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## G = Dic10⋊1C8order 320 = 26·5

### 1st semidirect product of Dic10 and C8 acting via C8/C2=C4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C20 — Dic10⋊1C8
 Chief series C1 — C5 — C10 — C2×C10 — C2×Dic5 — C4×Dic5 — C20⋊C8 — Dic10⋊1C8
 Lower central C5 — C10 — C20 — Dic10⋊1C8
 Upper central C1 — C22 — C2×C4 — C4⋊C4

Generators and relations for Dic101C8
G = < a,b,c | a20=c8=1, b2=a10, bab-1=a-1, cac-1=a3, cbc-1=a15b >

Subgroups: 258 in 70 conjugacy classes, 30 normal (28 characteristic)
C1, C2 [×3], C4 [×2], C4 [×6], C22, C5, C8 [×3], C2×C4, C2×C4 [×4], Q8 [×3], C10 [×3], C42 [×2], C4⋊C4, C4⋊C4, C2×C8 [×2], C2×Q8, Dic5 [×2], Dic5 [×3], C20 [×2], C20, C2×C10, C4×C8, C4⋊C8, C4×Q8, C5⋊C8 [×3], Dic10 [×2], Dic10, C2×Dic5 [×2], C2×Dic5, C2×C20, C2×C20, Q8⋊C8, C4×Dic5, C4×Dic5, C10.D4, C5×C4⋊C4, C2×C5⋊C8 [×2], C2×Dic10, C4×C5⋊C8, C20⋊C8, Dic53Q8, Dic101C8
Quotients: C1, C2 [×3], C4 [×2], C22, C8 [×2], C2×C4, D4 [×2], C22⋊C4, C2×C8, M4(2), SD16, Q16, F5, C22⋊C8, Q8⋊C4, C4≀C2, C2×F5, Q8⋊C8, D5⋊C8, C4.F5, C22⋊F5, D10⋊C8, D4⋊F5, Q8⋊F5, Dic101C8

Smallest permutation representation of Dic101C8
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 29 11 39)(2 28 12 38)(3 27 13 37)(4 26 14 36)(5 25 15 35)(6 24 16 34)(7 23 17 33)(8 22 18 32)(9 21 19 31)(10 40 20 30)(41 67 51 77)(42 66 52 76)(43 65 53 75)(44 64 54 74)(45 63 55 73)(46 62 56 72)(47 61 57 71)(48 80 58 70)(49 79 59 69)(50 78 60 68)(81 271 91 261)(82 270 92 280)(83 269 93 279)(84 268 94 278)(85 267 95 277)(86 266 96 276)(87 265 97 275)(88 264 98 274)(89 263 99 273)(90 262 100 272)(101 131 111 121)(102 130 112 140)(103 129 113 139)(104 128 114 138)(105 127 115 137)(106 126 116 136)(107 125 117 135)(108 124 118 134)(109 123 119 133)(110 122 120 132)(141 209 151 219)(142 208 152 218)(143 207 153 217)(144 206 154 216)(145 205 155 215)(146 204 156 214)(147 203 157 213)(148 202 158 212)(149 201 159 211)(150 220 160 210)(161 294 171 284)(162 293 172 283)(163 292 173 282)(164 291 174 281)(165 290 175 300)(166 289 176 299)(167 288 177 298)(168 287 178 297)(169 286 179 296)(170 285 180 295)(181 307 191 317)(182 306 192 316)(183 305 193 315)(184 304 194 314)(185 303 195 313)(186 302 196 312)(187 301 197 311)(188 320 198 310)(189 319 199 309)(190 318 200 308)(221 246 231 256)(222 245 232 255)(223 244 233 254)(224 243 234 253)(225 242 235 252)(226 241 236 251)(227 260 237 250)(228 259 238 249)(229 258 239 248)(230 257 240 247)
(1 270 236 293 41 183 158 108)(2 277 225 296 42 190 147 111)(3 264 234 299 43 197 156 114)(4 271 223 282 44 184 145 117)(5 278 232 285 45 191 154 120)(6 265 221 288 46 198 143 103)(7 272 230 291 47 185 152 106)(8 279 239 294 48 192 141 109)(9 266 228 297 49 199 150 112)(10 273 237 300 50 186 159 115)(11 280 226 283 51 193 148 118)(12 267 235 286 52 200 157 101)(13 274 224 289 53 187 146 104)(14 261 233 292 54 194 155 107)(15 268 222 295 55 181 144 110)(16 275 231 298 56 188 153 113)(17 262 240 281 57 195 142 116)(18 269 229 284 58 182 151 119)(19 276 238 287 59 189 160 102)(20 263 227 290 60 196 149 105)(21 81 259 173 79 314 220 125)(22 88 248 176 80 301 209 128)(23 95 257 179 61 308 218 131)(24 82 246 162 62 315 207 134)(25 89 255 165 63 302 216 137)(26 96 244 168 64 309 205 140)(27 83 253 171 65 316 214 123)(28 90 242 174 66 303 203 126)(29 97 251 177 67 310 212 129)(30 84 260 180 68 317 201 132)(31 91 249 163 69 304 210 135)(32 98 258 166 70 311 219 138)(33 85 247 169 71 318 208 121)(34 92 256 172 72 305 217 124)(35 99 245 175 73 312 206 127)(36 86 254 178 74 319 215 130)(37 93 243 161 75 306 204 133)(38 100 252 164 76 313 213 136)(39 87 241 167 77 320 202 139)(40 94 250 170 78 307 211 122)

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

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

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

38 conjugacy classes

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

38 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 4 4 4 4 4 8 8 type + + + + + - + + + - - image C1 C2 C2 C2 C4 C4 C8 D4 SD16 Q16 M4(2) C4≀C2 F5 C2×F5 D5⋊C8 C4.F5 C22⋊F5 D4⋊F5 Q8⋊F5 kernel Dic10⋊1C8 C4×C5⋊C8 C20⋊C8 Dic5⋊3Q8 C5×C4⋊C4 C2×Dic10 Dic10 C2×Dic5 Dic5 Dic5 C20 C10 C4⋊C4 C2×C4 C4 C4 C22 C2 C2 # reps 1 1 1 1 2 2 8 2 2 2 2 4 1 1 2 2 2 1 1

Matrix representation of Dic101C8 in GL8(𝔽41)

 1 39 0 0 0 0 0 0 1 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 1 0 0 0 0 0 0 40 0 1 0 0 0 0 0 40 0 0 1 0 0 0 0 40 0 0 0
,
 9 23 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 1 23 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 21 6 13 25 0 0 0 0 27 19 38 1 0 0 0 0 40 3 14 22 0 0 0 0 24 20 35 28
,
 11 30 0 0 0 0 0 0 26 30 0 0 0 0 0 0 0 0 26 23 0 0 0 0 0 0 12 15 0 0 0 0 0 0 0 0 6 23 17 28 0 0 0 0 23 10 25 34 0 0 0 0 31 16 7 10 0 0 0 0 13 33 35 18

G:=sub<GL(8,GF(41))| [1,1,0,0,0,0,0,0,39,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,40,40,40,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],[9,0,0,0,0,0,0,0,23,32,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,23,40,0,0,0,0,0,0,0,0,21,27,40,24,0,0,0,0,6,19,3,20,0,0,0,0,13,38,14,35,0,0,0,0,25,1,22,28],[11,26,0,0,0,0,0,0,30,30,0,0,0,0,0,0,0,0,26,12,0,0,0,0,0,0,23,15,0,0,0,0,0,0,0,0,6,23,31,13,0,0,0,0,23,10,16,33,0,0,0,0,17,25,7,35,0,0,0,0,28,34,10,18] >;

Dic101C8 in GAP, Magma, Sage, TeX

{\rm Dic}_{10}\rtimes_1C_8
% in TeX

G:=Group("Dic10:1C8");
// GroupNames label

G:=SmallGroup(320,210);
// by ID

G=gap.SmallGroup(320,210);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,120,268,1123,570,136,6278,3156]);
// 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^3,c*b*c^-1=a^15*b>;
// generators/relations

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