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G = Dic104C8order 320 = 26·5

2nd semidirect product of Dic10 and C8 acting via C8/C4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic104C8, C20.25Q16, C20.40SD16, C42.193D10, C20.18M4(2), C54(Q8⋊C8), C4⋊C8.5D5, C4.2(C8×D5), C10.23C4≀C2, C20.28(C2×C8), (C2×C20).226D4, (C2×C4).110D20, C4.2(C8⋊D5), C4⋊Dic5.27C4, C4.15(D4.D5), (C4×C20).42C22, (C4×Dic10).6C2, C4.13(C5⋊Q16), C2.2(D207C4), C2.8(D101C8), C10.21(C22⋊C8), C10.9(Q8⋊C4), (C2×Dic10).24C4, C2.1(C10.Q16), C22.35(D10⋊C4), (C5×C4⋊C8).5C2, (C4×C52C8).3C2, (C2×C4).66(C4×D5), (C2×C20).222(C2×C4), (C2×C4).266(C5⋊D4), (C2×C10).110(C22⋊C4), SmallGroup(320,42)

Series: Derived Chief Lower central Upper central

C1C20 — Dic104C8
C1C5C10C2×C10C2×C20C4×C20C4×Dic10 — Dic104C8
C5C10C20 — Dic104C8
C1C2×C4C42C4⋊C8

Generators and relations for Dic104C8
 G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a11, cbc-1=a5b >

Subgroups: 230 in 70 conjugacy classes, 35 normal (33 characteristic)
C1, C2 [×3], C4 [×4], C4 [×4], C22, C5, C8 [×3], C2×C4 [×3], C2×C4 [×2], Q8 [×3], C10 [×3], C42, C42, C4⋊C4 [×2], C2×C8 [×2], C2×Q8, Dic5 [×3], C20 [×4], C20, C2×C10, C4×C8, C4⋊C8, C4×Q8, C52C8 [×2], C40, Dic10 [×2], Dic10, C2×Dic5 [×2], C2×C20 [×3], Q8⋊C8, C2×C52C8, C4×Dic5, C10.D4, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C4×C52C8, C5×C4⋊C8, C4×Dic10, Dic104C8
Quotients: C1, C2 [×3], C4 [×2], C22, C8 [×2], C2×C4, D4 [×2], D5, C22⋊C4, C2×C8, M4(2), SD16, Q16, D10, C22⋊C8, Q8⋊C4, C4≀C2, C4×D5, D20, C5⋊D4, Q8⋊C8, C8×D5, C8⋊D5, D10⋊C4, D4.D5, C5⋊Q16, C10.Q16, D101C8, D207C4, Dic104C8

Smallest permutation representation of Dic104C8
Regular action on 320 points
Generators in S320
(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)
(1 27 11 37)(2 26 12 36)(3 25 13 35)(4 24 14 34)(5 23 15 33)(6 22 16 32)(7 21 17 31)(8 40 18 30)(9 39 19 29)(10 38 20 28)(41 91 51 81)(42 90 52 100)(43 89 53 99)(44 88 54 98)(45 87 55 97)(46 86 56 96)(47 85 57 95)(48 84 58 94)(49 83 59 93)(50 82 60 92)(61 165 71 175)(62 164 72 174)(63 163 73 173)(64 162 74 172)(65 161 75 171)(66 180 76 170)(67 179 77 169)(68 178 78 168)(69 177 79 167)(70 176 80 166)(101 267 111 277)(102 266 112 276)(103 265 113 275)(104 264 114 274)(105 263 115 273)(106 262 116 272)(107 261 117 271)(108 280 118 270)(109 279 119 269)(110 278 120 268)(121 303 131 313)(122 302 132 312)(123 301 133 311)(124 320 134 310)(125 319 135 309)(126 318 136 308)(127 317 137 307)(128 316 138 306)(129 315 139 305)(130 314 140 304)(141 300 151 290)(142 299 152 289)(143 298 153 288)(144 297 154 287)(145 296 155 286)(146 295 156 285)(147 294 157 284)(148 293 158 283)(149 292 159 282)(150 291 160 281)(181 256 191 246)(182 255 192 245)(183 254 193 244)(184 253 194 243)(185 252 195 242)(186 251 196 241)(187 250 197 260)(188 249 198 259)(189 248 199 258)(190 247 200 257)(201 225 211 235)(202 224 212 234)(203 223 213 233)(204 222 214 232)(205 221 215 231)(206 240 216 230)(207 239 217 229)(208 238 218 228)(209 237 219 227)(210 236 220 226)
(1 66 192 107 316 212 294 89)(2 77 193 118 317 203 295 100)(3 68 194 109 318 214 296 91)(4 79 195 120 319 205 297 82)(5 70 196 111 320 216 298 93)(6 61 197 102 301 207 299 84)(7 72 198 113 302 218 300 95)(8 63 199 104 303 209 281 86)(9 74 200 115 304 220 282 97)(10 65 181 106 305 211 283 88)(11 76 182 117 306 202 284 99)(12 67 183 108 307 213 285 90)(13 78 184 119 308 204 286 81)(14 69 185 110 309 215 287 92)(15 80 186 101 310 206 288 83)(16 71 187 112 311 217 289 94)(17 62 188 103 312 208 290 85)(18 73 189 114 313 219 291 96)(19 64 190 105 314 210 292 87)(20 75 191 116 315 201 293 98)(21 169 259 270 132 223 151 42)(22 180 260 261 133 234 152 53)(23 171 241 272 134 225 153 44)(24 162 242 263 135 236 154 55)(25 173 243 274 136 227 155 46)(26 164 244 265 137 238 156 57)(27 175 245 276 138 229 157 48)(28 166 246 267 139 240 158 59)(29 177 247 278 140 231 159 50)(30 168 248 269 121 222 160 41)(31 179 249 280 122 233 141 52)(32 170 250 271 123 224 142 43)(33 161 251 262 124 235 143 54)(34 172 252 273 125 226 144 45)(35 163 253 264 126 237 145 56)(36 174 254 275 127 228 146 47)(37 165 255 266 128 239 147 58)(38 176 256 277 129 230 148 49)(39 167 257 268 130 221 149 60)(40 178 258 279 131 232 150 51)

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

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

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

68 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K4L5A5B8A8B8C8D8E···8L10A···10F20A···20H20I···20P40A···40P
order12224444444444445588888···810···1020···2020···2040···40
size1111111122222020202022444410···102···22···24···44···4

68 irreducible representations

dim1111111222222222222444
type++++++-++--
imageC1C2C2C2C4C4C8D4D5M4(2)SD16Q16D10C4≀C2C4×D5D20C5⋊D4C8×D5C8⋊D5D4.D5C5⋊Q16D207C4
kernelDic104C8C4×C52C8C5×C4⋊C8C4×Dic10C4⋊Dic5C2×Dic10Dic10C2×C20C4⋊C8C20C20C20C42C10C2×C4C2×C4C2×C4C4C4C4C4C2
# reps1111228222222444488224

Matrix representation of Dic104C8 in GL4(𝔽41) generated by

0100
40000
00140
00834
,
401100
11100
00740
00734
,
203800
382100
00332
00258
G:=sub<GL(4,GF(41))| [0,40,0,0,1,0,0,0,0,0,1,8,0,0,40,34],[40,11,0,0,11,1,0,0,0,0,7,7,0,0,40,34],[20,38,0,0,38,21,0,0,0,0,33,25,0,0,2,8] >;

Dic104C8 in GAP, Magma, Sage, TeX

{\rm Dic}_{10}\rtimes_4C_8
% in TeX

G:=Group("Dic10:4C8");
// GroupNames label

G:=SmallGroup(320,42);
// by ID

G=gap.SmallGroup(320,42);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,141,36,100,1123,570,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=c^8=1,b^2=a^10,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=a^5*b>;
// generators/relations

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