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G = C8.6Dic10order 320 = 26·5

3rd non-split extension by C8 of Dic10 acting via Dic10/Dic5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C40.4Q8, C8.6Dic10, C4.28(Q8×D5), C52C8.4Q8, C4⋊C4.46D10, C2.D8.7D5, C20.60(C2×Q8), C53(C8.5Q8), (C2×C8).228D10, C2.13(C20⋊Q8), C10.18(C4⋊Q8), (C8×Dic5).3C2, C405C4.15C2, C10.74(C4○D8), (C2×C40).80C22, C4.25(C2×Dic10), C22.227(D4×D5), C20.Q8.9C2, C2.13(D83D5), (C2×C20).294C23, (C2×Dic5).146D4, C4.Dic10.10C2, C2.12(Q8.D10), C4⋊Dic5.120C22, (C4×Dic5).265C22, (C5×C2.D8).6C2, (C2×C10).299(C2×D4), (C5×C4⋊C4).87C22, (C2×C4).397(C22×D5), (C2×C52C8).240C22, SmallGroup(320,505)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C8.6Dic10
C1C5C10C2×C10C2×C20C4×Dic5C8×Dic5 — C8.6Dic10
C5C10C2×C20 — C8.6Dic10
C1C22C2×C4C2.D8

Generators and relations for C8.6Dic10
 G = < a,b,c | a8=b20=1, c2=b10, bab-1=a-1, ac=ca, cbc-1=a4b-1 >

Subgroups: 286 in 86 conjugacy classes, 43 normal (27 characteristic)
C1, C2 [×3], C4 [×2], C4 [×6], C22, C5, C8 [×2], C8 [×2], C2×C4, C2×C4 [×6], C10 [×3], C42, C4⋊C4 [×2], C4⋊C4 [×6], C2×C8, C2×C8, Dic5 [×4], C20 [×2], C20 [×2], C2×C10, C4×C8, C4.Q8 [×2], C2.D8, C2.D8, C42.C2 [×2], C52C8 [×2], C40 [×2], C2×Dic5 [×2], C2×Dic5 [×2], C2×C20, C2×C20 [×2], C8.5Q8, C2×C52C8, C4×Dic5, C10.D4 [×2], C4⋊Dic5 [×2], C4⋊Dic5 [×2], C5×C4⋊C4 [×2], C2×C40, C20.Q8 [×2], C8×Dic5, C405C4, C5×C2.D8, C4.Dic10 [×2], C8.6Dic10
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], Q8 [×4], C23, D5, C2×D4, C2×Q8 [×2], D10 [×3], C4⋊Q8, C4○D8 [×2], Dic10 [×2], C22×D5, C8.5Q8, C2×Dic10, D4×D5, Q8×D5, C20⋊Q8, D83D5, Q8.D10, C8.6Dic10

Smallest permutation representation of C8.6Dic10
Regular action on 320 points
Generators in S320
(1 236 117 275 85 201 49 132)(2 133 50 202 86 276 118 237)(3 238 119 277 87 203 51 134)(4 135 52 204 88 278 120 239)(5 240 101 279 89 205 53 136)(6 137 54 206 90 280 102 221)(7 222 103 261 91 207 55 138)(8 139 56 208 92 262 104 223)(9 224 105 263 93 209 57 140)(10 121 58 210 94 264 106 225)(11 226 107 265 95 211 59 122)(12 123 60 212 96 266 108 227)(13 228 109 267 97 213 41 124)(14 125 42 214 98 268 110 229)(15 230 111 269 99 215 43 126)(16 127 44 216 100 270 112 231)(17 232 113 271 81 217 45 128)(18 129 46 218 82 272 114 233)(19 234 115 273 83 219 47 130)(20 131 48 220 84 274 116 235)(21 167 155 73 310 250 286 186)(22 187 287 251 311 74 156 168)(23 169 157 75 312 252 288 188)(24 189 289 253 313 76 158 170)(25 171 159 77 314 254 290 190)(26 191 291 255 315 78 160 172)(27 173 141 79 316 256 292 192)(28 193 293 257 317 80 142 174)(29 175 143 61 318 258 294 194)(30 195 295 259 319 62 144 176)(31 177 145 63 320 260 296 196)(32 197 297 241 301 64 146 178)(33 179 147 65 302 242 298 198)(34 199 299 243 303 66 148 180)(35 161 149 67 304 244 300 200)(36 181 281 245 305 68 150 162)(37 163 151 69 306 246 282 182)(38 183 283 247 307 70 152 164)(39 165 153 71 308 248 284 184)(40 185 285 249 309 72 154 166)
(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)
(1 199 11 189)(2 65 12 75)(3 197 13 187)(4 63 14 73)(5 195 15 185)(6 61 16 71)(7 193 17 183)(8 79 18 69)(9 191 19 181)(10 77 20 67)(21 278 31 268)(22 134 32 124)(23 276 33 266)(24 132 34 122)(25 274 35 264)(26 130 36 140)(27 272 37 262)(28 128 38 138)(29 270 39 280)(30 126 40 136)(41 168 51 178)(42 250 52 260)(43 166 53 176)(44 248 54 258)(45 164 55 174)(46 246 56 256)(47 162 57 172)(48 244 58 254)(49 180 59 170)(50 242 60 252)(62 99 72 89)(64 97 74 87)(66 95 76 85)(68 93 78 83)(70 91 80 81)(82 182 92 192)(84 200 94 190)(86 198 96 188)(88 196 98 186)(90 194 100 184)(101 259 111 249)(102 175 112 165)(103 257 113 247)(104 173 114 163)(105 255 115 245)(106 171 116 161)(107 253 117 243)(108 169 118 179)(109 251 119 241)(110 167 120 177)(121 314 131 304)(123 312 133 302)(125 310 135 320)(127 308 137 318)(129 306 139 316)(141 233 151 223)(142 217 152 207)(143 231 153 221)(144 215 154 205)(145 229 155 239)(146 213 156 203)(147 227 157 237)(148 211 158 201)(149 225 159 235)(150 209 160 219)(202 298 212 288)(204 296 214 286)(206 294 216 284)(208 292 218 282)(210 290 220 300)(222 293 232 283)(224 291 234 281)(226 289 236 299)(228 287 238 297)(230 285 240 295)(261 317 271 307)(263 315 273 305)(265 313 275 303)(267 311 277 301)(269 309 279 319)

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

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

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

50 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J5A5B8A8B8C8D8E8F8G8H10A···10F20A20B20C20D20E···20L40A···40H
order12224444444444558888888810···102020202020···2040···40
size11112288101010104040222222101010102···244448···84···4

50 irreducible representations

dim111111222222224444
type++++++--++++--+-+
imageC1C2C2C2C2C2Q8Q8D4D5D10D10C4○D8Dic10Q8×D5D4×D5D83D5Q8.D10
kernelC8.6Dic10C20.Q8C8×Dic5C405C4C5×C2.D8C4.Dic10C52C8C40C2×Dic5C2.D8C4⋊C4C2×C8C10C8C4C22C2C2
# reps121112222242882244

Matrix representation of C8.6Dic10 in GL4(𝔽41) generated by

172400
29000
0010
0001
,
371200
2400
00252
003913
,
9000
0900
002020
002321
G:=sub<GL(4,GF(41))| [17,29,0,0,24,0,0,0,0,0,1,0,0,0,0,1],[37,2,0,0,12,4,0,0,0,0,25,39,0,0,2,13],[9,0,0,0,0,9,0,0,0,0,20,23,0,0,20,21] >;

C8.6Dic10 in GAP, Magma, Sage, TeX

C_8._6{\rm Dic}_{10}
% in TeX

G:=Group("C8.6Dic10");
// GroupNames label

G:=SmallGroup(320,505);
// by ID

G=gap.SmallGroup(320,505);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,926,219,58,438,102,12550]);
// Polycyclic

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

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