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## G = C11×C8⋊C4order 352 = 25·11

### Direct product of C11 and C8⋊C4

direct product, metacyclic, nilpotent (class 2), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — C11×C8⋊C4
 Chief series C1 — C2 — C22 — C2×C4 — C2×C44 — C2×C88 — C11×C8⋊C4
 Lower central C1 — C2 — C11×C8⋊C4
 Upper central C1 — C2×C44 — C11×C8⋊C4

Generators and relations for C11×C8⋊C4
G = < a,b,c | a11=b8=c4=1, ab=ba, ac=ca, cbc-1=b5 >

Smallest permutation representation of C11×C8⋊C4
Regular action on 352 points
Generators in S352
(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)
(1 66 118 30 133 19 154 342)(2 56 119 31 134 20 144 343)(3 57 120 32 135 21 145 344)(4 58 121 33 136 22 146 345)(5 59 111 23 137 12 147 346)(6 60 112 24 138 13 148 347)(7 61 113 25 139 14 149 348)(8 62 114 26 140 15 150 349)(9 63 115 27 141 16 151 350)(10 64 116 28 142 17 152 351)(11 65 117 29 143 18 153 352)(34 102 55 158 70 122 80 98)(35 103 45 159 71 123 81 99)(36 104 46 160 72 124 82 89)(37 105 47 161 73 125 83 90)(38 106 48 162 74 126 84 91)(39 107 49 163 75 127 85 92)(40 108 50 164 76 128 86 93)(41 109 51 165 77 129 87 94)(42 110 52 155 67 130 88 95)(43 100 53 156 68 131 78 96)(44 101 54 157 69 132 79 97)(166 334 246 298 210 274 186 254)(167 335 247 299 211 275 187 255)(168 336 248 300 212 265 177 256)(169 337 249 301 213 266 178 257)(170 338 250 302 214 267 179 258)(171 339 251 303 215 268 180 259)(172 340 252 304 216 269 181 260)(173 341 253 305 217 270 182 261)(174 331 243 306 218 271 183 262)(175 332 244 307 219 272 184 263)(176 333 245 308 220 273 185 264)(188 297 209 312 224 322 234 276)(189 287 199 313 225 323 235 277)(190 288 200 314 226 324 236 278)(191 289 201 315 227 325 237 279)(192 290 202 316 228 326 238 280)(193 291 203 317 229 327 239 281)(194 292 204 318 230 328 240 282)(195 293 205 319 231 329 241 283)(196 294 206 309 221 330 242 284)(197 295 207 310 222 320 232 285)(198 296 208 311 223 321 233 286)
(1 166 102 196)(2 167 103 197)(3 168 104 198)(4 169 105 188)(5 170 106 189)(6 171 107 190)(7 172 108 191)(8 173 109 192)(9 174 110 193)(10 175 100 194)(11 176 101 195)(12 338 84 287)(13 339 85 288)(14 340 86 289)(15 341 87 290)(16 331 88 291)(17 332 78 292)(18 333 79 293)(19 334 80 294)(20 335 81 295)(21 336 82 296)(22 337 83 297)(23 258 74 277)(24 259 75 278)(25 260 76 279)(26 261 77 280)(27 262 67 281)(28 263 68 282)(29 264 69 283)(30 254 70 284)(31 255 71 285)(32 256 72 286)(33 257 73 276)(34 309 342 298)(35 310 343 299)(36 311 344 300)(37 312 345 301)(38 313 346 302)(39 314 347 303)(40 315 348 304)(41 316 349 305)(42 317 350 306)(43 318 351 307)(44 319 352 308)(45 320 56 275)(46 321 57 265)(47 322 58 266)(48 323 59 267)(49 324 60 268)(50 325 61 269)(51 326 62 270)(52 327 63 271)(53 328 64 272)(54 329 65 273)(55 330 66 274)(89 233 145 177)(90 234 146 178)(91 235 147 179)(92 236 148 180)(93 237 149 181)(94 238 150 182)(95 239 151 183)(96 240 152 184)(97 241 153 185)(98 242 154 186)(99 232 144 187)(111 250 162 199)(112 251 163 200)(113 252 164 201)(114 253 165 202)(115 243 155 203)(116 244 156 204)(117 245 157 205)(118 246 158 206)(119 247 159 207)(120 248 160 208)(121 249 161 209)(122 221 133 210)(123 222 134 211)(124 223 135 212)(125 224 136 213)(126 225 137 214)(127 226 138 215)(128 227 139 216)(129 228 140 217)(130 229 141 218)(131 230 142 219)(132 231 143 220)

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

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

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

220 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 4H 8A ··· 8H 11A ··· 11J 22A ··· 22AD 44A ··· 44AN 44AO ··· 44CB 88A ··· 88CB order 1 2 2 2 4 4 4 4 4 4 4 4 8 ··· 8 11 ··· 11 22 ··· 22 44 ··· 44 44 ··· 44 88 ··· 88 size 1 1 1 1 1 1 1 1 2 2 2 2 2 ··· 2 1 ··· 1 1 ··· 1 1 ··· 1 2 ··· 2 2 ··· 2

220 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 type + + + image C1 C2 C2 C4 C4 C11 C22 C22 C44 C44 M4(2) C11×M4(2) kernel C11×C8⋊C4 C4×C44 C2×C88 C88 C2×C44 C8⋊C4 C42 C2×C8 C8 C2×C4 C22 C2 # reps 1 1 2 8 4 10 10 20 80 40 4 40

Matrix representation of C11×C8⋊C4 in GL3(𝔽89) generated by

 1 0 0 0 8 0 0 0 8
,
 34 0 0 0 58 47 0 47 31
,
 34 0 0 0 0 1 0 88 0
G:=sub<GL(3,GF(89))| [1,0,0,0,8,0,0,0,8],[34,0,0,0,58,47,0,47,31],[34,0,0,0,0,88,0,1,0] >;

C11×C8⋊C4 in GAP, Magma, Sage, TeX

C_{11}\times C_8\rtimes C_4
% in TeX

G:=Group("C11xC8:C4");
// GroupNames label

G:=SmallGroup(352,46);
// by ID

G=gap.SmallGroup(352,46);
# by ID

G:=PCGroup([6,-2,-2,-11,-2,-2,-2,264,2137,535,117]);
// Polycyclic

G:=Group<a,b,c|a^11=b^8=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^5>;
// generators/relations

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