metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Q8⋊4Dic10, C20.23Q16, C42.54D10, (C5×Q8)⋊4Q8, (C4×Q8).3D5, C5⋊4(C4.Q16), (C2×C20).64D4, (Q8×C20).3C2, C20.29(C2×Q8), C4⋊C4.249D10, C10.34(C2×Q16), C20⋊3C8.15C2, C20.56(C4○D4), C4.63(C4○D20), (C4×C20).92C22, (C2×Q8).156D10, C20⋊2Q8.15C2, C4.13(C2×Dic10), Q8⋊Dic5.8C2, C4.11(C5⋊Q16), C2.9(D4⋊D10), (C2×C20).343C23, C10.D8.10C2, C10.65(C22⋊Q8), C10.110(C8⋊C22), C4⋊Dic5.140C22, (Q8×C10).191C22, C2.16(C20.48D4), C2.6(C2×C5⋊Q16), (C2×C10).474(C2×D4), (C2×C4).248(C5⋊D4), (C5×C4⋊C4).280C22, (C2×C5⋊2C8).98C22, (C2×C4).443(C22×D5), C22.153(C2×C5⋊D4), SmallGroup(320,648)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.23Q16
G = < a,b,c | a20=b8=1, c2=a10b4, bab-1=a-1, ac=ca, cbc-1=b-1 >
Subgroups: 310 in 96 conjugacy classes, 47 normal (31 characteristic)
C1, C2, C4, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, Q8, C10, C42, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, C2×Q8, Dic5, C20, C20, C20, C2×C10, Q8⋊C4, C4⋊C8, C2.D8, C4×Q8, C4⋊Q8, C5⋊2C8, Dic10, C2×Dic5, C2×C20, C2×C20, C5×Q8, C5×Q8, C4.Q16, C2×C5⋊2C8, C4⋊Dic5, C4⋊Dic5, C4×C20, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C2×Dic10, Q8×C10, C20⋊3C8, C10.D8, Q8⋊Dic5, C20⋊2Q8, Q8×C20, C20.23Q16
Quotients: C1, C2, C22, D4, Q8, C23, D5, Q16, C2×D4, C2×Q8, C4○D4, D10, C22⋊Q8, C2×Q16, C8⋊C22, Dic10, C5⋊D4, C22×D5, C4.Q16, C5⋊Q16, C2×Dic10, C4○D20, C2×C5⋊D4, C20.48D4, C2×C5⋊Q16, D4⋊D10, C20.23Q16
►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 76 136 189 90 146 222 169)(2 75 137 188 91 145 223 168)(3 74 138 187 92 144 224 167)(4 73 139 186 93 143 225 166)(5 72 140 185 94 142 226 165)(6 71 121 184 95 141 227 164)(7 70 122 183 96 160 228 163)(8 69 123 182 97 159 229 162)(9 68 124 181 98 158 230 161)(10 67 125 200 99 157 231 180)(11 66 126 199 100 156 232 179)(12 65 127 198 81 155 233 178)(13 64 128 197 82 154 234 177)(14 63 129 196 83 153 235 176)(15 62 130 195 84 152 236 175)(16 61 131 194 85 151 237 174)(17 80 132 193 86 150 238 173)(18 79 133 192 87 149 239 172)(19 78 134 191 88 148 240 171)(20 77 135 190 89 147 221 170)(21 209 254 300 49 277 101 318)(22 208 255 299 50 276 102 317)(23 207 256 298 51 275 103 316)(24 206 257 297 52 274 104 315)(25 205 258 296 53 273 105 314)(26 204 259 295 54 272 106 313)(27 203 260 294 55 271 107 312)(28 202 241 293 56 270 108 311)(29 201 242 292 57 269 109 310)(30 220 243 291 58 268 110 309)(31 219 244 290 59 267 111 308)(32 218 245 289 60 266 112 307)(33 217 246 288 41 265 113 306)(34 216 247 287 42 264 114 305)(35 215 248 286 43 263 115 304)(36 214 249 285 44 262 116 303)(37 213 250 284 45 261 117 302)(38 212 251 283 46 280 118 301)(39 211 252 282 47 279 119 320)(40 210 253 281 48 278 120 319)
(1 317 100 289)(2 318 81 290)(3 319 82 291)(4 320 83 292)(5 301 84 293)(6 302 85 294)(7 303 86 295)(8 304 87 296)(9 305 88 297)(10 306 89 298)(11 307 90 299)(12 308 91 300)(13 309 92 281)(14 310 93 282)(15 311 94 283)(16 312 95 284)(17 313 96 285)(18 314 97 286)(19 315 98 287)(20 316 99 288)(21 198 59 168)(22 199 60 169)(23 200 41 170)(24 181 42 171)(25 182 43 172)(26 183 44 173)(27 184 45 174)(28 185 46 175)(29 186 47 176)(30 187 48 177)(31 188 49 178)(32 189 50 179)(33 190 51 180)(34 191 52 161)(35 192 53 162)(36 193 54 163)(37 194 55 164)(38 195 56 165)(39 196 57 166)(40 197 58 167)(61 107 141 250)(62 108 142 251)(63 109 143 252)(64 110 144 253)(65 111 145 254)(66 112 146 255)(67 113 147 256)(68 114 148 257)(69 115 149 258)(70 116 150 259)(71 117 151 260)(72 118 152 241)(73 119 153 242)(74 120 154 243)(75 101 155 244)(76 102 156 245)(77 103 157 246)(78 104 158 247)(79 105 159 248)(80 106 160 249)(121 261 237 203)(122 262 238 204)(123 263 239 205)(124 264 240 206)(125 265 221 207)(126 266 222 208)(127 267 223 209)(128 268 224 210)(129 269 225 211)(130 270 226 212)(131 271 227 213)(132 272 228 214)(133 273 229 215)(134 274 230 216)(135 275 231 217)(136 276 232 218)(137 277 233 219)(138 278 234 220)(139 279 235 201)(140 280 236 202)
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), (1,76,136,189,90,146,222,169)(2,75,137,188,91,145,223,168)(3,74,138,187,92,144,224,167)(4,73,139,186,93,143,225,166)(5,72,140,185,94,142,226,165)(6,71,121,184,95,141,227,164)(7,70,122,183,96,160,228,163)(8,69,123,182,97,159,229,162)(9,68,124,181,98,158,230,161)(10,67,125,200,99,157,231,180)(11,66,126,199,100,156,232,179)(12,65,127,198,81,155,233,178)(13,64,128,197,82,154,234,177)(14,63,129,196,83,153,235,176)(15,62,130,195,84,152,236,175)(16,61,131,194,85,151,237,174)(17,80,132,193,86,150,238,173)(18,79,133,192,87,149,239,172)(19,78,134,191,88,148,240,171)(20,77,135,190,89,147,221,170)(21,209,254,300,49,277,101,318)(22,208,255,299,50,276,102,317)(23,207,256,298,51,275,103,316)(24,206,257,297,52,274,104,315)(25,205,258,296,53,273,105,314)(26,204,259,295,54,272,106,313)(27,203,260,294,55,271,107,312)(28,202,241,293,56,270,108,311)(29,201,242,292,57,269,109,310)(30,220,243,291,58,268,110,309)(31,219,244,290,59,267,111,308)(32,218,245,289,60,266,112,307)(33,217,246,288,41,265,113,306)(34,216,247,287,42,264,114,305)(35,215,248,286,43,263,115,304)(36,214,249,285,44,262,116,303)(37,213,250,284,45,261,117,302)(38,212,251,283,46,280,118,301)(39,211,252,282,47,279,119,320)(40,210,253,281,48,278,120,319), (1,317,100,289)(2,318,81,290)(3,319,82,291)(4,320,83,292)(5,301,84,293)(6,302,85,294)(7,303,86,295)(8,304,87,296)(9,305,88,297)(10,306,89,298)(11,307,90,299)(12,308,91,300)(13,309,92,281)(14,310,93,282)(15,311,94,283)(16,312,95,284)(17,313,96,285)(18,314,97,286)(19,315,98,287)(20,316,99,288)(21,198,59,168)(22,199,60,169)(23,200,41,170)(24,181,42,171)(25,182,43,172)(26,183,44,173)(27,184,45,174)(28,185,46,175)(29,186,47,176)(30,187,48,177)(31,188,49,178)(32,189,50,179)(33,190,51,180)(34,191,52,161)(35,192,53,162)(36,193,54,163)(37,194,55,164)(38,195,56,165)(39,196,57,166)(40,197,58,167)(61,107,141,250)(62,108,142,251)(63,109,143,252)(64,110,144,253)(65,111,145,254)(66,112,146,255)(67,113,147,256)(68,114,148,257)(69,115,149,258)(70,116,150,259)(71,117,151,260)(72,118,152,241)(73,119,153,242)(74,120,154,243)(75,101,155,244)(76,102,156,245)(77,103,157,246)(78,104,158,247)(79,105,159,248)(80,106,160,249)(121,261,237,203)(122,262,238,204)(123,263,239,205)(124,264,240,206)(125,265,221,207)(126,266,222,208)(127,267,223,209)(128,268,224,210)(129,269,225,211)(130,270,226,212)(131,271,227,213)(132,272,228,214)(133,273,229,215)(134,274,230,216)(135,275,231,217)(136,276,232,218)(137,277,233,219)(138,278,234,220)(139,279,235,201)(140,280,236,202)>;
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), (1,76,136,189,90,146,222,169)(2,75,137,188,91,145,223,168)(3,74,138,187,92,144,224,167)(4,73,139,186,93,143,225,166)(5,72,140,185,94,142,226,165)(6,71,121,184,95,141,227,164)(7,70,122,183,96,160,228,163)(8,69,123,182,97,159,229,162)(9,68,124,181,98,158,230,161)(10,67,125,200,99,157,231,180)(11,66,126,199,100,156,232,179)(12,65,127,198,81,155,233,178)(13,64,128,197,82,154,234,177)(14,63,129,196,83,153,235,176)(15,62,130,195,84,152,236,175)(16,61,131,194,85,151,237,174)(17,80,132,193,86,150,238,173)(18,79,133,192,87,149,239,172)(19,78,134,191,88,148,240,171)(20,77,135,190,89,147,221,170)(21,209,254,300,49,277,101,318)(22,208,255,299,50,276,102,317)(23,207,256,298,51,275,103,316)(24,206,257,297,52,274,104,315)(25,205,258,296,53,273,105,314)(26,204,259,295,54,272,106,313)(27,203,260,294,55,271,107,312)(28,202,241,293,56,270,108,311)(29,201,242,292,57,269,109,310)(30,220,243,291,58,268,110,309)(31,219,244,290,59,267,111,308)(32,218,245,289,60,266,112,307)(33,217,246,288,41,265,113,306)(34,216,247,287,42,264,114,305)(35,215,248,286,43,263,115,304)(36,214,249,285,44,262,116,303)(37,213,250,284,45,261,117,302)(38,212,251,283,46,280,118,301)(39,211,252,282,47,279,119,320)(40,210,253,281,48,278,120,319), (1,317,100,289)(2,318,81,290)(3,319,82,291)(4,320,83,292)(5,301,84,293)(6,302,85,294)(7,303,86,295)(8,304,87,296)(9,305,88,297)(10,306,89,298)(11,307,90,299)(12,308,91,300)(13,309,92,281)(14,310,93,282)(15,311,94,283)(16,312,95,284)(17,313,96,285)(18,314,97,286)(19,315,98,287)(20,316,99,288)(21,198,59,168)(22,199,60,169)(23,200,41,170)(24,181,42,171)(25,182,43,172)(26,183,44,173)(27,184,45,174)(28,185,46,175)(29,186,47,176)(30,187,48,177)(31,188,49,178)(32,189,50,179)(33,190,51,180)(34,191,52,161)(35,192,53,162)(36,193,54,163)(37,194,55,164)(38,195,56,165)(39,196,57,166)(40,197,58,167)(61,107,141,250)(62,108,142,251)(63,109,143,252)(64,110,144,253)(65,111,145,254)(66,112,146,255)(67,113,147,256)(68,114,148,257)(69,115,149,258)(70,116,150,259)(71,117,151,260)(72,118,152,241)(73,119,153,242)(74,120,154,243)(75,101,155,244)(76,102,156,245)(77,103,157,246)(78,104,158,247)(79,105,159,248)(80,106,160,249)(121,261,237,203)(122,262,238,204)(123,263,239,205)(124,264,240,206)(125,265,221,207)(126,266,222,208)(127,267,223,209)(128,268,224,210)(129,269,225,211)(130,270,226,212)(131,271,227,213)(132,272,228,214)(133,273,229,215)(134,274,230,216)(135,275,231,217)(136,276,232,218)(137,277,233,219)(138,278,234,220)(139,279,235,201)(140,280,236,202) );
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)], [(1,76,136,189,90,146,222,169),(2,75,137,188,91,145,223,168),(3,74,138,187,92,144,224,167),(4,73,139,186,93,143,225,166),(5,72,140,185,94,142,226,165),(6,71,121,184,95,141,227,164),(7,70,122,183,96,160,228,163),(8,69,123,182,97,159,229,162),(9,68,124,181,98,158,230,161),(10,67,125,200,99,157,231,180),(11,66,126,199,100,156,232,179),(12,65,127,198,81,155,233,178),(13,64,128,197,82,154,234,177),(14,63,129,196,83,153,235,176),(15,62,130,195,84,152,236,175),(16,61,131,194,85,151,237,174),(17,80,132,193,86,150,238,173),(18,79,133,192,87,149,239,172),(19,78,134,191,88,148,240,171),(20,77,135,190,89,147,221,170),(21,209,254,300,49,277,101,318),(22,208,255,299,50,276,102,317),(23,207,256,298,51,275,103,316),(24,206,257,297,52,274,104,315),(25,205,258,296,53,273,105,314),(26,204,259,295,54,272,106,313),(27,203,260,294,55,271,107,312),(28,202,241,293,56,270,108,311),(29,201,242,292,57,269,109,310),(30,220,243,291,58,268,110,309),(31,219,244,290,59,267,111,308),(32,218,245,289,60,266,112,307),(33,217,246,288,41,265,113,306),(34,216,247,287,42,264,114,305),(35,215,248,286,43,263,115,304),(36,214,249,285,44,262,116,303),(37,213,250,284,45,261,117,302),(38,212,251,283,46,280,118,301),(39,211,252,282,47,279,119,320),(40,210,253,281,48,278,120,319)], [(1,317,100,289),(2,318,81,290),(3,319,82,291),(4,320,83,292),(5,301,84,293),(6,302,85,294),(7,303,86,295),(8,304,87,296),(9,305,88,297),(10,306,89,298),(11,307,90,299),(12,308,91,300),(13,309,92,281),(14,310,93,282),(15,311,94,283),(16,312,95,284),(17,313,96,285),(18,314,97,286),(19,315,98,287),(20,316,99,288),(21,198,59,168),(22,199,60,169),(23,200,41,170),(24,181,42,171),(25,182,43,172),(26,183,44,173),(27,184,45,174),(28,185,46,175),(29,186,47,176),(30,187,48,177),(31,188,49,178),(32,189,50,179),(33,190,51,180),(34,191,52,161),(35,192,53,162),(36,193,54,163),(37,194,55,164),(38,195,56,165),(39,196,57,166),(40,197,58,167),(61,107,141,250),(62,108,142,251),(63,109,143,252),(64,110,144,253),(65,111,145,254),(66,112,146,255),(67,113,147,256),(68,114,148,257),(69,115,149,258),(70,116,150,259),(71,117,151,260),(72,118,152,241),(73,119,153,242),(74,120,154,243),(75,101,155,244),(76,102,156,245),(77,103,157,246),(78,104,158,247),(79,105,159,248),(80,106,160,249),(121,261,237,203),(122,262,238,204),(123,263,239,205),(124,264,240,206),(125,265,221,207),(126,266,222,208),(127,267,223,209),(128,268,224,210),(129,269,225,211),(130,270,226,212),(131,271,227,213),(132,272,228,214),(133,273,229,215),(134,274,230,216),(135,275,231,217),(136,276,232,218),(137,277,233,219),(138,278,234,220),(139,279,235,201),(140,280,236,202)]])
59 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20AF |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 40 | 40 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
59 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | - | + | + | + | - | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | Q8 | D5 | Q16 | C4○D4 | D10 | D10 | D10 | C5⋊D4 | Dic10 | C4○D20 | C8⋊C22 | C5⋊Q16 | D4⋊D10 |
| kernel | C20.23Q16 | C20⋊3C8 | C10.D8 | Q8⋊Dic5 | C20⋊2Q8 | Q8×C20 | C2×C20 | C5×Q8 | C4×Q8 | C20 | C20 | C42 | C4⋊C4 | C2×Q8 | C2×C4 | Q8 | C4 | C10 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 8 | 8 | 8 | 1 | 4 | 4 |
Matrix representation of C20.23Q16 ►in GL6(𝔽41)
| 35 | 1 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 8 | 29 | 0 | 0 | 0 | 0 |
| 36 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 24 |
| 0 | 0 | 0 | 0 | 29 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 37 | 4 |
| 0 | 0 | 0 | 0 | 6 | 4 |
G:=sub<GL(6,GF(41))| [35,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[8,36,0,0,0,0,29,33,0,0,0,0,0,0,0,32,0,0,0,0,32,0,0,0,0,0,0,0,24,29,0,0,0,0,24,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,37,6,0,0,0,0,4,4] >;
C20.23Q16 in GAP, Magma, Sage, TeX
C_{20}._{23}Q_{16} % in TeX
G:=Group("C20.23Q16"); // GroupNames label
G:=SmallGroup(320,648);
// by ID
G=gap.SmallGroup(320,648);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,336,253,120,254,268,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10*b^4,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations