metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.5Q16, C20.9SD16, C42.10D10, C4⋊Q8.1D5, C4.8(Q8⋊D5), (C2×C20).107D4, (Q8×C10).12C4, (C2×Q8).2Dic5, C20⋊3C8.12C2, C4.6(C5⋊Q16), C5⋊3(C4.6Q16), (C4×C20).48C22, C2.5(C20.D4), C2.4(Q8⋊Dic5), C10.19(Q8⋊C4), C10.17(C4.D4), C22.42(C23.D5), (C5×C4⋊Q8).1C2, (C2×C20).345(C2×C4), (C2×C4).12(C2×Dic5), (C2×C4).177(C5⋊D4), (C2×C10).168(C22⋊C4), SmallGroup(320,104)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.5Q16
G = < a,b,c | a20=b8=1, c2=a10b4, bab-1=a-1, cac-1=a11, cbc-1=a15b-1 >
Subgroups: 174 in 64 conjugacy classes, 35 normal (13 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, C2×C4, Q8, C10, C10, C42, C4⋊C4, C2×C8, C2×Q8, C20, C20, C2×C10, C4⋊C8, C4⋊Q8, C5⋊2C8, C2×C20, C2×C20, C2×C20, C5×Q8, C4.6Q16, C2×C5⋊2C8, C4×C20, C5×C4⋊C4, Q8×C10, C20⋊3C8, C5×C4⋊Q8, C20.5Q16
Quotients: C1, C2, C4, C22, C2×C4, D4, D5, C22⋊C4, SD16, Q16, Dic5, D10, C4.D4, Q8⋊C4, C2×Dic5, C5⋊D4, C4.6Q16, Q8⋊D5, C5⋊Q16, C23.D5, C20.D4, Q8⋊Dic5, C20.5Q16
►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 90 47 294 247 38 170 109)(2 89 48 293 248 37 171 108)(3 88 49 292 249 36 172 107)(4 87 50 291 250 35 173 106)(5 86 51 290 251 34 174 105)(6 85 52 289 252 33 175 104)(7 84 53 288 253 32 176 103)(8 83 54 287 254 31 177 102)(9 82 55 286 255 30 178 101)(10 81 56 285 256 29 179 120)(11 100 57 284 257 28 180 119)(12 99 58 283 258 27 161 118)(13 98 59 282 259 26 162 117)(14 97 60 281 260 25 163 116)(15 96 41 300 241 24 164 115)(16 95 42 299 242 23 165 114)(17 94 43 298 243 22 166 113)(18 93 44 297 244 21 167 112)(19 92 45 296 245 40 168 111)(20 91 46 295 246 39 169 110)(61 141 123 182 221 213 313 268)(62 160 124 181 222 212 314 267)(63 159 125 200 223 211 315 266)(64 158 126 199 224 210 316 265)(65 157 127 198 225 209 317 264)(66 156 128 197 226 208 318 263)(67 155 129 196 227 207 319 262)(68 154 130 195 228 206 320 261)(69 153 131 194 229 205 301 280)(70 152 132 193 230 204 302 279)(71 151 133 192 231 203 303 278)(72 150 134 191 232 202 304 277)(73 149 135 190 233 201 305 276)(74 148 136 189 234 220 306 275)(75 147 137 188 235 219 307 274)(76 146 138 187 236 218 308 273)(77 145 139 186 237 217 309 272)(78 144 140 185 238 216 310 271)(79 143 121 184 239 215 311 270)(80 142 122 183 240 214 312 269)
(1 190 257 266)(2 181 258 277)(3 192 259 268)(4 183 260 279)(5 194 241 270)(6 185 242 261)(7 196 243 272)(8 187 244 263)(9 198 245 274)(10 189 246 265)(11 200 247 276)(12 191 248 267)(13 182 249 278)(14 193 250 269)(15 184 251 280)(16 195 252 271)(17 186 253 262)(18 197 254 273)(19 188 255 264)(20 199 256 275)(21 303 83 123)(22 314 84 134)(23 305 85 125)(24 316 86 136)(25 307 87 127)(26 318 88 138)(27 309 89 129)(28 320 90 140)(29 311 91 131)(30 302 92 122)(31 313 93 133)(32 304 94 124)(33 315 95 135)(34 306 96 126)(35 317 97 137)(36 308 98 128)(37 319 99 139)(38 310 100 130)(39 301 81 121)(40 312 82 132)(41 143 174 205)(42 154 175 216)(43 145 176 207)(44 156 177 218)(45 147 178 209)(46 158 179 220)(47 149 180 211)(48 160 161 202)(49 151 162 213)(50 142 163 204)(51 153 164 215)(52 144 165 206)(53 155 166 217)(54 146 167 208)(55 157 168 219)(56 148 169 210)(57 159 170 201)(58 150 171 212)(59 141 172 203)(60 152 173 214)(61 112 231 287)(62 103 232 298)(63 114 233 289)(64 105 234 300)(65 116 235 291)(66 107 236 282)(67 118 237 293)(68 109 238 284)(69 120 239 295)(70 111 240 286)(71 102 221 297)(72 113 222 288)(73 104 223 299)(74 115 224 290)(75 106 225 281)(76 117 226 292)(77 108 227 283)(78 119 228 294)(79 110 229 285)(80 101 230 296)
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), (1,90,47,294,247,38,170,109)(2,89,48,293,248,37,171,108)(3,88,49,292,249,36,172,107)(4,87,50,291,250,35,173,106)(5,86,51,290,251,34,174,105)(6,85,52,289,252,33,175,104)(7,84,53,288,253,32,176,103)(8,83,54,287,254,31,177,102)(9,82,55,286,255,30,178,101)(10,81,56,285,256,29,179,120)(11,100,57,284,257,28,180,119)(12,99,58,283,258,27,161,118)(13,98,59,282,259,26,162,117)(14,97,60,281,260,25,163,116)(15,96,41,300,241,24,164,115)(16,95,42,299,242,23,165,114)(17,94,43,298,243,22,166,113)(18,93,44,297,244,21,167,112)(19,92,45,296,245,40,168,111)(20,91,46,295,246,39,169,110)(61,141,123,182,221,213,313,268)(62,160,124,181,222,212,314,267)(63,159,125,200,223,211,315,266)(64,158,126,199,224,210,316,265)(65,157,127,198,225,209,317,264)(66,156,128,197,226,208,318,263)(67,155,129,196,227,207,319,262)(68,154,130,195,228,206,320,261)(69,153,131,194,229,205,301,280)(70,152,132,193,230,204,302,279)(71,151,133,192,231,203,303,278)(72,150,134,191,232,202,304,277)(73,149,135,190,233,201,305,276)(74,148,136,189,234,220,306,275)(75,147,137,188,235,219,307,274)(76,146,138,187,236,218,308,273)(77,145,139,186,237,217,309,272)(78,144,140,185,238,216,310,271)(79,143,121,184,239,215,311,270)(80,142,122,183,240,214,312,269), (1,190,257,266)(2,181,258,277)(3,192,259,268)(4,183,260,279)(5,194,241,270)(6,185,242,261)(7,196,243,272)(8,187,244,263)(9,198,245,274)(10,189,246,265)(11,200,247,276)(12,191,248,267)(13,182,249,278)(14,193,250,269)(15,184,251,280)(16,195,252,271)(17,186,253,262)(18,197,254,273)(19,188,255,264)(20,199,256,275)(21,303,83,123)(22,314,84,134)(23,305,85,125)(24,316,86,136)(25,307,87,127)(26,318,88,138)(27,309,89,129)(28,320,90,140)(29,311,91,131)(30,302,92,122)(31,313,93,133)(32,304,94,124)(33,315,95,135)(34,306,96,126)(35,317,97,137)(36,308,98,128)(37,319,99,139)(38,310,100,130)(39,301,81,121)(40,312,82,132)(41,143,174,205)(42,154,175,216)(43,145,176,207)(44,156,177,218)(45,147,178,209)(46,158,179,220)(47,149,180,211)(48,160,161,202)(49,151,162,213)(50,142,163,204)(51,153,164,215)(52,144,165,206)(53,155,166,217)(54,146,167,208)(55,157,168,219)(56,148,169,210)(57,159,170,201)(58,150,171,212)(59,141,172,203)(60,152,173,214)(61,112,231,287)(62,103,232,298)(63,114,233,289)(64,105,234,300)(65,116,235,291)(66,107,236,282)(67,118,237,293)(68,109,238,284)(69,120,239,295)(70,111,240,286)(71,102,221,297)(72,113,222,288)(73,104,223,299)(74,115,224,290)(75,106,225,281)(76,117,226,292)(77,108,227,283)(78,119,228,294)(79,110,229,285)(80,101,230,296)>;
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), (1,90,47,294,247,38,170,109)(2,89,48,293,248,37,171,108)(3,88,49,292,249,36,172,107)(4,87,50,291,250,35,173,106)(5,86,51,290,251,34,174,105)(6,85,52,289,252,33,175,104)(7,84,53,288,253,32,176,103)(8,83,54,287,254,31,177,102)(9,82,55,286,255,30,178,101)(10,81,56,285,256,29,179,120)(11,100,57,284,257,28,180,119)(12,99,58,283,258,27,161,118)(13,98,59,282,259,26,162,117)(14,97,60,281,260,25,163,116)(15,96,41,300,241,24,164,115)(16,95,42,299,242,23,165,114)(17,94,43,298,243,22,166,113)(18,93,44,297,244,21,167,112)(19,92,45,296,245,40,168,111)(20,91,46,295,246,39,169,110)(61,141,123,182,221,213,313,268)(62,160,124,181,222,212,314,267)(63,159,125,200,223,211,315,266)(64,158,126,199,224,210,316,265)(65,157,127,198,225,209,317,264)(66,156,128,197,226,208,318,263)(67,155,129,196,227,207,319,262)(68,154,130,195,228,206,320,261)(69,153,131,194,229,205,301,280)(70,152,132,193,230,204,302,279)(71,151,133,192,231,203,303,278)(72,150,134,191,232,202,304,277)(73,149,135,190,233,201,305,276)(74,148,136,189,234,220,306,275)(75,147,137,188,235,219,307,274)(76,146,138,187,236,218,308,273)(77,145,139,186,237,217,309,272)(78,144,140,185,238,216,310,271)(79,143,121,184,239,215,311,270)(80,142,122,183,240,214,312,269), (1,190,257,266)(2,181,258,277)(3,192,259,268)(4,183,260,279)(5,194,241,270)(6,185,242,261)(7,196,243,272)(8,187,244,263)(9,198,245,274)(10,189,246,265)(11,200,247,276)(12,191,248,267)(13,182,249,278)(14,193,250,269)(15,184,251,280)(16,195,252,271)(17,186,253,262)(18,197,254,273)(19,188,255,264)(20,199,256,275)(21,303,83,123)(22,314,84,134)(23,305,85,125)(24,316,86,136)(25,307,87,127)(26,318,88,138)(27,309,89,129)(28,320,90,140)(29,311,91,131)(30,302,92,122)(31,313,93,133)(32,304,94,124)(33,315,95,135)(34,306,96,126)(35,317,97,137)(36,308,98,128)(37,319,99,139)(38,310,100,130)(39,301,81,121)(40,312,82,132)(41,143,174,205)(42,154,175,216)(43,145,176,207)(44,156,177,218)(45,147,178,209)(46,158,179,220)(47,149,180,211)(48,160,161,202)(49,151,162,213)(50,142,163,204)(51,153,164,215)(52,144,165,206)(53,155,166,217)(54,146,167,208)(55,157,168,219)(56,148,169,210)(57,159,170,201)(58,150,171,212)(59,141,172,203)(60,152,173,214)(61,112,231,287)(62,103,232,298)(63,114,233,289)(64,105,234,300)(65,116,235,291)(66,107,236,282)(67,118,237,293)(68,109,238,284)(69,120,239,295)(70,111,240,286)(71,102,221,297)(72,113,222,288)(73,104,223,299)(74,115,224,290)(75,106,225,281)(76,117,226,292)(77,108,227,283)(78,119,228,294)(79,110,229,285)(80,101,230,296) );
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)], [(1,90,47,294,247,38,170,109),(2,89,48,293,248,37,171,108),(3,88,49,292,249,36,172,107),(4,87,50,291,250,35,173,106),(5,86,51,290,251,34,174,105),(6,85,52,289,252,33,175,104),(7,84,53,288,253,32,176,103),(8,83,54,287,254,31,177,102),(9,82,55,286,255,30,178,101),(10,81,56,285,256,29,179,120),(11,100,57,284,257,28,180,119),(12,99,58,283,258,27,161,118),(13,98,59,282,259,26,162,117),(14,97,60,281,260,25,163,116),(15,96,41,300,241,24,164,115),(16,95,42,299,242,23,165,114),(17,94,43,298,243,22,166,113),(18,93,44,297,244,21,167,112),(19,92,45,296,245,40,168,111),(20,91,46,295,246,39,169,110),(61,141,123,182,221,213,313,268),(62,160,124,181,222,212,314,267),(63,159,125,200,223,211,315,266),(64,158,126,199,224,210,316,265),(65,157,127,198,225,209,317,264),(66,156,128,197,226,208,318,263),(67,155,129,196,227,207,319,262),(68,154,130,195,228,206,320,261),(69,153,131,194,229,205,301,280),(70,152,132,193,230,204,302,279),(71,151,133,192,231,203,303,278),(72,150,134,191,232,202,304,277),(73,149,135,190,233,201,305,276),(74,148,136,189,234,220,306,275),(75,147,137,188,235,219,307,274),(76,146,138,187,236,218,308,273),(77,145,139,186,237,217,309,272),(78,144,140,185,238,216,310,271),(79,143,121,184,239,215,311,270),(80,142,122,183,240,214,312,269)], [(1,190,257,266),(2,181,258,277),(3,192,259,268),(4,183,260,279),(5,194,241,270),(6,185,242,261),(7,196,243,272),(8,187,244,263),(9,198,245,274),(10,189,246,265),(11,200,247,276),(12,191,248,267),(13,182,249,278),(14,193,250,269),(15,184,251,280),(16,195,252,271),(17,186,253,262),(18,197,254,273),(19,188,255,264),(20,199,256,275),(21,303,83,123),(22,314,84,134),(23,305,85,125),(24,316,86,136),(25,307,87,127),(26,318,88,138),(27,309,89,129),(28,320,90,140),(29,311,91,131),(30,302,92,122),(31,313,93,133),(32,304,94,124),(33,315,95,135),(34,306,96,126),(35,317,97,137),(36,308,98,128),(37,319,99,139),(38,310,100,130),(39,301,81,121),(40,312,82,132),(41,143,174,205),(42,154,175,216),(43,145,176,207),(44,156,177,218),(45,147,178,209),(46,158,179,220),(47,149,180,211),(48,160,161,202),(49,151,162,213),(50,142,163,204),(51,153,164,215),(52,144,165,206),(53,155,166,217),(54,146,167,208),(55,157,168,219),(56,148,169,210),(57,159,170,201),(58,150,171,212),(59,141,172,203),(60,152,173,214),(61,112,231,287),(62,103,232,298),(63,114,233,289),(64,105,234,300),(65,116,235,291),(66,107,236,282),(67,118,237,293),(68,109,238,284),(69,120,239,295),(70,111,240,286),(71,102,221,297),(72,113,222,288),(73,104,223,299),(74,115,224,290),(75,106,225,281),(76,117,226,292),(77,108,227,283),(78,119,228,294),(79,110,229,285),(80,101,230,296)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10F | 20A | ··· | 20L | 20M | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 2 | 2 | 20 | ··· | 20 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | - | + | + | - | ||||
| image | C1 | C2 | C2 | C4 | D4 | D5 | SD16 | Q16 | D10 | Dic5 | C5⋊D4 | C4.D4 | Q8⋊D5 | C5⋊Q16 | C20.D4 |
| kernel | C20.5Q16 | C20⋊3C8 | C5×C4⋊Q8 | Q8×C10 | C2×C20 | C4⋊Q8 | C20 | C20 | C42 | C2×Q8 | C2×C4 | C10 | C4 | C4 | C2 |
| # reps | 1 | 2 | 1 | 4 | 2 | 2 | 4 | 4 | 2 | 4 | 8 | 1 | 4 | 4 | 4 |
Matrix representation of C20.5Q16 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 1 | 34 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 30 | 22 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 32 | 0 | 0 |
| 0 | 0 | 27 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 39 |
| 0 | 0 | 0 | 0 | 39 | 35 |
| 31 | 37 | 0 | 0 | 0 | 0 |
| 15 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 34 |
| 0 | 0 | 0 | 0 | 34 | 14 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,1,0,0,0,0,40,34,0,0,0,0,0,0,0,40,0,0,0,0,1,0],[30,28,0,0,0,0,22,0,0,0,0,0,0,0,11,27,0,0,0,0,32,30,0,0,0,0,0,0,6,39,0,0,0,0,39,35],[31,15,0,0,0,0,37,10,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,27,34,0,0,0,0,34,14] >;
C20.5Q16 in GAP, Magma, Sage, TeX
C_{20}._5Q_{16} % in TeX
G:=Group("C20.5Q16"); // GroupNames label
G:=SmallGroup(320,104);
// by ID
G=gap.SmallGroup(320,104);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,232,219,100,1571,570,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10*b^4,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=a^15*b^-1>;
// generators/relations