metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.7Q16, Dic10⋊3Q8, C4.7Dic20, C42.41D10, C4⋊C8.8D5, C4.46(Q8×D5), C5⋊2(C4.Q16), (C2×C8).24D10, C10.8(C2×Q16), C40⋊5C4.9C2, (C2×C20).126D4, (C2×C4).137D20, C20.105(C2×Q8), (C4×C20).76C22, (C2×C40).28C22, C20⋊2Q8.12C2, C2.10(C2×Dic20), C20.289(C4○D4), C2.21(C8⋊D10), C10.18(C8⋊C22), (C2×C20).760C23, (C4×Dic10).12C2, C20.44D4.4C2, C22.123(C2×D20), C10.33(C22⋊Q8), C4⋊Dic5.21C22, C4.113(D4⋊2D5), C2.14(D10⋊2Q8), (C2×Dic10).222C22, (C5×C4⋊C8).13C2, (C2×C10).143(C2×D4), (C2×C4).705(C22×D5), SmallGroup(320,477)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.7Q16
G = < a,b,c | a20=b8=1, c2=b4, bab-1=a11, cac-1=a9, cbc-1=a10b-1 >
Subgroups: 374 in 96 conjugacy classes, 45 normal (29 characteristic)
C1, C2, C4, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C42, C42, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C20, C2×C10, Q8⋊C4, C4⋊C8, C2.D8, C4×Q8, C4⋊Q8, C40, Dic10, Dic10, C2×Dic5, C2×C20, C4.Q16, C4×Dic5, C10.D4, C4⋊Dic5, C4⋊Dic5, C4⋊Dic5, C4×C20, C2×C40, C2×Dic10, C2×Dic10, C20.44D4, C40⋊5C4, C5×C4⋊C8, C4×Dic10, C20⋊2Q8, C20.7Q16
Quotients: C1, C2, C22, D4, Q8, C23, D5, Q16, C2×D4, C2×Q8, C4○D4, D10, C22⋊Q8, C2×Q16, C8⋊C22, D20, C22×D5, C4.Q16, Dic20, C2×D20, D4⋊2D5, Q8×D5, D10⋊2Q8, C2×Dic20, C8⋊D10, C20.7Q16
►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)
(1 173 290 21 58 98 124 237)(2 164 291 32 59 89 125 228)(3 175 292 23 60 100 126 239)(4 166 293 34 41 91 127 230)(5 177 294 25 42 82 128 221)(6 168 295 36 43 93 129 232)(7 179 296 27 44 84 130 223)(8 170 297 38 45 95 131 234)(9 161 298 29 46 86 132 225)(10 172 299 40 47 97 133 236)(11 163 300 31 48 88 134 227)(12 174 281 22 49 99 135 238)(13 165 282 33 50 90 136 229)(14 176 283 24 51 81 137 240)(15 167 284 35 52 92 138 231)(16 178 285 26 53 83 139 222)(17 169 286 37 54 94 140 233)(18 180 287 28 55 85 121 224)(19 171 288 39 56 96 122 235)(20 162 289 30 57 87 123 226)(61 264 106 148 253 317 190 207)(62 275 107 159 254 308 191 218)(63 266 108 150 255 319 192 209)(64 277 109 141 256 310 193 220)(65 268 110 152 257 301 194 211)(66 279 111 143 258 312 195 202)(67 270 112 154 259 303 196 213)(68 261 113 145 260 314 197 204)(69 272 114 156 241 305 198 215)(70 263 115 147 242 316 199 206)(71 274 116 158 243 307 200 217)(72 265 117 149 244 318 181 208)(73 276 118 160 245 309 182 219)(74 267 119 151 246 320 183 210)(75 278 120 142 247 311 184 201)(76 269 101 153 248 302 185 212)(77 280 102 144 249 313 186 203)(78 271 103 155 250 304 187 214)(79 262 104 146 251 315 188 205)(80 273 105 157 252 306 189 216)
(1 80 58 252)(2 69 59 241)(3 78 60 250)(4 67 41 259)(5 76 42 248)(6 65 43 257)(7 74 44 246)(8 63 45 255)(9 72 46 244)(10 61 47 253)(11 70 48 242)(12 79 49 251)(13 68 50 260)(14 77 51 249)(15 66 52 258)(16 75 53 247)(17 64 54 256)(18 73 55 245)(19 62 56 254)(20 71 57 243)(21 316 237 263)(22 305 238 272)(23 314 239 261)(24 303 240 270)(25 312 221 279)(26 301 222 268)(27 310 223 277)(28 319 224 266)(29 308 225 275)(30 317 226 264)(31 306 227 273)(32 315 228 262)(33 304 229 271)(34 313 230 280)(35 302 231 269)(36 311 232 278)(37 320 233 267)(38 309 234 276)(39 318 235 265)(40 307 236 274)(81 154 176 213)(82 143 177 202)(83 152 178 211)(84 141 179 220)(85 150 180 209)(86 159 161 218)(87 148 162 207)(88 157 163 216)(89 146 164 205)(90 155 165 214)(91 144 166 203)(92 153 167 212)(93 142 168 201)(94 151 169 210)(95 160 170 219)(96 149 171 208)(97 158 172 217)(98 147 173 206)(99 156 174 215)(100 145 175 204)(101 294 185 128)(102 283 186 137)(103 292 187 126)(104 281 188 135)(105 290 189 124)(106 299 190 133)(107 288 191 122)(108 297 192 131)(109 286 193 140)(110 295 194 129)(111 284 195 138)(112 293 196 127)(113 282 197 136)(114 291 198 125)(115 300 199 134)(116 289 200 123)(117 298 181 132)(118 287 182 121)(119 296 183 130)(120 285 184 139)
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), (1,173,290,21,58,98,124,237)(2,164,291,32,59,89,125,228)(3,175,292,23,60,100,126,239)(4,166,293,34,41,91,127,230)(5,177,294,25,42,82,128,221)(6,168,295,36,43,93,129,232)(7,179,296,27,44,84,130,223)(8,170,297,38,45,95,131,234)(9,161,298,29,46,86,132,225)(10,172,299,40,47,97,133,236)(11,163,300,31,48,88,134,227)(12,174,281,22,49,99,135,238)(13,165,282,33,50,90,136,229)(14,176,283,24,51,81,137,240)(15,167,284,35,52,92,138,231)(16,178,285,26,53,83,139,222)(17,169,286,37,54,94,140,233)(18,180,287,28,55,85,121,224)(19,171,288,39,56,96,122,235)(20,162,289,30,57,87,123,226)(61,264,106,148,253,317,190,207)(62,275,107,159,254,308,191,218)(63,266,108,150,255,319,192,209)(64,277,109,141,256,310,193,220)(65,268,110,152,257,301,194,211)(66,279,111,143,258,312,195,202)(67,270,112,154,259,303,196,213)(68,261,113,145,260,314,197,204)(69,272,114,156,241,305,198,215)(70,263,115,147,242,316,199,206)(71,274,116,158,243,307,200,217)(72,265,117,149,244,318,181,208)(73,276,118,160,245,309,182,219)(74,267,119,151,246,320,183,210)(75,278,120,142,247,311,184,201)(76,269,101,153,248,302,185,212)(77,280,102,144,249,313,186,203)(78,271,103,155,250,304,187,214)(79,262,104,146,251,315,188,205)(80,273,105,157,252,306,189,216), (1,80,58,252)(2,69,59,241)(3,78,60,250)(4,67,41,259)(5,76,42,248)(6,65,43,257)(7,74,44,246)(8,63,45,255)(9,72,46,244)(10,61,47,253)(11,70,48,242)(12,79,49,251)(13,68,50,260)(14,77,51,249)(15,66,52,258)(16,75,53,247)(17,64,54,256)(18,73,55,245)(19,62,56,254)(20,71,57,243)(21,316,237,263)(22,305,238,272)(23,314,239,261)(24,303,240,270)(25,312,221,279)(26,301,222,268)(27,310,223,277)(28,319,224,266)(29,308,225,275)(30,317,226,264)(31,306,227,273)(32,315,228,262)(33,304,229,271)(34,313,230,280)(35,302,231,269)(36,311,232,278)(37,320,233,267)(38,309,234,276)(39,318,235,265)(40,307,236,274)(81,154,176,213)(82,143,177,202)(83,152,178,211)(84,141,179,220)(85,150,180,209)(86,159,161,218)(87,148,162,207)(88,157,163,216)(89,146,164,205)(90,155,165,214)(91,144,166,203)(92,153,167,212)(93,142,168,201)(94,151,169,210)(95,160,170,219)(96,149,171,208)(97,158,172,217)(98,147,173,206)(99,156,174,215)(100,145,175,204)(101,294,185,128)(102,283,186,137)(103,292,187,126)(104,281,188,135)(105,290,189,124)(106,299,190,133)(107,288,191,122)(108,297,192,131)(109,286,193,140)(110,295,194,129)(111,284,195,138)(112,293,196,127)(113,282,197,136)(114,291,198,125)(115,300,199,134)(116,289,200,123)(117,298,181,132)(118,287,182,121)(119,296,183,130)(120,285,184,139)>;
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), (1,173,290,21,58,98,124,237)(2,164,291,32,59,89,125,228)(3,175,292,23,60,100,126,239)(4,166,293,34,41,91,127,230)(5,177,294,25,42,82,128,221)(6,168,295,36,43,93,129,232)(7,179,296,27,44,84,130,223)(8,170,297,38,45,95,131,234)(9,161,298,29,46,86,132,225)(10,172,299,40,47,97,133,236)(11,163,300,31,48,88,134,227)(12,174,281,22,49,99,135,238)(13,165,282,33,50,90,136,229)(14,176,283,24,51,81,137,240)(15,167,284,35,52,92,138,231)(16,178,285,26,53,83,139,222)(17,169,286,37,54,94,140,233)(18,180,287,28,55,85,121,224)(19,171,288,39,56,96,122,235)(20,162,289,30,57,87,123,226)(61,264,106,148,253,317,190,207)(62,275,107,159,254,308,191,218)(63,266,108,150,255,319,192,209)(64,277,109,141,256,310,193,220)(65,268,110,152,257,301,194,211)(66,279,111,143,258,312,195,202)(67,270,112,154,259,303,196,213)(68,261,113,145,260,314,197,204)(69,272,114,156,241,305,198,215)(70,263,115,147,242,316,199,206)(71,274,116,158,243,307,200,217)(72,265,117,149,244,318,181,208)(73,276,118,160,245,309,182,219)(74,267,119,151,246,320,183,210)(75,278,120,142,247,311,184,201)(76,269,101,153,248,302,185,212)(77,280,102,144,249,313,186,203)(78,271,103,155,250,304,187,214)(79,262,104,146,251,315,188,205)(80,273,105,157,252,306,189,216), (1,80,58,252)(2,69,59,241)(3,78,60,250)(4,67,41,259)(5,76,42,248)(6,65,43,257)(7,74,44,246)(8,63,45,255)(9,72,46,244)(10,61,47,253)(11,70,48,242)(12,79,49,251)(13,68,50,260)(14,77,51,249)(15,66,52,258)(16,75,53,247)(17,64,54,256)(18,73,55,245)(19,62,56,254)(20,71,57,243)(21,316,237,263)(22,305,238,272)(23,314,239,261)(24,303,240,270)(25,312,221,279)(26,301,222,268)(27,310,223,277)(28,319,224,266)(29,308,225,275)(30,317,226,264)(31,306,227,273)(32,315,228,262)(33,304,229,271)(34,313,230,280)(35,302,231,269)(36,311,232,278)(37,320,233,267)(38,309,234,276)(39,318,235,265)(40,307,236,274)(81,154,176,213)(82,143,177,202)(83,152,178,211)(84,141,179,220)(85,150,180,209)(86,159,161,218)(87,148,162,207)(88,157,163,216)(89,146,164,205)(90,155,165,214)(91,144,166,203)(92,153,167,212)(93,142,168,201)(94,151,169,210)(95,160,170,219)(96,149,171,208)(97,158,172,217)(98,147,173,206)(99,156,174,215)(100,145,175,204)(101,294,185,128)(102,283,186,137)(103,292,187,126)(104,281,188,135)(105,290,189,124)(106,299,190,133)(107,288,191,122)(108,297,192,131)(109,286,193,140)(110,295,194,129)(111,284,195,138)(112,293,196,127)(113,282,197,136)(114,291,198,125)(115,300,199,134)(116,289,200,123)(117,298,181,132)(118,287,182,121)(119,296,183,130)(120,285,184,139) );
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)], [(1,173,290,21,58,98,124,237),(2,164,291,32,59,89,125,228),(3,175,292,23,60,100,126,239),(4,166,293,34,41,91,127,230),(5,177,294,25,42,82,128,221),(6,168,295,36,43,93,129,232),(7,179,296,27,44,84,130,223),(8,170,297,38,45,95,131,234),(9,161,298,29,46,86,132,225),(10,172,299,40,47,97,133,236),(11,163,300,31,48,88,134,227),(12,174,281,22,49,99,135,238),(13,165,282,33,50,90,136,229),(14,176,283,24,51,81,137,240),(15,167,284,35,52,92,138,231),(16,178,285,26,53,83,139,222),(17,169,286,37,54,94,140,233),(18,180,287,28,55,85,121,224),(19,171,288,39,56,96,122,235),(20,162,289,30,57,87,123,226),(61,264,106,148,253,317,190,207),(62,275,107,159,254,308,191,218),(63,266,108,150,255,319,192,209),(64,277,109,141,256,310,193,220),(65,268,110,152,257,301,194,211),(66,279,111,143,258,312,195,202),(67,270,112,154,259,303,196,213),(68,261,113,145,260,314,197,204),(69,272,114,156,241,305,198,215),(70,263,115,147,242,316,199,206),(71,274,116,158,243,307,200,217),(72,265,117,149,244,318,181,208),(73,276,118,160,245,309,182,219),(74,267,119,151,246,320,183,210),(75,278,120,142,247,311,184,201),(76,269,101,153,248,302,185,212),(77,280,102,144,249,313,186,203),(78,271,103,155,250,304,187,214),(79,262,104,146,251,315,188,205),(80,273,105,157,252,306,189,216)], [(1,80,58,252),(2,69,59,241),(3,78,60,250),(4,67,41,259),(5,76,42,248),(6,65,43,257),(7,74,44,246),(8,63,45,255),(9,72,46,244),(10,61,47,253),(11,70,48,242),(12,79,49,251),(13,68,50,260),(14,77,51,249),(15,66,52,258),(16,75,53,247),(17,64,54,256),(18,73,55,245),(19,62,56,254),(20,71,57,243),(21,316,237,263),(22,305,238,272),(23,314,239,261),(24,303,240,270),(25,312,221,279),(26,301,222,268),(27,310,223,277),(28,319,224,266),(29,308,225,275),(30,317,226,264),(31,306,227,273),(32,315,228,262),(33,304,229,271),(34,313,230,280),(35,302,231,269),(36,311,232,278),(37,320,233,267),(38,309,234,276),(39,318,235,265),(40,307,236,274),(81,154,176,213),(82,143,177,202),(83,152,178,211),(84,141,179,220),(85,150,180,209),(86,159,161,218),(87,148,162,207),(88,157,163,216),(89,146,164,205),(90,155,165,214),(91,144,166,203),(92,153,167,212),(93,142,168,201),(94,151,169,210),(95,160,170,219),(96,149,171,208),(97,158,172,217),(98,147,173,206),(99,156,174,215),(100,145,175,204),(101,294,185,128),(102,283,186,137),(103,292,187,126),(104,281,188,135),(105,290,189,124),(106,299,190,133),(107,288,191,122),(108,297,192,131),(109,286,193,140),(110,295,194,129),(111,284,195,138),(112,293,196,127),(113,282,197,136),(114,291,198,125),(115,300,199,134),(116,289,200,123),(117,298,181,132),(118,287,182,121),(119,296,183,130),(120,285,184,139)]])
59 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 20A | ··· | 20H | 20I | ··· | 20P | 40A | ··· | 40P |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 20 | 20 | 20 | 20 | 40 | 40 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
59 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | - | + | + | + | - | + | - | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D5 | Q16 | C4○D4 | D10 | D10 | D20 | Dic20 | C8⋊C22 | D4⋊2D5 | Q8×D5 | C8⋊D10 |
| kernel | C20.7Q16 | C20.44D4 | C40⋊5C4 | C5×C4⋊C8 | C4×Dic10 | C20⋊2Q8 | Dic10 | C2×C20 | C4⋊C8 | C20 | C20 | C42 | C2×C8 | C2×C4 | C4 | C10 | C4 | C4 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 8 | 16 | 1 | 2 | 2 | 4 |
Matrix representation of C20.7Q16 ►in GL4(𝔽41) generated by
| 16 | 0 | 0 | 0 |
| 25 | 18 | 0 | 0 |
| 0 | 0 | 29 | 36 |
| 0 | 0 | 29 | 12 |
| 38 | 0 | 0 | 0 |
| 6 | 27 | 0 | 0 |
| 0 | 0 | 15 | 37 |
| 0 | 0 | 36 | 26 |
| 28 | 17 | 0 | 0 |
| 31 | 13 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(41))| [16,25,0,0,0,18,0,0,0,0,29,29,0,0,36,12],[38,6,0,0,0,27,0,0,0,0,15,36,0,0,37,26],[28,31,0,0,17,13,0,0,0,0,1,0,0,0,0,1] >;
C20.7Q16 in GAP, Magma, Sage, TeX
C_{20}._7Q_{16} % in TeX
G:=Group("C20.7Q16"); // GroupNames label
G:=SmallGroup(320,477);
// by ID
G=gap.SmallGroup(320,477);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,254,219,310,1123,136,12550]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,b*a*b^-1=a^11,c*a*c^-1=a^9,c*b*c^-1=a^10*b^-1>;
// generators/relations