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G = C8×Dic13order 416 = 25·13

Direct product of C8 and Dic13

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C8×Dic13, C1047C4, C26.8C42, C134(C4×C8), C132C89C4, C2.2(C8×D13), C52.61(C2×C4), C26.12(C2×C8), (C2×C8).10D13, C4.20(C4×D13), (C2×C4).90D26, (C2×C104).11C2, C2.2(C4×Dic13), C22.8(C4×D13), C4.12(C2×Dic13), (C2×C52).104C22, (C4×Dic13).14C2, (C2×Dic13).15C4, (C2×C26).29(C2×C4), (C2×C132C8).14C2, SmallGroup(416,20)

Series: Derived Chief Lower central Upper central

C1C13 — C8×Dic13
C1C13C26C2×C26C2×C52C4×Dic13 — C8×Dic13
C13 — C8×Dic13
C1C2×C8

Generators and relations for C8×Dic13
 G = < a,b,c | a8=b26=1, c2=b13, ab=ba, ac=ca, cbc-1=b-1 >

13C4
13C4
13C4
13C4
13C8
13C2×C4
13C2×C4
13C8
13C42
13C2×C8
13C4×C8

Smallest permutation representation of C8×Dic13
Regular action on 416 points
Generators in S416
(1 309 47 217 399 342 280 72)(2 310 48 218 400 343 281 73)(3 311 49 219 401 344 282 74)(4 312 50 220 402 345 283 75)(5 287 51 221 403 346 284 76)(6 288 52 222 404 347 285 77)(7 289 27 223 405 348 286 78)(8 290 28 224 406 349 261 53)(9 291 29 225 407 350 262 54)(10 292 30 226 408 351 263 55)(11 293 31 227 409 352 264 56)(12 294 32 228 410 353 265 57)(13 295 33 229 411 354 266 58)(14 296 34 230 412 355 267 59)(15 297 35 231 413 356 268 60)(16 298 36 232 414 357 269 61)(17 299 37 233 415 358 270 62)(18 300 38 234 416 359 271 63)(19 301 39 209 391 360 272 64)(20 302 40 210 392 361 273 65)(21 303 41 211 393 362 274 66)(22 304 42 212 394 363 275 67)(23 305 43 213 395 364 276 68)(24 306 44 214 396 339 277 69)(25 307 45 215 397 340 278 70)(26 308 46 216 398 341 279 71)(79 116 161 378 206 322 138 252)(80 117 162 379 207 323 139 253)(81 118 163 380 208 324 140 254)(82 119 164 381 183 325 141 255)(83 120 165 382 184 326 142 256)(84 121 166 383 185 327 143 257)(85 122 167 384 186 328 144 258)(86 123 168 385 187 329 145 259)(87 124 169 386 188 330 146 260)(88 125 170 387 189 331 147 235)(89 126 171 388 190 332 148 236)(90 127 172 389 191 333 149 237)(91 128 173 390 192 334 150 238)(92 129 174 365 193 335 151 239)(93 130 175 366 194 336 152 240)(94 105 176 367 195 337 153 241)(95 106 177 368 196 338 154 242)(96 107 178 369 197 313 155 243)(97 108 179 370 198 314 156 244)(98 109 180 371 199 315 131 245)(99 110 181 372 200 316 132 246)(100 111 182 373 201 317 133 247)(101 112 157 374 202 318 134 248)(102 113 158 375 203 319 135 249)(103 114 159 376 204 320 136 250)(104 115 160 377 205 321 137 251)
(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)(391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416)
(1 129 14 116)(2 128 15 115)(3 127 16 114)(4 126 17 113)(5 125 18 112)(6 124 19 111)(7 123 20 110)(8 122 21 109)(9 121 22 108)(10 120 23 107)(11 119 24 106)(12 118 25 105)(13 117 26 130)(27 385 40 372)(28 384 41 371)(29 383 42 370)(30 382 43 369)(31 381 44 368)(32 380 45 367)(33 379 46 366)(34 378 47 365)(35 377 48 390)(36 376 49 389)(37 375 50 388)(38 374 51 387)(39 373 52 386)(53 85 66 98)(54 84 67 97)(55 83 68 96)(56 82 69 95)(57 81 70 94)(58 80 71 93)(59 79 72 92)(60 104 73 91)(61 103 74 90)(62 102 75 89)(63 101 76 88)(64 100 77 87)(65 99 78 86)(131 349 144 362)(132 348 145 361)(133 347 146 360)(134 346 147 359)(135 345 148 358)(136 344 149 357)(137 343 150 356)(138 342 151 355)(139 341 152 354)(140 340 153 353)(141 339 154 352)(142 364 155 351)(143 363 156 350)(157 287 170 300)(158 312 171 299)(159 311 172 298)(160 310 173 297)(161 309 174 296)(162 308 175 295)(163 307 176 294)(164 306 177 293)(165 305 178 292)(166 304 179 291)(167 303 180 290)(168 302 181 289)(169 301 182 288)(183 214 196 227)(184 213 197 226)(185 212 198 225)(186 211 199 224)(187 210 200 223)(188 209 201 222)(189 234 202 221)(190 233 203 220)(191 232 204 219)(192 231 205 218)(193 230 206 217)(194 229 207 216)(195 228 208 215)(235 271 248 284)(236 270 249 283)(237 269 250 282)(238 268 251 281)(239 267 252 280)(240 266 253 279)(241 265 254 278)(242 264 255 277)(243 263 256 276)(244 262 257 275)(245 261 258 274)(246 286 259 273)(247 285 260 272)(313 408 326 395)(314 407 327 394)(315 406 328 393)(316 405 329 392)(317 404 330 391)(318 403 331 416)(319 402 332 415)(320 401 333 414)(321 400 334 413)(322 399 335 412)(323 398 336 411)(324 397 337 410)(325 396 338 409)

G:=sub<Sym(416)| (1,309,47,217,399,342,280,72)(2,310,48,218,400,343,281,73)(3,311,49,219,401,344,282,74)(4,312,50,220,402,345,283,75)(5,287,51,221,403,346,284,76)(6,288,52,222,404,347,285,77)(7,289,27,223,405,348,286,78)(8,290,28,224,406,349,261,53)(9,291,29,225,407,350,262,54)(10,292,30,226,408,351,263,55)(11,293,31,227,409,352,264,56)(12,294,32,228,410,353,265,57)(13,295,33,229,411,354,266,58)(14,296,34,230,412,355,267,59)(15,297,35,231,413,356,268,60)(16,298,36,232,414,357,269,61)(17,299,37,233,415,358,270,62)(18,300,38,234,416,359,271,63)(19,301,39,209,391,360,272,64)(20,302,40,210,392,361,273,65)(21,303,41,211,393,362,274,66)(22,304,42,212,394,363,275,67)(23,305,43,213,395,364,276,68)(24,306,44,214,396,339,277,69)(25,307,45,215,397,340,278,70)(26,308,46,216,398,341,279,71)(79,116,161,378,206,322,138,252)(80,117,162,379,207,323,139,253)(81,118,163,380,208,324,140,254)(82,119,164,381,183,325,141,255)(83,120,165,382,184,326,142,256)(84,121,166,383,185,327,143,257)(85,122,167,384,186,328,144,258)(86,123,168,385,187,329,145,259)(87,124,169,386,188,330,146,260)(88,125,170,387,189,331,147,235)(89,126,171,388,190,332,148,236)(90,127,172,389,191,333,149,237)(91,128,173,390,192,334,150,238)(92,129,174,365,193,335,151,239)(93,130,175,366,194,336,152,240)(94,105,176,367,195,337,153,241)(95,106,177,368,196,338,154,242)(96,107,178,369,197,313,155,243)(97,108,179,370,198,314,156,244)(98,109,180,371,199,315,131,245)(99,110,181,372,200,316,132,246)(100,111,182,373,201,317,133,247)(101,112,157,374,202,318,134,248)(102,113,158,375,203,319,135,249)(103,114,159,376,204,320,136,250)(104,115,160,377,205,321,137,251), (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)(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416), (1,129,14,116)(2,128,15,115)(3,127,16,114)(4,126,17,113)(5,125,18,112)(6,124,19,111)(7,123,20,110)(8,122,21,109)(9,121,22,108)(10,120,23,107)(11,119,24,106)(12,118,25,105)(13,117,26,130)(27,385,40,372)(28,384,41,371)(29,383,42,370)(30,382,43,369)(31,381,44,368)(32,380,45,367)(33,379,46,366)(34,378,47,365)(35,377,48,390)(36,376,49,389)(37,375,50,388)(38,374,51,387)(39,373,52,386)(53,85,66,98)(54,84,67,97)(55,83,68,96)(56,82,69,95)(57,81,70,94)(58,80,71,93)(59,79,72,92)(60,104,73,91)(61,103,74,90)(62,102,75,89)(63,101,76,88)(64,100,77,87)(65,99,78,86)(131,349,144,362)(132,348,145,361)(133,347,146,360)(134,346,147,359)(135,345,148,358)(136,344,149,357)(137,343,150,356)(138,342,151,355)(139,341,152,354)(140,340,153,353)(141,339,154,352)(142,364,155,351)(143,363,156,350)(157,287,170,300)(158,312,171,299)(159,311,172,298)(160,310,173,297)(161,309,174,296)(162,308,175,295)(163,307,176,294)(164,306,177,293)(165,305,178,292)(166,304,179,291)(167,303,180,290)(168,302,181,289)(169,301,182,288)(183,214,196,227)(184,213,197,226)(185,212,198,225)(186,211,199,224)(187,210,200,223)(188,209,201,222)(189,234,202,221)(190,233,203,220)(191,232,204,219)(192,231,205,218)(193,230,206,217)(194,229,207,216)(195,228,208,215)(235,271,248,284)(236,270,249,283)(237,269,250,282)(238,268,251,281)(239,267,252,280)(240,266,253,279)(241,265,254,278)(242,264,255,277)(243,263,256,276)(244,262,257,275)(245,261,258,274)(246,286,259,273)(247,285,260,272)(313,408,326,395)(314,407,327,394)(315,406,328,393)(316,405,329,392)(317,404,330,391)(318,403,331,416)(319,402,332,415)(320,401,333,414)(321,400,334,413)(322,399,335,412)(323,398,336,411)(324,397,337,410)(325,396,338,409)>;

G:=Group( (1,309,47,217,399,342,280,72)(2,310,48,218,400,343,281,73)(3,311,49,219,401,344,282,74)(4,312,50,220,402,345,283,75)(5,287,51,221,403,346,284,76)(6,288,52,222,404,347,285,77)(7,289,27,223,405,348,286,78)(8,290,28,224,406,349,261,53)(9,291,29,225,407,350,262,54)(10,292,30,226,408,351,263,55)(11,293,31,227,409,352,264,56)(12,294,32,228,410,353,265,57)(13,295,33,229,411,354,266,58)(14,296,34,230,412,355,267,59)(15,297,35,231,413,356,268,60)(16,298,36,232,414,357,269,61)(17,299,37,233,415,358,270,62)(18,300,38,234,416,359,271,63)(19,301,39,209,391,360,272,64)(20,302,40,210,392,361,273,65)(21,303,41,211,393,362,274,66)(22,304,42,212,394,363,275,67)(23,305,43,213,395,364,276,68)(24,306,44,214,396,339,277,69)(25,307,45,215,397,340,278,70)(26,308,46,216,398,341,279,71)(79,116,161,378,206,322,138,252)(80,117,162,379,207,323,139,253)(81,118,163,380,208,324,140,254)(82,119,164,381,183,325,141,255)(83,120,165,382,184,326,142,256)(84,121,166,383,185,327,143,257)(85,122,167,384,186,328,144,258)(86,123,168,385,187,329,145,259)(87,124,169,386,188,330,146,260)(88,125,170,387,189,331,147,235)(89,126,171,388,190,332,148,236)(90,127,172,389,191,333,149,237)(91,128,173,390,192,334,150,238)(92,129,174,365,193,335,151,239)(93,130,175,366,194,336,152,240)(94,105,176,367,195,337,153,241)(95,106,177,368,196,338,154,242)(96,107,178,369,197,313,155,243)(97,108,179,370,198,314,156,244)(98,109,180,371,199,315,131,245)(99,110,181,372,200,316,132,246)(100,111,182,373,201,317,133,247)(101,112,157,374,202,318,134,248)(102,113,158,375,203,319,135,249)(103,114,159,376,204,320,136,250)(104,115,160,377,205,321,137,251), (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)(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416), (1,129,14,116)(2,128,15,115)(3,127,16,114)(4,126,17,113)(5,125,18,112)(6,124,19,111)(7,123,20,110)(8,122,21,109)(9,121,22,108)(10,120,23,107)(11,119,24,106)(12,118,25,105)(13,117,26,130)(27,385,40,372)(28,384,41,371)(29,383,42,370)(30,382,43,369)(31,381,44,368)(32,380,45,367)(33,379,46,366)(34,378,47,365)(35,377,48,390)(36,376,49,389)(37,375,50,388)(38,374,51,387)(39,373,52,386)(53,85,66,98)(54,84,67,97)(55,83,68,96)(56,82,69,95)(57,81,70,94)(58,80,71,93)(59,79,72,92)(60,104,73,91)(61,103,74,90)(62,102,75,89)(63,101,76,88)(64,100,77,87)(65,99,78,86)(131,349,144,362)(132,348,145,361)(133,347,146,360)(134,346,147,359)(135,345,148,358)(136,344,149,357)(137,343,150,356)(138,342,151,355)(139,341,152,354)(140,340,153,353)(141,339,154,352)(142,364,155,351)(143,363,156,350)(157,287,170,300)(158,312,171,299)(159,311,172,298)(160,310,173,297)(161,309,174,296)(162,308,175,295)(163,307,176,294)(164,306,177,293)(165,305,178,292)(166,304,179,291)(167,303,180,290)(168,302,181,289)(169,301,182,288)(183,214,196,227)(184,213,197,226)(185,212,198,225)(186,211,199,224)(187,210,200,223)(188,209,201,222)(189,234,202,221)(190,233,203,220)(191,232,204,219)(192,231,205,218)(193,230,206,217)(194,229,207,216)(195,228,208,215)(235,271,248,284)(236,270,249,283)(237,269,250,282)(238,268,251,281)(239,267,252,280)(240,266,253,279)(241,265,254,278)(242,264,255,277)(243,263,256,276)(244,262,257,275)(245,261,258,274)(246,286,259,273)(247,285,260,272)(313,408,326,395)(314,407,327,394)(315,406,328,393)(316,405,329,392)(317,404,330,391)(318,403,331,416)(319,402,332,415)(320,401,333,414)(321,400,334,413)(322,399,335,412)(323,398,336,411)(324,397,337,410)(325,396,338,409) );

G=PermutationGroup([(1,309,47,217,399,342,280,72),(2,310,48,218,400,343,281,73),(3,311,49,219,401,344,282,74),(4,312,50,220,402,345,283,75),(5,287,51,221,403,346,284,76),(6,288,52,222,404,347,285,77),(7,289,27,223,405,348,286,78),(8,290,28,224,406,349,261,53),(9,291,29,225,407,350,262,54),(10,292,30,226,408,351,263,55),(11,293,31,227,409,352,264,56),(12,294,32,228,410,353,265,57),(13,295,33,229,411,354,266,58),(14,296,34,230,412,355,267,59),(15,297,35,231,413,356,268,60),(16,298,36,232,414,357,269,61),(17,299,37,233,415,358,270,62),(18,300,38,234,416,359,271,63),(19,301,39,209,391,360,272,64),(20,302,40,210,392,361,273,65),(21,303,41,211,393,362,274,66),(22,304,42,212,394,363,275,67),(23,305,43,213,395,364,276,68),(24,306,44,214,396,339,277,69),(25,307,45,215,397,340,278,70),(26,308,46,216,398,341,279,71),(79,116,161,378,206,322,138,252),(80,117,162,379,207,323,139,253),(81,118,163,380,208,324,140,254),(82,119,164,381,183,325,141,255),(83,120,165,382,184,326,142,256),(84,121,166,383,185,327,143,257),(85,122,167,384,186,328,144,258),(86,123,168,385,187,329,145,259),(87,124,169,386,188,330,146,260),(88,125,170,387,189,331,147,235),(89,126,171,388,190,332,148,236),(90,127,172,389,191,333,149,237),(91,128,173,390,192,334,150,238),(92,129,174,365,193,335,151,239),(93,130,175,366,194,336,152,240),(94,105,176,367,195,337,153,241),(95,106,177,368,196,338,154,242),(96,107,178,369,197,313,155,243),(97,108,179,370,198,314,156,244),(98,109,180,371,199,315,131,245),(99,110,181,372,200,316,132,246),(100,111,182,373,201,317,133,247),(101,112,157,374,202,318,134,248),(102,113,158,375,203,319,135,249),(103,114,159,376,204,320,136,250),(104,115,160,377,205,321,137,251)], [(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),(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416)], [(1,129,14,116),(2,128,15,115),(3,127,16,114),(4,126,17,113),(5,125,18,112),(6,124,19,111),(7,123,20,110),(8,122,21,109),(9,121,22,108),(10,120,23,107),(11,119,24,106),(12,118,25,105),(13,117,26,130),(27,385,40,372),(28,384,41,371),(29,383,42,370),(30,382,43,369),(31,381,44,368),(32,380,45,367),(33,379,46,366),(34,378,47,365),(35,377,48,390),(36,376,49,389),(37,375,50,388),(38,374,51,387),(39,373,52,386),(53,85,66,98),(54,84,67,97),(55,83,68,96),(56,82,69,95),(57,81,70,94),(58,80,71,93),(59,79,72,92),(60,104,73,91),(61,103,74,90),(62,102,75,89),(63,101,76,88),(64,100,77,87),(65,99,78,86),(131,349,144,362),(132,348,145,361),(133,347,146,360),(134,346,147,359),(135,345,148,358),(136,344,149,357),(137,343,150,356),(138,342,151,355),(139,341,152,354),(140,340,153,353),(141,339,154,352),(142,364,155,351),(143,363,156,350),(157,287,170,300),(158,312,171,299),(159,311,172,298),(160,310,173,297),(161,309,174,296),(162,308,175,295),(163,307,176,294),(164,306,177,293),(165,305,178,292),(166,304,179,291),(167,303,180,290),(168,302,181,289),(169,301,182,288),(183,214,196,227),(184,213,197,226),(185,212,198,225),(186,211,199,224),(187,210,200,223),(188,209,201,222),(189,234,202,221),(190,233,203,220),(191,232,204,219),(192,231,205,218),(193,230,206,217),(194,229,207,216),(195,228,208,215),(235,271,248,284),(236,270,249,283),(237,269,250,282),(238,268,251,281),(239,267,252,280),(240,266,253,279),(241,265,254,278),(242,264,255,277),(243,263,256,276),(244,262,257,275),(245,261,258,274),(246,286,259,273),(247,285,260,272),(313,408,326,395),(314,407,327,394),(315,406,328,393),(316,405,329,392),(317,404,330,391),(318,403,331,416),(319,402,332,415),(320,401,333,414),(321,400,334,413),(322,399,335,412),(323,398,336,411),(324,397,337,410),(325,396,338,409)])

128 conjugacy classes

class 1 2A2B2C4A4B4C4D4E···4L8A···8H8I···8P13A···13F26A···26R52A···52X104A···104AV
order122244444···48···88···813···1326···2652···52104···104
size1111111113···131···113···132···22···22···22···2

128 irreducible representations

dim11111111222222
type+++++-+
imageC1C2C2C2C4C4C4C8D13Dic13D26C4×D13C4×D13C8×D13
kernelC8×Dic13C2×C132C8C4×Dic13C2×C104C132C8C104C2×Dic13Dic13C2×C8C8C2×C4C4C22C2
# reps1111444166126121248

Matrix representation of C8×Dic13 in GL3(𝔽313) generated by

31200
050
005
,
31200
00312
01289
,
2500
016970
057144
G:=sub<GL(3,GF(313))| [312,0,0,0,5,0,0,0,5],[312,0,0,0,0,1,0,312,289],[25,0,0,0,169,57,0,70,144] >;

C8×Dic13 in GAP, Magma, Sage, TeX

C_8\times {\rm Dic}_{13}
% in TeX

G:=Group("C8xDic13");
// GroupNames label

G:=SmallGroup(416,20);
// by ID

G=gap.SmallGroup(416,20);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,24,55,69,13829]);
// Polycyclic

G:=Group<a,b,c|a^8=b^26=1,c^2=b^13,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C8×Dic13 in TeX

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