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G = C8⋊Dic10order 320 = 26·5

1st semidirect product of C8 and Dic10 acting via Dic10/C10=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C401Q8, C81Dic10, C42.13D10, C51(C8⋊Q8), (C2×C8).52D10, (C2×C20).34D4, (C2×C4).23D20, C8⋊C4.1D5, C10.5(C4⋊Q8), C20.72(C2×Q8), C406C4.2C2, (C4×C20).1C22, C202Q8.6C2, C405C4.10C2, C2.6(C8⋊D10), C10.1(C8⋊C22), (C2×C40).53C22, C2.9(C202Q8), C4.38(C2×Dic10), C22.95(C2×D20), C4⋊Dic5.7C22, C20.6Q8.2C2, (C2×C20).729C23, C2.6(C8.D10), C10.1(C8.C22), (C5×C8⋊C4).1C2, (C2×C10).112(C2×D4), (C2×C4).673(C22×D5), SmallGroup(320,329)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C8⋊Dic10
C1C5C10C20C2×C20C4⋊Dic5C202Q8 — C8⋊Dic10
C5C10C2×C20 — C8⋊Dic10
C1C22C42C8⋊C4

Generators and relations for C8⋊Dic10
 G = < a,b,c | a8=b20=1, c2=b10, bab-1=a5, cac-1=a-1, cbc-1=b-1 >

Subgroups: 350 in 90 conjugacy classes, 47 normal (25 characteristic)
C1, C2 [×3], C4 [×2], C4 [×6], C22, C5, C8 [×4], C2×C4 [×3], C2×C4 [×4], Q8 [×2], C10 [×3], C42, C4⋊C4 [×7], C2×C8 [×2], C2×Q8, Dic5 [×4], C20 [×2], C20 [×2], C2×C10, C8⋊C4, C4.Q8 [×2], C2.D8 [×2], C42.C2, C4⋊Q8, C40 [×4], Dic10 [×2], C2×Dic5 [×4], C2×C20 [×3], C8⋊Q8, C10.D4 [×2], C4⋊Dic5 [×2], C4⋊Dic5 [×2], C4⋊Dic5, C4×C20, C2×C40 [×2], C2×Dic10, C406C4 [×2], C405C4 [×2], C5×C8⋊C4, C202Q8, C20.6Q8, C8⋊Dic10
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], Q8 [×4], C23, D5, C2×D4, C2×Q8 [×2], D10 [×3], C4⋊Q8, C8⋊C22, C8.C22, Dic10 [×4], D20 [×2], C22×D5, C8⋊Q8, C2×Dic10 [×2], C2×D20, C202Q8, C8⋊D10, C8.D10, C8⋊Dic10

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

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

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

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

56 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H5A5B8A8B8C8D10A···10F20A···20H20I···20P40A···40P
order12224444444455888810···1020···2020···2040···40
size11112244404040402244442···22···24···44···4

56 irreducible representations

dim11111122222224444
type++++++-++++-++-+-
imageC1C2C2C2C2C2Q8D4D5D10D10Dic10D20C8⋊C22C8.C22C8⋊D10C8.D10
kernelC8⋊Dic10C406C4C405C4C5×C8⋊C4C202Q8C20.6Q8C40C2×C20C8⋊C4C42C2×C8C8C2×C4C10C10C2C2
# reps122111422241681144

Matrix representation of C8⋊Dic10 in GL6(𝔽41)

100000
010000
0018372022
004351620
00321564
0039323723
,
010000
4000000
003231540
001818915
00562318
00552338
,
3200000
20380000
001328237
0024283715
003523511
0023322236

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,18,4,32,39,0,0,37,35,15,32,0,0,20,16,6,37,0,0,22,20,4,23],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,3,18,5,5,0,0,23,18,6,5,0,0,15,9,23,23,0,0,40,15,18,38],[3,20,0,0,0,0,20,38,0,0,0,0,0,0,13,24,35,23,0,0,28,28,23,32,0,0,2,37,5,22,0,0,37,15,11,36] >;

C8⋊Dic10 in GAP, Magma, Sage, TeX

C_8\rtimes {\rm Dic}_{10}
% in TeX

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

G:=SmallGroup(320,329);
// by ID

G=gap.SmallGroup(320,329);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,253,120,254,387,58,1123,136,12550]);
// Polycyclic

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

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