metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.11Q16, C20.20SD16, C42.226D10, C4⋊Q8.12D5, C4⋊C4.87D10, (C2×C20).162D4, C4.5(D4.D5), C10.45(C2×Q16), C4.5(C5⋊Q16), C5⋊4(C4.SD16), C20.87(C4○D4), C20⋊2Q8.23C2, C10.61(C2×SD16), (C2×C20).411C23, (C4×C20).140C22, C4.18(Q8⋊2D5), C10.Q16.15C2, C10.60(C4.4D4), C2.13(C20.23D4), (C2×Dic10).120C22, (C5×C4⋊Q8).12C2, (C4×C5⋊2C8).15C2, C2.15(C2×D4.D5), C2.16(C2×C5⋊Q16), (C2×C10).542(C2×D4), (C2×C4).139(C5⋊D4), (C5×C4⋊C4).134C22, (C2×C4).508(C22×D5), C22.214(C2×C5⋊D4), (C2×C5⋊2C8).273C22, SmallGroup(320,720)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.11Q16
G = < a,b,c | a20=b8=1, c2=a10b4, bab-1=a9, cac-1=a11, cbc-1=a10b-1 >
Subgroups: 318 in 98 conjugacy classes, 47 normal (23 characteristic)
C1, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C4×C8, Q8⋊C4, C4⋊Q8, C4⋊Q8, C5⋊2C8, Dic10, C2×Dic5, C2×C20, C2×C20, C5×Q8, C4.SD16, C2×C5⋊2C8, C4⋊Dic5, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C2×Dic10, Q8×C10, C4×C5⋊2C8, C10.Q16, C20⋊2Q8, C5×C4⋊Q8, C20.11Q16
Quotients: C1, C2, C22, D4, C23, D5, SD16, Q16, C2×D4, C4○D4, D10, C4.4D4, C2×SD16, C2×Q16, C5⋊D4, C22×D5, C4.SD16, D4.D5, C5⋊Q16, Q8⋊2D5, C2×C5⋊D4, C2×D4.D5, C2×C5⋊Q16, C20.23D4, C20.11Q16
►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 74 266 143 284 204 258 110)(2 63 267 152 285 213 259 119)(3 72 268 141 286 202 260 108)(4 61 269 150 287 211 241 117)(5 70 270 159 288 220 242 106)(6 79 271 148 289 209 243 115)(7 68 272 157 290 218 244 104)(8 77 273 146 291 207 245 113)(9 66 274 155 292 216 246 102)(10 75 275 144 293 205 247 111)(11 64 276 153 294 214 248 120)(12 73 277 142 295 203 249 109)(13 62 278 151 296 212 250 118)(14 71 279 160 297 201 251 107)(15 80 280 149 298 210 252 116)(16 69 261 158 299 219 253 105)(17 78 262 147 300 208 254 114)(18 67 263 156 281 217 255 103)(19 76 264 145 282 206 256 112)(20 65 265 154 283 215 257 101)(21 99 197 129 48 301 175 223)(22 88 198 138 49 310 176 232)(23 97 199 127 50 319 177 221)(24 86 200 136 51 308 178 230)(25 95 181 125 52 317 179 239)(26 84 182 134 53 306 180 228)(27 93 183 123 54 315 161 237)(28 82 184 132 55 304 162 226)(29 91 185 121 56 313 163 235)(30 100 186 130 57 302 164 224)(31 89 187 139 58 311 165 233)(32 98 188 128 59 320 166 222)(33 87 189 137 60 309 167 231)(34 96 190 126 41 318 168 240)(35 85 191 135 42 307 169 229)(36 94 192 124 43 316 170 238)(37 83 193 133 44 305 171 227)(38 92 194 122 45 314 172 236)(39 81 195 131 46 303 173 225)(40 90 196 140 47 312 174 234)
(1 165 294 197)(2 176 295 188)(3 167 296 199)(4 178 297 190)(5 169 298 181)(6 180 299 192)(7 171 300 183)(8 162 281 194)(9 173 282 185)(10 164 283 196)(11 175 284 187)(12 166 285 198)(13 177 286 189)(14 168 287 200)(15 179 288 191)(16 170 289 182)(17 161 290 193)(18 172 291 184)(19 163 292 195)(20 174 293 186)(21 266 58 248)(22 277 59 259)(23 268 60 250)(24 279 41 241)(25 270 42 252)(26 261 43 243)(27 272 44 254)(28 263 45 245)(29 274 46 256)(30 265 47 247)(31 276 48 258)(32 267 49 249)(33 278 50 260)(34 269 51 251)(35 280 52 242)(36 271 53 253)(37 262 54 244)(38 273 55 255)(39 264 56 246)(40 275 57 257)(61 318 201 86)(62 309 202 97)(63 320 203 88)(64 311 204 99)(65 302 205 90)(66 313 206 81)(67 304 207 92)(68 315 208 83)(69 306 209 94)(70 317 210 85)(71 308 211 96)(72 319 212 87)(73 310 213 98)(74 301 214 89)(75 312 215 100)(76 303 216 91)(77 314 217 82)(78 305 218 93)(79 316 219 84)(80 307 220 95)(101 224 144 140)(102 235 145 131)(103 226 146 122)(104 237 147 133)(105 228 148 124)(106 239 149 135)(107 230 150 126)(108 221 151 137)(109 232 152 128)(110 223 153 139)(111 234 154 130)(112 225 155 121)(113 236 156 132)(114 227 157 123)(115 238 158 134)(116 229 159 125)(117 240 160 136)(118 231 141 127)(119 222 142 138)(120 233 143 129)
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), (1,74,266,143,284,204,258,110)(2,63,267,152,285,213,259,119)(3,72,268,141,286,202,260,108)(4,61,269,150,287,211,241,117)(5,70,270,159,288,220,242,106)(6,79,271,148,289,209,243,115)(7,68,272,157,290,218,244,104)(8,77,273,146,291,207,245,113)(9,66,274,155,292,216,246,102)(10,75,275,144,293,205,247,111)(11,64,276,153,294,214,248,120)(12,73,277,142,295,203,249,109)(13,62,278,151,296,212,250,118)(14,71,279,160,297,201,251,107)(15,80,280,149,298,210,252,116)(16,69,261,158,299,219,253,105)(17,78,262,147,300,208,254,114)(18,67,263,156,281,217,255,103)(19,76,264,145,282,206,256,112)(20,65,265,154,283,215,257,101)(21,99,197,129,48,301,175,223)(22,88,198,138,49,310,176,232)(23,97,199,127,50,319,177,221)(24,86,200,136,51,308,178,230)(25,95,181,125,52,317,179,239)(26,84,182,134,53,306,180,228)(27,93,183,123,54,315,161,237)(28,82,184,132,55,304,162,226)(29,91,185,121,56,313,163,235)(30,100,186,130,57,302,164,224)(31,89,187,139,58,311,165,233)(32,98,188,128,59,320,166,222)(33,87,189,137,60,309,167,231)(34,96,190,126,41,318,168,240)(35,85,191,135,42,307,169,229)(36,94,192,124,43,316,170,238)(37,83,193,133,44,305,171,227)(38,92,194,122,45,314,172,236)(39,81,195,131,46,303,173,225)(40,90,196,140,47,312,174,234), (1,165,294,197)(2,176,295,188)(3,167,296,199)(4,178,297,190)(5,169,298,181)(6,180,299,192)(7,171,300,183)(8,162,281,194)(9,173,282,185)(10,164,283,196)(11,175,284,187)(12,166,285,198)(13,177,286,189)(14,168,287,200)(15,179,288,191)(16,170,289,182)(17,161,290,193)(18,172,291,184)(19,163,292,195)(20,174,293,186)(21,266,58,248)(22,277,59,259)(23,268,60,250)(24,279,41,241)(25,270,42,252)(26,261,43,243)(27,272,44,254)(28,263,45,245)(29,274,46,256)(30,265,47,247)(31,276,48,258)(32,267,49,249)(33,278,50,260)(34,269,51,251)(35,280,52,242)(36,271,53,253)(37,262,54,244)(38,273,55,255)(39,264,56,246)(40,275,57,257)(61,318,201,86)(62,309,202,97)(63,320,203,88)(64,311,204,99)(65,302,205,90)(66,313,206,81)(67,304,207,92)(68,315,208,83)(69,306,209,94)(70,317,210,85)(71,308,211,96)(72,319,212,87)(73,310,213,98)(74,301,214,89)(75,312,215,100)(76,303,216,91)(77,314,217,82)(78,305,218,93)(79,316,219,84)(80,307,220,95)(101,224,144,140)(102,235,145,131)(103,226,146,122)(104,237,147,133)(105,228,148,124)(106,239,149,135)(107,230,150,126)(108,221,151,137)(109,232,152,128)(110,223,153,139)(111,234,154,130)(112,225,155,121)(113,236,156,132)(114,227,157,123)(115,238,158,134)(116,229,159,125)(117,240,160,136)(118,231,141,127)(119,222,142,138)(120,233,143,129)>;
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), (1,74,266,143,284,204,258,110)(2,63,267,152,285,213,259,119)(3,72,268,141,286,202,260,108)(4,61,269,150,287,211,241,117)(5,70,270,159,288,220,242,106)(6,79,271,148,289,209,243,115)(7,68,272,157,290,218,244,104)(8,77,273,146,291,207,245,113)(9,66,274,155,292,216,246,102)(10,75,275,144,293,205,247,111)(11,64,276,153,294,214,248,120)(12,73,277,142,295,203,249,109)(13,62,278,151,296,212,250,118)(14,71,279,160,297,201,251,107)(15,80,280,149,298,210,252,116)(16,69,261,158,299,219,253,105)(17,78,262,147,300,208,254,114)(18,67,263,156,281,217,255,103)(19,76,264,145,282,206,256,112)(20,65,265,154,283,215,257,101)(21,99,197,129,48,301,175,223)(22,88,198,138,49,310,176,232)(23,97,199,127,50,319,177,221)(24,86,200,136,51,308,178,230)(25,95,181,125,52,317,179,239)(26,84,182,134,53,306,180,228)(27,93,183,123,54,315,161,237)(28,82,184,132,55,304,162,226)(29,91,185,121,56,313,163,235)(30,100,186,130,57,302,164,224)(31,89,187,139,58,311,165,233)(32,98,188,128,59,320,166,222)(33,87,189,137,60,309,167,231)(34,96,190,126,41,318,168,240)(35,85,191,135,42,307,169,229)(36,94,192,124,43,316,170,238)(37,83,193,133,44,305,171,227)(38,92,194,122,45,314,172,236)(39,81,195,131,46,303,173,225)(40,90,196,140,47,312,174,234), (1,165,294,197)(2,176,295,188)(3,167,296,199)(4,178,297,190)(5,169,298,181)(6,180,299,192)(7,171,300,183)(8,162,281,194)(9,173,282,185)(10,164,283,196)(11,175,284,187)(12,166,285,198)(13,177,286,189)(14,168,287,200)(15,179,288,191)(16,170,289,182)(17,161,290,193)(18,172,291,184)(19,163,292,195)(20,174,293,186)(21,266,58,248)(22,277,59,259)(23,268,60,250)(24,279,41,241)(25,270,42,252)(26,261,43,243)(27,272,44,254)(28,263,45,245)(29,274,46,256)(30,265,47,247)(31,276,48,258)(32,267,49,249)(33,278,50,260)(34,269,51,251)(35,280,52,242)(36,271,53,253)(37,262,54,244)(38,273,55,255)(39,264,56,246)(40,275,57,257)(61,318,201,86)(62,309,202,97)(63,320,203,88)(64,311,204,99)(65,302,205,90)(66,313,206,81)(67,304,207,92)(68,315,208,83)(69,306,209,94)(70,317,210,85)(71,308,211,96)(72,319,212,87)(73,310,213,98)(74,301,214,89)(75,312,215,100)(76,303,216,91)(77,314,217,82)(78,305,218,93)(79,316,219,84)(80,307,220,95)(101,224,144,140)(102,235,145,131)(103,226,146,122)(104,237,147,133)(105,228,148,124)(106,239,149,135)(107,230,150,126)(108,221,151,137)(109,232,152,128)(110,223,153,139)(111,234,154,130)(112,225,155,121)(113,236,156,132)(114,227,157,123)(115,238,158,134)(116,229,159,125)(117,240,160,136)(118,231,141,127)(119,222,142,138)(120,233,143,129) );
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)], [(1,74,266,143,284,204,258,110),(2,63,267,152,285,213,259,119),(3,72,268,141,286,202,260,108),(4,61,269,150,287,211,241,117),(5,70,270,159,288,220,242,106),(6,79,271,148,289,209,243,115),(7,68,272,157,290,218,244,104),(8,77,273,146,291,207,245,113),(9,66,274,155,292,216,246,102),(10,75,275,144,293,205,247,111),(11,64,276,153,294,214,248,120),(12,73,277,142,295,203,249,109),(13,62,278,151,296,212,250,118),(14,71,279,160,297,201,251,107),(15,80,280,149,298,210,252,116),(16,69,261,158,299,219,253,105),(17,78,262,147,300,208,254,114),(18,67,263,156,281,217,255,103),(19,76,264,145,282,206,256,112),(20,65,265,154,283,215,257,101),(21,99,197,129,48,301,175,223),(22,88,198,138,49,310,176,232),(23,97,199,127,50,319,177,221),(24,86,200,136,51,308,178,230),(25,95,181,125,52,317,179,239),(26,84,182,134,53,306,180,228),(27,93,183,123,54,315,161,237),(28,82,184,132,55,304,162,226),(29,91,185,121,56,313,163,235),(30,100,186,130,57,302,164,224),(31,89,187,139,58,311,165,233),(32,98,188,128,59,320,166,222),(33,87,189,137,60,309,167,231),(34,96,190,126,41,318,168,240),(35,85,191,135,42,307,169,229),(36,94,192,124,43,316,170,238),(37,83,193,133,44,305,171,227),(38,92,194,122,45,314,172,236),(39,81,195,131,46,303,173,225),(40,90,196,140,47,312,174,234)], [(1,165,294,197),(2,176,295,188),(3,167,296,199),(4,178,297,190),(5,169,298,181),(6,180,299,192),(7,171,300,183),(8,162,281,194),(9,173,282,185),(10,164,283,196),(11,175,284,187),(12,166,285,198),(13,177,286,189),(14,168,287,200),(15,179,288,191),(16,170,289,182),(17,161,290,193),(18,172,291,184),(19,163,292,195),(20,174,293,186),(21,266,58,248),(22,277,59,259),(23,268,60,250),(24,279,41,241),(25,270,42,252),(26,261,43,243),(27,272,44,254),(28,263,45,245),(29,274,46,256),(30,265,47,247),(31,276,48,258),(32,267,49,249),(33,278,50,260),(34,269,51,251),(35,280,52,242),(36,271,53,253),(37,262,54,244),(38,273,55,255),(39,264,56,246),(40,275,57,257),(61,318,201,86),(62,309,202,97),(63,320,203,88),(64,311,204,99),(65,302,205,90),(66,313,206,81),(67,304,207,92),(68,315,208,83),(69,306,209,94),(70,317,210,85),(71,308,211,96),(72,319,212,87),(73,310,213,98),(74,301,214,89),(75,312,215,100),(76,303,216,91),(77,314,217,82),(78,305,218,93),(79,316,219,84),(80,307,220,95),(101,224,144,140),(102,235,145,131),(103,226,146,122),(104,237,147,133),(105,228,148,124),(106,239,149,135),(107,230,150,126),(108,221,151,137),(109,232,152,128),(110,223,153,139),(111,234,154,130),(112,225,155,121),(113,236,156,132),(114,227,157,123),(115,238,158,134),(116,229,159,125),(117,240,160,136),(118,231,141,127),(119,222,142,138),(120,233,143,129)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10F | 20A | ··· | 20L | 20M | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 8 | 8 | 40 | 40 | 2 | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | - | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D5 | SD16 | Q16 | C4○D4 | D10 | D10 | C5⋊D4 | D4.D5 | C5⋊Q16 | Q8⋊2D5 |
| kernel | C20.11Q16 | C4×C5⋊2C8 | C10.Q16 | C20⋊2Q8 | C5×C4⋊Q8 | C2×C20 | C4⋊Q8 | C20 | C20 | C20 | C42 | C4⋊C4 | C2×C4 | C4 | C4 | C4 |
| # reps | 1 | 1 | 4 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 2 | 4 | 8 | 4 | 4 | 4 |
Matrix representation of C20.11Q16 ►in GL6(𝔽41)
| 34 | 1 | 0 | 0 | 0 | 0 |
| 33 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 31 |
| 0 | 0 | 0 | 0 | 0 | 9 |
| 11 | 2 | 0 | 0 | 0 | 0 |
| 22 | 30 | 0 | 0 | 0 | 0 |
| 0 | 0 | 38 | 0 | 0 | 0 |
| 0 | 0 | 10 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 14 |
| 0 | 0 | 0 | 0 | 0 | 38 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 9 | 0 | 0 |
| 0 | 0 | 8 | 38 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 24 |
| 0 | 0 | 0 | 0 | 34 | 28 |
G:=sub<GL(6,GF(41))| [34,33,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,32,0,0,0,0,0,31,9],[11,22,0,0,0,0,2,30,0,0,0,0,0,0,38,10,0,0,0,0,0,27,0,0,0,0,0,0,14,0,0,0,0,0,14,38],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,3,8,0,0,0,0,9,38,0,0,0,0,0,0,13,34,0,0,0,0,24,28] >;
C20.11Q16 in GAP, Magma, Sage, TeX
C_{20}._{11}Q_{16} % in TeX
G:=Group("C20.11Q16"); // GroupNames label
G:=SmallGroup(320,720);
// by ID
G=gap.SmallGroup(320,720);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,120,254,219,100,1123,297,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^10*b^4,b*a*b^-1=a^9,c*a*c^-1=a^11,c*b*c^-1=a^10*b^-1>;
// generators/relations