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G = C52.44D4order 416 = 25·13

1st non-split extension by C52 of D4 acting via D4/C22=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C52.44D4, C26.1Q16, Dic265C4, C2.1Dic52, C26.1SD16, C22.7D52, (C2×C8).2D13, C4.7(C4×D13), C52.38(C2×C4), (C2×C104).2C2, (C2×C4).67D26, (C2×C26).12D4, C523C4.1C2, C133(Q8⋊C4), C2.1(C104⋊C2), C4.19(C13⋊D4), (C2×C52).80C22, (C2×Dic26).1C2, C2.7(D26⋊C4), C26.16(C22⋊C4), SmallGroup(416,23)

Series: Derived Chief Lower central Upper central

C1C52 — C52.44D4
C1C13C26C52C2×C52C523C4 — C52.44D4
C13C26C52 — C52.44D4
C1C22C2×C4C2×C8

Generators and relations for C52.44D4
 G = < a,b,c | a52=b4=1, c2=a26, bab-1=cac-1=a-1, cbc-1=a13b-1 >

26C4
26C4
52C4
2C8
13Q8
13Q8
26C2×C4
26Q8
26C2×C4
2Dic13
2Dic13
4Dic13
13C2×Q8
13C4⋊C4
2C2×Dic13
2C2×Dic13
2C104
2Dic26
13Q8⋊C4

Smallest permutation representation of C52.44D4
Regular action on 416 points
Generators in S416
(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)
(1 298 358 198)(2 297 359 197)(3 296 360 196)(4 295 361 195)(5 294 362 194)(6 293 363 193)(7 292 364 192)(8 291 313 191)(9 290 314 190)(10 289 315 189)(11 288 316 188)(12 287 317 187)(13 286 318 186)(14 285 319 185)(15 284 320 184)(16 283 321 183)(17 282 322 182)(18 281 323 181)(19 280 324 180)(20 279 325 179)(21 278 326 178)(22 277 327 177)(23 276 328 176)(24 275 329 175)(25 274 330 174)(26 273 331 173)(27 272 332 172)(28 271 333 171)(29 270 334 170)(30 269 335 169)(31 268 336 168)(32 267 337 167)(33 266 338 166)(34 265 339 165)(35 264 340 164)(36 263 341 163)(37 262 342 162)(38 261 343 161)(39 312 344 160)(40 311 345 159)(41 310 346 158)(42 309 347 157)(43 308 348 208)(44 307 349 207)(45 306 350 206)(46 305 351 205)(47 304 352 204)(48 303 353 203)(49 302 354 202)(50 301 355 201)(51 300 356 200)(52 299 357 199)(53 153 251 366)(54 152 252 365)(55 151 253 416)(56 150 254 415)(57 149 255 414)(58 148 256 413)(59 147 257 412)(60 146 258 411)(61 145 259 410)(62 144 260 409)(63 143 209 408)(64 142 210 407)(65 141 211 406)(66 140 212 405)(67 139 213 404)(68 138 214 403)(69 137 215 402)(70 136 216 401)(71 135 217 400)(72 134 218 399)(73 133 219 398)(74 132 220 397)(75 131 221 396)(76 130 222 395)(77 129 223 394)(78 128 224 393)(79 127 225 392)(80 126 226 391)(81 125 227 390)(82 124 228 389)(83 123 229 388)(84 122 230 387)(85 121 231 386)(86 120 232 385)(87 119 233 384)(88 118 234 383)(89 117 235 382)(90 116 236 381)(91 115 237 380)(92 114 238 379)(93 113 239 378)(94 112 240 377)(95 111 241 376)(96 110 242 375)(97 109 243 374)(98 108 244 373)(99 107 245 372)(100 106 246 371)(101 105 247 370)(102 156 248 369)(103 155 249 368)(104 154 250 367)
(1 147 27 121)(2 146 28 120)(3 145 29 119)(4 144 30 118)(5 143 31 117)(6 142 32 116)(7 141 33 115)(8 140 34 114)(9 139 35 113)(10 138 36 112)(11 137 37 111)(12 136 38 110)(13 135 39 109)(14 134 40 108)(15 133 41 107)(16 132 42 106)(17 131 43 105)(18 130 44 156)(19 129 45 155)(20 128 46 154)(21 127 47 153)(22 126 48 152)(23 125 49 151)(24 124 50 150)(25 123 51 149)(26 122 52 148)(53 265 79 291)(54 264 80 290)(55 263 81 289)(56 262 82 288)(57 261 83 287)(58 312 84 286)(59 311 85 285)(60 310 86 284)(61 309 87 283)(62 308 88 282)(63 307 89 281)(64 306 90 280)(65 305 91 279)(66 304 92 278)(67 303 93 277)(68 302 94 276)(69 301 95 275)(70 300 96 274)(71 299 97 273)(72 298 98 272)(73 297 99 271)(74 296 100 270)(75 295 101 269)(76 294 102 268)(77 293 103 267)(78 292 104 266)(157 233 183 259)(158 232 184 258)(159 231 185 257)(160 230 186 256)(161 229 187 255)(162 228 188 254)(163 227 189 253)(164 226 190 252)(165 225 191 251)(166 224 192 250)(167 223 193 249)(168 222 194 248)(169 221 195 247)(170 220 196 246)(171 219 197 245)(172 218 198 244)(173 217 199 243)(174 216 200 242)(175 215 201 241)(176 214 202 240)(177 213 203 239)(178 212 204 238)(179 211 205 237)(180 210 206 236)(181 209 207 235)(182 260 208 234)(313 405 339 379)(314 404 340 378)(315 403 341 377)(316 402 342 376)(317 401 343 375)(318 400 344 374)(319 399 345 373)(320 398 346 372)(321 397 347 371)(322 396 348 370)(323 395 349 369)(324 394 350 368)(325 393 351 367)(326 392 352 366)(327 391 353 365)(328 390 354 416)(329 389 355 415)(330 388 356 414)(331 387 357 413)(332 386 358 412)(333 385 359 411)(334 384 360 410)(335 383 361 409)(336 382 362 408)(337 381 363 407)(338 380 364 406)

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

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

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

110 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F8A8B8C8D13A···13F26A···26R52A···52X104A···104AV
order1222444444888813···1326···2652···52104···104
size1111225252525222222···22···22···22···2

110 irreducible representations

dim1111122222222222
type++++++-+++-
imageC1C2C2C2C4D4D4SD16Q16D13D26C4×D13C13⋊D4D52C104⋊C2Dic52
kernelC52.44D4C523C4C2×C104C2×Dic26Dic26C52C2×C26C26C26C2×C8C2×C4C4C4C22C2C2
# reps111141122661212122424

Matrix representation of C52.44D4 in GL4(𝔽313) generated by

30422700
29120700
0026261
00179256
,
13224100
2918100
0016816
00251145
,
1753000
10613800
0095111
00305218
G:=sub<GL(4,GF(313))| [304,291,0,0,227,207,0,0,0,0,26,179,0,0,261,256],[132,29,0,0,241,181,0,0,0,0,168,251,0,0,16,145],[175,106,0,0,30,138,0,0,0,0,95,305,0,0,111,218] >;

C52.44D4 in GAP, Magma, Sage, TeX

C_{52}._{44}D_4
% in TeX

G:=Group("C52.44D4");
// GroupNames label

G:=SmallGroup(416,23);
// by ID

G=gap.SmallGroup(416,23);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,48,73,79,362,86,13829]);
// Polycyclic

G:=Group<a,b,c|a^52=b^4=1,c^2=a^26,b*a*b^-1=c*a*c^-1=a^-1,c*b*c^-1=a^13*b^-1>;
// generators/relations

Export

Subgroup lattice of C52.44D4 in TeX

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