Copied to
clipboard

## G = Dic20⋊15C4order 320 = 26·5

### 9th semidirect product of Dic20 and C4 acting via C4/C2=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C20 — Dic20⋊15C4
 Chief series C1 — C5 — C10 — C20 — C2×C20 — C4×Dic5 — Dic5⋊3Q8 — Dic20⋊15C4
 Lower central C5 — C10 — C20 — Dic20⋊15C4
 Upper central C1 — C22 — C2×C4 — C4.Q8

Generators and relations for Dic2015C4
G = < a,b,c | a40=c4=1, b2=a20, bab-1=a-1, cac-1=a11, cbc-1=a20b >

Subgroups: 358 in 108 conjugacy classes, 49 normal (21 characteristic)
C1, C2, C2 [×2], C4 [×2], C4 [×8], C22, C5, C8 [×2], C8, C2×C4, C2×C4 [×6], Q8 [×6], C10, C10 [×2], C42 [×3], C4⋊C4 [×2], C4⋊C4 [×2], C2×C8, C2×C8, Q16 [×4], C2×Q8 [×2], Dic5 [×6], C20 [×2], C20 [×2], C2×C10, C8⋊C4, Q8⋊C4 [×2], C4.Q8, C4×Q8 [×2], C2×Q16, C52C8, C40 [×2], Dic10 [×4], Dic10 [×2], C2×Dic5 [×2], C2×Dic5 [×2], C2×C20, C2×C20 [×2], Q16⋊C4, Dic20 [×4], C2×C52C8, C4×Dic5, C4×Dic5 [×2], C10.D4 [×2], C5×C4⋊C4 [×2], C2×C40, C2×Dic10 [×2], C10.Q16 [×2], C408C4, C5×C4.Q8, Dic53Q8 [×2], C2×Dic20, Dic2015C4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], C23, D5, C22×C4, C2×D4, C4○D4, D10 [×3], C4×D4, C8.C22 [×2], C4×D5 [×2], C22×D5, Q16⋊C4, C2×C4×D5, D4×D5, Q82D5, D208C4, SD16⋊D5 [×2], Dic2015C4

Smallest permutation representation of Dic2015C4
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)
(1 318 21 298)(2 317 22 297)(3 316 23 296)(4 315 24 295)(5 314 25 294)(6 313 26 293)(7 312 27 292)(8 311 28 291)(9 310 29 290)(10 309 30 289)(11 308 31 288)(12 307 32 287)(13 306 33 286)(14 305 34 285)(15 304 35 284)(16 303 36 283)(17 302 37 282)(18 301 38 281)(19 300 39 320)(20 299 40 319)(41 165 61 185)(42 164 62 184)(43 163 63 183)(44 162 64 182)(45 161 65 181)(46 200 66 180)(47 199 67 179)(48 198 68 178)(49 197 69 177)(50 196 70 176)(51 195 71 175)(52 194 72 174)(53 193 73 173)(54 192 74 172)(55 191 75 171)(56 190 76 170)(57 189 77 169)(58 188 78 168)(59 187 79 167)(60 186 80 166)(81 234 101 214)(82 233 102 213)(83 232 103 212)(84 231 104 211)(85 230 105 210)(86 229 106 209)(87 228 107 208)(88 227 108 207)(89 226 109 206)(90 225 110 205)(91 224 111 204)(92 223 112 203)(93 222 113 202)(94 221 114 201)(95 220 115 240)(96 219 116 239)(97 218 117 238)(98 217 118 237)(99 216 119 236)(100 215 120 235)(121 277 141 257)(122 276 142 256)(123 275 143 255)(124 274 144 254)(125 273 145 253)(126 272 146 252)(127 271 147 251)(128 270 148 250)(129 269 149 249)(130 268 150 248)(131 267 151 247)(132 266 152 246)(133 265 153 245)(134 264 154 244)(135 263 155 243)(136 262 156 242)(137 261 157 241)(138 260 158 280)(139 259 159 279)(140 258 160 278)
(1 264 231 164)(2 275 232 175)(3 246 233 186)(4 257 234 197)(5 268 235 168)(6 279 236 179)(7 250 237 190)(8 261 238 161)(9 272 239 172)(10 243 240 183)(11 254 201 194)(12 265 202 165)(13 276 203 176)(14 247 204 187)(15 258 205 198)(16 269 206 169)(17 280 207 180)(18 251 208 191)(19 262 209 162)(20 273 210 173)(21 244 211 184)(22 255 212 195)(23 266 213 166)(24 277 214 177)(25 248 215 188)(26 259 216 199)(27 270 217 170)(28 241 218 181)(29 252 219 192)(30 263 220 163)(31 274 221 174)(32 245 222 185)(33 256 223 196)(34 267 224 167)(35 278 225 178)(36 249 226 189)(37 260 227 200)(38 271 228 171)(39 242 229 182)(40 253 230 193)(41 307 133 93)(42 318 134 104)(43 289 135 115)(44 300 136 86)(45 311 137 97)(46 282 138 108)(47 293 139 119)(48 304 140 90)(49 315 141 101)(50 286 142 112)(51 297 143 83)(52 308 144 94)(53 319 145 105)(54 290 146 116)(55 301 147 87)(56 312 148 98)(57 283 149 109)(58 294 150 120)(59 305 151 91)(60 316 152 102)(61 287 153 113)(62 298 154 84)(63 309 155 95)(64 320 156 106)(65 291 157 117)(66 302 158 88)(67 313 159 99)(68 284 160 110)(69 295 121 81)(70 306 122 92)(71 317 123 103)(72 288 124 114)(73 299 125 85)(74 310 126 96)(75 281 127 107)(76 292 128 118)(77 303 129 89)(78 314 130 100)(79 285 131 111)(80 296 132 82)

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

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

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

50 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 4M 4N 5A 5B 8A 8B 8C 8D 10A ··· 10F 20A 20B 20C 20D 20E ··· 20L 40A ··· 40H order 1 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 8 8 8 8 10 ··· 10 20 20 20 20 20 ··· 20 40 ··· 40 size 1 1 1 1 2 2 4 4 4 4 10 10 10 10 20 20 20 20 2 2 4 4 20 20 2 ··· 2 4 4 4 4 8 ··· 8 4 ··· 4

50 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 4 4 4 4 type + + + + + + + + + + - + + - image C1 C2 C2 C2 C2 C2 C4 D4 D5 C4○D4 D10 D10 C4×D5 C8.C22 Q8⋊2D5 D4×D5 SD16⋊D5 kernel Dic20⋊15C4 C10.Q16 C40⋊8C4 C5×C4.Q8 Dic5⋊3Q8 C2×Dic20 Dic20 C2×Dic5 C4.Q8 C20 C4⋊C4 C2×C8 C8 C10 C4 C22 C2 # reps 1 2 1 1 2 1 8 2 2 2 4 2 8 2 2 2 8

Matrix representation of Dic2015C4 in GL6(𝔽41)

 0 1 0 0 0 0 40 6 0 0 0 0 0 0 19 20 32 5 0 0 6 0 34 39 0 0 28 15 35 8 0 0 20 8 35 28
,
 39 25 0 0 0 0 13 2 0 0 0 0 0 0 12 2 40 0 0 0 34 8 20 21 0 0 8 40 28 1 0 0 1 20 22 34
,
 32 0 0 0 0 0 0 32 0 0 0 0 0 0 40 0 39 0 0 0 0 0 40 1 0 0 1 0 1 0 0 0 1 40 1 0

G:=sub<GL(6,GF(41))| [0,40,0,0,0,0,1,6,0,0,0,0,0,0,19,6,28,20,0,0,20,0,15,8,0,0,32,34,35,35,0,0,5,39,8,28],[39,13,0,0,0,0,25,2,0,0,0,0,0,0,12,34,8,1,0,0,2,8,40,20,0,0,40,20,28,22,0,0,0,21,1,34],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,40,0,1,1,0,0,0,0,0,40,0,0,39,40,1,1,0,0,0,1,0,0] >;

Dic2015C4 in GAP, Magma, Sage, TeX

{\rm Dic}_{20}\rtimes_{15}C_4
% in TeX

G:=Group("Dic20:15C4");
// GroupNames label

G:=SmallGroup(320,480);
// by ID

G=gap.SmallGroup(320,480);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,344,758,135,100,570,297,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^40=c^4=1,b^2=a^20,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=a^20*b>;
// generators/relations

׿
×
𝔽