,137),(82,138,128,102,372),(83,373,103,113,139),(84,140,114,104,374),(85,375,105,115,141),(86,142,116,106,376),(87,377,107,117,143),(88,144,118,108,378),(89,379,109,119,129),(90,130,120,110,380),(91,381,111,121,131),(92,132,122,112,382),(93,383,97,123,133),(94,134,124,98,384),(95,369,99,125,135),(96,136,126,100,370),(177,362,296,344,253),(178,254,345,297,363),(179,364,298,346,255),(180,256,347,299,365),(181,366,300,348,241),(182,242,349,301,367),(183,368,302,350,243),(184,244,351,303,353),(185,354,304,352,245),(186,246,337,289,355),(187,356,290,338,247),(188,248,339,291,357),(189,358,292,340,249),(190,250,341,293,359),(191,360,294,342,251),(192,252,343,295,361)], [(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)]])
112 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | ··· | 5L | 8A | 8B | 8C | 8D | 10A | ··· | 10L | 16A | ··· | 16H | 20A | ··· | 20X | 40A | ··· | 40AV |
| order | 1 | 2 | 4 | 4 | 5 | ··· | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 16 | ··· | 16 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 25 | ··· | 25 | 2 | ··· | 2 | 2 | ··· | 2 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | |||||
| image | C1 | C2 | C4 | C8 | C16 | D5 | Dic5 | C5⋊2C8 | C5⋊2C16 |
| kernel | C52⋊7C16 | C5×C40 | C5×C20 | C5×C10 | C52 | C40 | C20 | C10 | C5 |
| # reps | 1 | 1 | 2 | 4 | 8 | 12 | 12 | 24 | 48 |
Matrix representation of C52⋊7C16 ►in GL4(𝔽241) generated by
| 51 | 240 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 |
| 240 | 51 | 0 | 0 |
| 0 | 0 | 190 | 1 |
| 0 | 0 | 50 | 240 |
| 55 | 50 | 0 | 0 |
| 204 | 186 | 0 | 0 |
| 0 | 0 | 181 | 28 |
| 0 | 0 | 179 | 60 |
G:=sub<GL(4,GF(241))| [51,1,0,0,240,0,0,0,0,0,1,0,0,0,0,1],[0,240,0,0,1,51,0,0,0,0,190,50,0,0,1,240],[55,204,0,0,50,186,0,0,0,0,181,179,0,0,28,60] >;
C52⋊7C16 in GAP, Magma, Sage, TeX
C_5^2\rtimes_7C_{16} % in TeX
G:=Group("C5^2:7C16"); // GroupNames label
G:=SmallGroup(400,50);
// by ID
G=gap.SmallGroup(400,50);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-5,-5,12,31,50,1924,11525]);
// Polycyclic
G:=Group<a,b,c|a^5=b^5=c^16=1,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
Export