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G = C20.7Q16order 320 = 26·5

7th non-split extension by C20 of Q16 acting via Q16/C4=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C20.7Q16, Dic103Q8, C4.7Dic20, C42.41D10, C4⋊C8.8D5, C4.46(Q8×D5), C52(C4.Q16), (C2×C8).24D10, C10.8(C2×Q16), C405C4.9C2, (C2×C20).126D4, (C2×C4).137D20, C20.105(C2×Q8), (C4×C20).76C22, (C2×C40).28C22, C202Q8.12C2, C2.10(C2×Dic20), C20.289(C4○D4), C2.21(C8⋊D10), C10.18(C8⋊C22), (C2×C20).760C23, (C4×Dic10).12C2, C20.44D4.4C2, C22.123(C2×D20), C10.33(C22⋊Q8), C4⋊Dic5.21C22, C4.113(D42D5), C2.14(D102Q8), (C2×Dic10).222C22, (C5×C4⋊C8).13C2, (C2×C10).143(C2×D4), (C2×C4).705(C22×D5), SmallGroup(320,477)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C20.7Q16
C1C5C10C20C2×C20C2×Dic10C4×Dic10 — C20.7Q16
C5C10C2×C20 — C20.7Q16
C1C22C42C4⋊C8

Generators and relations for C20.7Q16
 G = < a,b,c | a20=b8=1, c2=b4, bab-1=a11, cac-1=a9, cbc-1=a10b-1 >

Subgroups: 374 in 96 conjugacy classes, 45 normal (29 characteristic)
C1, C2 [×3], C4 [×2], C4 [×2], C4 [×6], C22, C5, C8 [×2], C2×C4 [×3], C2×C4 [×4], Q8 [×5], C10 [×3], C42, C42, C4⋊C4 [×5], C2×C8 [×2], C2×Q8 [×2], Dic5 [×5], C20 [×2], C20 [×2], C20, C2×C10, Q8⋊C4 [×2], C4⋊C8, C2.D8 [×2], C4×Q8, C4⋊Q8, C40 [×2], Dic10 [×2], Dic10 [×3], C2×Dic5 [×4], C2×C20 [×3], C4.Q16, C4×Dic5, C10.D4, C4⋊Dic5, C4⋊Dic5 [×2], C4⋊Dic5, C4×C20, C2×C40 [×2], C2×Dic10, C2×Dic10, C20.44D4 [×2], C405C4 [×2], C5×C4⋊C8, C4×Dic10, C202Q8, C20.7Q16
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], Q8 [×2], C23, D5, Q16 [×2], C2×D4, C2×Q8, C4○D4, D10 [×3], C22⋊Q8, C2×Q16, C8⋊C22, D20 [×2], C22×D5, C4.Q16, Dic20 [×2], C2×D20, D42D5, Q8×D5, D102Q8, C2×Dic20, C8⋊D10, C20.7Q16

Smallest permutation representation of C20.7Q16
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 78 133 56 222 203 184 250)(2 69 134 47 223 214 185 241)(3 80 135 58 224 205 186 252)(4 71 136 49 225 216 187 243)(5 62 137 60 226 207 188 254)(6 73 138 51 227 218 189 245)(7 64 139 42 228 209 190 256)(8 75 140 53 229 220 191 247)(9 66 121 44 230 211 192 258)(10 77 122 55 231 202 193 249)(11 68 123 46 232 213 194 260)(12 79 124 57 233 204 195 251)(13 70 125 48 234 215 196 242)(14 61 126 59 235 206 197 253)(15 72 127 50 236 217 198 244)(16 63 128 41 237 208 199 255)(17 74 129 52 238 219 200 246)(18 65 130 43 239 210 181 257)(19 76 131 54 240 201 182 248)(20 67 132 45 221 212 183 259)(21 162 85 273 295 305 156 106)(22 173 86 264 296 316 157 117)(23 164 87 275 297 307 158 108)(24 175 88 266 298 318 159 119)(25 166 89 277 299 309 160 110)(26 177 90 268 300 320 141 101)(27 168 91 279 281 311 142 112)(28 179 92 270 282 302 143 103)(29 170 93 261 283 313 144 114)(30 161 94 272 284 304 145 105)(31 172 95 263 285 315 146 116)(32 163 96 274 286 306 147 107)(33 174 97 265 287 317 148 118)(34 165 98 276 288 308 149 109)(35 176 99 267 289 319 150 120)(36 167 100 278 290 310 151 111)(37 178 81 269 291 301 152 102)(38 169 82 280 292 312 153 113)(39 180 83 271 293 303 154 104)(40 171 84 262 294 314 155 115)
(1 112 222 279)(2 101 223 268)(3 110 224 277)(4 119 225 266)(5 108 226 275)(6 117 227 264)(7 106 228 273)(8 115 229 262)(9 104 230 271)(10 113 231 280)(11 102 232 269)(12 111 233 278)(13 120 234 267)(14 109 235 276)(15 118 236 265)(16 107 237 274)(17 116 238 263)(18 105 239 272)(19 114 240 261)(20 103 221 270)(21 52 295 246)(22 41 296 255)(23 50 297 244)(24 59 298 253)(25 48 299 242)(26 57 300 251)(27 46 281 260)(28 55 282 249)(29 44 283 258)(30 53 284 247)(31 42 285 256)(32 51 286 245)(33 60 287 254)(34 49 288 243)(35 58 289 252)(36 47 290 241)(37 56 291 250)(38 45 292 259)(39 54 293 248)(40 43 294 257)(61 159 206 88)(62 148 207 97)(63 157 208 86)(64 146 209 95)(65 155 210 84)(66 144 211 93)(67 153 212 82)(68 142 213 91)(69 151 214 100)(70 160 215 89)(71 149 216 98)(72 158 217 87)(73 147 218 96)(74 156 219 85)(75 145 220 94)(76 154 201 83)(77 143 202 92)(78 152 203 81)(79 141 204 90)(80 150 205 99)(121 303 192 180)(122 312 193 169)(123 301 194 178)(124 310 195 167)(125 319 196 176)(126 308 197 165)(127 317 198 174)(128 306 199 163)(129 315 200 172)(130 304 181 161)(131 313 182 170)(132 302 183 179)(133 311 184 168)(134 320 185 177)(135 309 186 166)(136 318 187 175)(137 307 188 164)(138 316 189 173)(139 305 190 162)(140 314 191 171)

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

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

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

59 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K5A5B8A8B8C8D10A···10F20A···20H20I···20P40A···40P
order12224444444444455888810···1020···2020···2040···40
size1111222242020202040402244442···22···24···44···4

59 irreducible representations

dim1111112222222224444
type++++++-++-+++-+--+
imageC1C2C2C2C2C2Q8D4D5Q16C4○D4D10D10D20Dic20C8⋊C22D42D5Q8×D5C8⋊D10
kernelC20.7Q16C20.44D4C405C4C5×C4⋊C8C4×Dic10C202Q8Dic10C2×C20C4⋊C8C20C20C42C2×C8C2×C4C4C10C4C4C2
# reps12211122242248161224

Matrix representation of C20.7Q16 in GL4(𝔽41) generated by

16000
251800
002936
002912
,
38000
62700
001537
003626
,
281700
311300
0010
0001
G:=sub<GL(4,GF(41))| [16,25,0,0,0,18,0,0,0,0,29,29,0,0,36,12],[38,6,0,0,0,27,0,0,0,0,15,36,0,0,37,26],[28,31,0,0,17,13,0,0,0,0,1,0,0,0,0,1] >;

C20.7Q16 in GAP, Magma, Sage, TeX

C_{20}._7Q_{16}
% in TeX

G:=Group("C20.7Q16");
// GroupNames label

G:=SmallGroup(320,477);
// by ID

G=gap.SmallGroup(320,477);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,254,219,310,1123,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,b*a*b^-1=a^11,c*a*c^-1=a^9,c*b*c^-1=a^10*b^-1>;
// generators/relations

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