Copied to
clipboard

G = Dic105C8order 320 = 26·5

3rd semidirect product of Dic10 and C8 acting via C8/C4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic105C8, C42.197D10, C54(C8×Q8), C4.4(C8×D5), C4⋊C8.13D5, C52C812Q8, C4.52(Q8×D5), C20.34(C2×C8), C10.26(C4×Q8), (C2×C8).213D10, C4⋊Dic5.28C4, C20.110(C2×Q8), Dic5.4(C2×C8), C10.50(C8○D4), (C4×C20).56C22, C10.32(C22×C8), (C4×Dic10).9C2, (C8×Dic5).18C2, C20.8Q8.8C2, C20.302(C4○D4), (C2×C20).827C23, (C2×C40).206C22, (C2×Dic10).25C4, C10.D4.21C4, C4.128(D42D5), C2.2(Dic53Q8), C2.3(D20.2C4), (C4×Dic5).305C22, C2.10(D5×C2×C8), (C5×C4⋊C8).17C2, (C4×C52C8).5C2, (C2×C4).70(C4×D5), C22.45(C2×C4×D5), (C2×C20).329(C2×C4), (C2×Dic5).97(C2×C4), (C2×C4).769(C22×D5), (C2×C10).183(C22×C4), (C2×C52C8).353C22, SmallGroup(320,457)

Series: Derived Chief Lower central Upper central

C1C10 — Dic105C8
C1C5C10C2×C10C2×C20C2×C52C8C4×C52C8 — Dic105C8
C5C10 — Dic105C8
C1C2×C4C4⋊C8

Generators and relations for Dic105C8
 G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a11, bc=cb >

Subgroups: 254 in 102 conjugacy classes, 61 normal (31 characteristic)
C1, C2 [×3], C4 [×2], C4 [×2], C4 [×7], C22, C5, C8 [×5], C2×C4 [×3], C2×C4 [×4], Q8 [×4], C10 [×3], C42, C42 [×2], C4⋊C4 [×3], C2×C8 [×2], C2×C8 [×2], C2×Q8, Dic5 [×4], Dic5 [×2], C20 [×2], C20 [×2], C20, C2×C10, C4×C8 [×3], C4⋊C8, C4⋊C8 [×2], C4×Q8, C52C8 [×2], C52C8, C40 [×2], Dic10 [×4], C2×Dic5 [×4], C2×C20 [×3], C8×Q8, C2×C52C8 [×2], C4×Dic5 [×2], C10.D4 [×2], C4⋊Dic5, C4×C20, C2×C40 [×2], C2×Dic10, C4×C52C8, C8×Dic5 [×2], C20.8Q8 [×2], C5×C4⋊C8, C4×Dic10, Dic105C8
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C8 [×4], C2×C4 [×6], Q8 [×2], C23, D5, C2×C8 [×6], C22×C4, C2×Q8, C4○D4, D10 [×3], C4×Q8, C22×C8, C8○D4, C4×D5 [×2], C22×D5, C8×Q8, C8×D5 [×2], C2×C4×D5, D42D5, Q8×D5, Dic53Q8, D5×C2×C8, D20.2C4, Dic105C8

Smallest permutation representation of Dic105C8
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)
(1 220 11 210)(2 219 12 209)(3 218 13 208)(4 217 14 207)(5 216 15 206)(6 215 16 205)(7 214 17 204)(8 213 18 203)(9 212 19 202)(10 211 20 201)(21 116 31 106)(22 115 32 105)(23 114 33 104)(24 113 34 103)(25 112 35 102)(26 111 36 101)(27 110 37 120)(28 109 38 119)(29 108 39 118)(30 107 40 117)(41 239 51 229)(42 238 52 228)(43 237 53 227)(44 236 54 226)(45 235 55 225)(46 234 56 224)(47 233 57 223)(48 232 58 222)(49 231 59 221)(50 230 60 240)(61 317 71 307)(62 316 72 306)(63 315 73 305)(64 314 74 304)(65 313 75 303)(66 312 76 302)(67 311 77 301)(68 310 78 320)(69 309 79 319)(70 308 80 318)(81 180 91 170)(82 179 92 169)(83 178 93 168)(84 177 94 167)(85 176 95 166)(86 175 96 165)(87 174 97 164)(88 173 98 163)(89 172 99 162)(90 171 100 161)(121 147 131 157)(122 146 132 156)(123 145 133 155)(124 144 134 154)(125 143 135 153)(126 142 136 152)(127 141 137 151)(128 160 138 150)(129 159 139 149)(130 158 140 148)(181 265 191 275)(182 264 192 274)(183 263 193 273)(184 262 194 272)(185 261 195 271)(186 280 196 270)(187 279 197 269)(188 278 198 268)(189 277 199 267)(190 276 200 266)(241 282 251 292)(242 281 252 291)(243 300 253 290)(244 299 254 289)(245 298 255 288)(246 297 256 287)(247 296 257 286)(248 295 258 285)(249 294 259 284)(250 293 260 283)
(1 67 292 28 181 225 87 121)(2 78 293 39 182 236 88 132)(3 69 294 30 183 227 89 123)(4 80 295 21 184 238 90 134)(5 71 296 32 185 229 91 125)(6 62 297 23 186 240 92 136)(7 73 298 34 187 231 93 127)(8 64 299 25 188 222 94 138)(9 75 300 36 189 233 95 129)(10 66 281 27 190 224 96 140)(11 77 282 38 191 235 97 131)(12 68 283 29 192 226 98 122)(13 79 284 40 193 237 99 133)(14 70 285 31 194 228 100 124)(15 61 286 22 195 239 81 135)(16 72 287 33 196 230 82 126)(17 63 288 24 197 221 83 137)(18 74 289 35 198 232 84 128)(19 65 290 26 199 223 85 139)(20 76 291 37 200 234 86 130)(41 170 143 216 307 257 105 261)(42 161 144 207 308 248 106 272)(43 172 145 218 309 259 107 263)(44 163 146 209 310 250 108 274)(45 174 147 220 311 241 109 265)(46 165 148 211 312 252 110 276)(47 176 149 202 313 243 111 267)(48 167 150 213 314 254 112 278)(49 178 151 204 315 245 113 269)(50 169 152 215 316 256 114 280)(51 180 153 206 317 247 115 271)(52 171 154 217 318 258 116 262)(53 162 155 208 319 249 117 273)(54 173 156 219 320 260 118 264)(55 164 157 210 301 251 119 275)(56 175 158 201 302 242 120 266)(57 166 159 212 303 253 101 277)(58 177 160 203 304 244 102 268)(59 168 141 214 305 255 103 279)(60 179 142 205 306 246 104 270)

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

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

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

80 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I···4P5A5B8A···8H8I···8P8Q8R8S8T10A···10F20A···20H20I···20P40A···40P
order1222444444444···4558···88···8888810···1020···2020···2040···40
size11111111222210···10222···25···5101010102···22···24···44···4

80 irreducible representations

dim111111111122222222444
type++++++-+++--
imageC1C2C2C2C2C2C4C4C4C8Q8D5C4○D4D10D10C8○D4C4×D5C8×D5D42D5Q8×D5D20.2C4
kernelDic105C8C4×C52C8C8×Dic5C20.8Q8C5×C4⋊C8C4×Dic10C10.D4C4⋊Dic5C2×Dic10Dic10C52C8C4⋊C8C20C42C2×C8C10C2×C4C4C4C4C2
# reps11221142216222244816224

Matrix representation of Dic105C8 in GL4(𝔽41) generated by

04000
13500
00033
00360
,
64000
353500
004035
00141
,
14000
01400
002739
003214
G:=sub<GL(4,GF(41))| [0,1,0,0,40,35,0,0,0,0,0,36,0,0,33,0],[6,35,0,0,40,35,0,0,0,0,40,14,0,0,35,1],[14,0,0,0,0,14,0,0,0,0,27,32,0,0,39,14] >;

Dic105C8 in GAP, Magma, Sage, TeX

{\rm Dic}_{10}\rtimes_5C_8
% in TeX

G:=Group("Dic10:5C8");
// GroupNames label

G:=SmallGroup(320,457);
// by ID

G=gap.SmallGroup(320,457);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,64,135,142,102,12550]);
// 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,b*c=c*b>;
// generators/relations

׿
×
𝔽