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G = C20.26Q16order 320 = 26·5

5th non-split extension by C20 of Q16 acting via Q16/Q8=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C20.26Q16, C20.50SD16, C42.195D10, C20.22M4(2), C55(Q8⋊C8), Q8⋊(C52C8), (C5×Q8)⋊3C8, C10.27C4≀C2, (C4×Q8).1D5, C20.32(C2×C8), C4⋊C4.4Dic5, (Q8×C20).1C2, (C2×C20).490D4, C4.16(Q8⋊D5), (Q8×C10).17C4, (C2×Q8).4Dic5, C203C8.11C2, (C4×C20).46C22, C4.14(C5⋊Q16), C4.2(C4.Dic5), C10.31(C22⋊C8), C2.2(Q8⋊Dic5), C10.17(Q8⋊C4), C2.3(D42Dic5), C2.6(C20.55D4), C22.30(C23.D5), C4.2(C2×C52C8), (C5×C4⋊C4).19C4, (C4×C52C8).4C2, (C2×C20).233(C2×C4), (C2×C4).38(C2×Dic5), (C2×C4).162(C5⋊D4), (C2×C10).157(C22⋊C4), SmallGroup(320,93)

Series: Derived Chief Lower central Upper central

C1C20 — C20.26Q16
C1C5C10C2×C10C2×C20C4×C20C203C8 — C20.26Q16
C5C10C20 — C20.26Q16
C1C2×C4C42C4×Q8

Generators and relations for C20.26Q16
 G = < a,b,c | a20=b8=1, c2=a10b4, bab-1=a9, ac=ca, cbc-1=a5b-1 >

Subgroups: 166 in 70 conjugacy classes, 39 normal (35 characteristic)
C1, C2 [×3], C4 [×4], C4 [×4], C22, C5, C8 [×3], C2×C4 [×3], C2×C4 [×2], Q8 [×2], Q8, C10 [×3], C42, C42, C4⋊C4, C4⋊C4, C2×C8 [×2], C2×Q8, C20 [×4], C20 [×4], C2×C10, C4×C8, C4⋊C8, C4×Q8, C52C8 [×3], C2×C20 [×3], C2×C20 [×2], C5×Q8 [×2], C5×Q8, Q8⋊C8, C2×C52C8 [×2], C4×C20, C4×C20, C5×C4⋊C4, C5×C4⋊C4, Q8×C10, C4×C52C8, C203C8, Q8×C20, C20.26Q16
Quotients: C1, C2 [×3], C4 [×2], C22, C8 [×2], C2×C4, D4 [×2], D5, C22⋊C4, C2×C8, M4(2), SD16, Q16, Dic5 [×2], D10, C22⋊C8, Q8⋊C4, C4≀C2, C52C8 [×2], C2×Dic5, C5⋊D4 [×2], Q8⋊C8, C2×C52C8, C4.Dic5, Q8⋊D5, C5⋊Q16, C23.D5, C20.55D4, Q8⋊Dic5, D42Dic5, C20.26Q16

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

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

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

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

68 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K4L5A5B8A···8H8I8J8K8L10A···10F20A···20H20I···20AF
order1222444444444444558···8888810···1020···2020···20
size11111111222244442210···10202020202···22···24···4

68 irreducible representations

dim1111111222222222222444
type++++++-+--+-
imageC1C2C2C2C4C4C8D4D5M4(2)SD16Q16D10Dic5Dic5C4≀C2C5⋊D4C52C8C4.Dic5Q8⋊D5C5⋊Q16D42Dic5
kernelC20.26Q16C4×C52C8C203C8Q8×C20C5×C4⋊C4Q8×C10C5×Q8C2×C20C4×Q8C20C20C20C42C4⋊C4C2×Q8C10C2×C4Q8C4C4C4C2
# reps1111228222222224888224

Matrix representation of C20.26Q16 in GL4(𝔽41) generated by

9900
41300
0090
0009
,
283100
261300
00039
002531
,
1000
0100
002011
001221
G:=sub<GL(4,GF(41))| [9,4,0,0,9,13,0,0,0,0,9,0,0,0,0,9],[28,26,0,0,31,13,0,0,0,0,0,25,0,0,39,31],[1,0,0,0,0,1,0,0,0,0,20,12,0,0,11,21] >;

C20.26Q16 in GAP, Magma, Sage, TeX

C_{20}._{26}Q_{16}
% in TeX

G:=Group("C20.26Q16");
// GroupNames label

G:=SmallGroup(320,93);
// by ID

G=gap.SmallGroup(320,93);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,232,100,1123,570,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=b^8=1,c^2=a^10*b^4,b*a*b^-1=a^9,a*c=c*a,c*b*c^-1=a^5*b^-1>;
// generators/relations

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