Copied to
clipboard

## G = Dic10⋊C8order 320 = 26·5

### 2nd semidirect product of Dic10 and C8 acting via C8/C2=C4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C10 — Dic10⋊C8
 Chief series C1 — C5 — C10 — Dic5 — C2×Dic5 — C2×C5⋊C8 — C4×C5⋊C8 — Dic10⋊C8
 Lower central C5 — C10 — Dic10⋊C8
 Upper central C1 — C22 — C4⋊C4

Generators and relations for Dic10⋊C8
G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a13, bc=cb >

Subgroups: 282 in 102 conjugacy classes, 56 normal (26 characteristic)
C1, C2 [×3], C4 [×2], C4 [×9], C22, C5, C8 [×5], C2×C4, C2×C4 [×2], C2×C4 [×4], Q8 [×4], C10 [×3], C42 [×3], C4⋊C4, C4⋊C4 [×2], C2×C8 [×4], C2×Q8, Dic5 [×2], Dic5 [×4], Dic5, C20 [×2], C20 [×2], C2×C10, C4×C8 [×3], C4⋊C8 [×3], C4×Q8, C5⋊C8 [×2], C5⋊C8 [×3], Dic10 [×4], C2×Dic5 [×2], C2×Dic5 [×2], C2×C20, C2×C20 [×2], C8×Q8, C4×Dic5, C4×Dic5 [×2], C10.D4 [×2], C5×C4⋊C4, C2×C5⋊C8 [×2], C2×C5⋊C8 [×2], C2×Dic10, C4×C5⋊C8, C4×C5⋊C8 [×2], C20⋊C8, Dic5⋊C8 [×2], Dic53Q8, Dic10⋊C8
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C8 [×4], C2×C4 [×6], Q8 [×2], C23, C2×C8 [×6], C22×C4, C2×Q8, C4○D4, F5, C4×Q8, C22×C8, C8○D4, C2×F5 [×3], C8×Q8, D5⋊C8 [×2], C22×F5, C2×D5⋊C8, D4.F5, Q8×F5, Dic10⋊C8

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

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

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

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

50 conjugacy classes

 class 1 2A 2B 2C 4A ··· 4F 4G 4H 4I 4J 4K ··· 4P 5 8A ··· 8H 8I ··· 8T 10A 10B 10C 20A ··· 20F order 1 2 2 2 4 ··· 4 4 4 4 4 4 ··· 4 5 8 ··· 8 8 ··· 8 10 10 10 20 ··· 20 size 1 1 1 1 2 ··· 2 5 5 5 5 10 ··· 10 4 5 ··· 5 10 ··· 10 4 4 4 8 ··· 8

50 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 2 2 2 4 4 4 8 8 type + + + + + - + + - - image C1 C2 C2 C2 C2 C4 C4 C4 C8 Q8 C4○D4 C8○D4 F5 C2×F5 D5⋊C8 D4.F5 Q8×F5 kernel Dic10⋊C8 C4×C5⋊C8 C20⋊C8 Dic5⋊C8 Dic5⋊3Q8 C10.D4 C5×C4⋊C4 C2×Dic10 Dic10 C5⋊C8 Dic5 C10 C4⋊C4 C2×C4 C4 C2 C2 # reps 1 3 1 2 1 4 2 2 16 2 2 4 1 3 4 1 1

Matrix representation of Dic10⋊C8 in GL8(𝔽41)

 22 2 0 0 0 0 0 0 24 19 0 0 0 0 0 0 0 0 30 1 0 0 0 0 0 0 1 11 0 0 0 0 0 0 0 0 1 40 0 0 0 0 0 0 1 0 40 0 0 0 0 0 1 0 0 40 0 0 0 0 1 0 0 0
,
 32 0 0 0 0 0 0 0 34 9 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 19 30 17 16 0 0 0 0 8 6 33 16 0 0 0 0 25 22 33 35 0 0 0 0 0 22 11 24
,
 14 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 13 14 13 33 0 0 0 0 26 6 22 5 0 0 0 0 35 19 36 18 0 0 0 0 8 32 28 27

G:=sub<GL(8,GF(41))| [22,24,0,0,0,0,0,0,2,19,0,0,0,0,0,0,0,0,30,1,0,0,0,0,0,0,1,11,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0],[32,34,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,19,8,25,0,0,0,0,0,30,6,22,22,0,0,0,0,17,33,33,11,0,0,0,0,16,16,35,24],[14,0,0,0,0,0,0,0,0,14,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,13,26,35,8,0,0,0,0,14,6,19,32,0,0,0,0,13,22,36,28,0,0,0,0,33,5,18,27] >;

Dic10⋊C8 in GAP, Magma, Sage, TeX

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

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

G:=SmallGroup(320,1041);
// by ID

G=gap.SmallGroup(320,1041);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,120,219,268,136,6278,1595]);
// 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^13,b*c=c*b>;
// generators/relations

׿
×
𝔽