metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C20.26M4(2), Dic5.12SD16, C5⋊2C8⋊4C8, C5⋊2(C8⋊2C8), (C2×C8).5F5, (C2×C40).2C4, C10.5(C4⋊C8), C20.12(C2×C8), C4.7(D5⋊C8), C20⋊C8.9C2, C2.2(C40⋊C4), C10.4(C4.Q8), (C8×Dic5).11C2, (C2×Dic5).29Q8, C22.17(C4⋊F5), C2.2(D10.Q8), C10.3(C8.C4), C4.4(C22.F5), (C2×Dic5).172D4, C2.4(Dic5⋊C8), (C4×Dic5).342C22, (C2×C5⋊2C8).21C4, (C2×C4).119(C2×F5), (C2×C10).10(C4⋊C4), (C2×C20).116(C2×C4), SmallGroup(320,221)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C20.26M4(2)
G = < a,b,c | a20=b8=1, c2=a5, bab-1=a3, ac=ca, cbc-1=a15b5 >
Smallest permutation representation of C20.26M4(2)
►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 65 279 24 147 250 165 87)(2 72 268 27 148 257 174 90)(3 79 277 30 149 244 163 93)(4 66 266 33 150 251 172 96)(5 73 275 36 151 258 161 99)(6 80 264 39 152 245 170 82)(7 67 273 22 153 252 179 85)(8 74 262 25 154 259 168 88)(9 61 271 28 155 246 177 91)(10 68 280 31 156 253 166 94)(11 75 269 34 157 260 175 97)(12 62 278 37 158 247 164 100)(13 69 267 40 159 254 173 83)(14 76 276 23 160 241 162 86)(15 63 265 26 141 248 171 89)(16 70 274 29 142 255 180 92)(17 77 263 32 143 242 169 95)(18 64 272 35 144 249 178 98)(19 71 261 38 145 256 167 81)(20 78 270 21 146 243 176 84)(41 289 307 195 129 236 114 216)(42 296 316 198 130 223 103 219)(43 283 305 181 131 230 112 202)(44 290 314 184 132 237 101 205)(45 297 303 187 133 224 110 208)(46 284 312 190 134 231 119 211)(47 291 301 193 135 238 108 214)(48 298 310 196 136 225 117 217)(49 285 319 199 137 232 106 220)(50 292 308 182 138 239 115 203)(51 299 317 185 139 226 104 206)(52 286 306 188 140 233 113 209)(53 293 315 191 121 240 102 212)(54 300 304 194 122 227 111 215)(55 287 313 197 123 234 120 218)(56 294 302 200 124 221 109 201)(57 281 311 183 125 228 118 204)(58 288 320 186 126 235 107 207)(59 295 309 189 127 222 116 210)(60 282 318 192 128 229 105 213)
(1 103 6 108 11 113 16 118)(2 104 7 109 12 114 17 119)(3 105 8 110 13 115 18 120)(4 106 9 111 14 116 19 101)(5 107 10 112 15 117 20 102)(21 235 26 240 31 225 36 230)(22 236 27 221 32 226 37 231)(23 237 28 222 33 227 38 232)(24 238 29 223 34 228 39 233)(25 239 30 224 35 229 40 234)(41 263 46 268 51 273 56 278)(42 264 47 269 52 274 57 279)(43 265 48 270 53 275 58 280)(44 266 49 271 54 276 59 261)(45 267 50 272 55 277 60 262)(61 189 66 194 71 199 76 184)(62 190 67 195 72 200 77 185)(63 191 68 196 73 181 78 186)(64 192 69 197 74 182 79 187)(65 193 70 198 75 183 80 188)(81 285 86 290 91 295 96 300)(82 286 87 291 92 296 97 281)(83 287 88 292 93 297 98 282)(84 288 89 293 94 298 99 283)(85 289 90 294 95 299 100 284)(121 161 126 166 131 171 136 176)(122 162 127 167 132 172 137 177)(123 163 128 168 133 173 138 178)(124 164 129 169 134 174 139 179)(125 165 130 170 135 175 140 180)(141 310 146 315 151 320 156 305)(142 311 147 316 152 301 157 306)(143 312 148 317 153 302 158 307)(144 313 149 318 154 303 159 308)(145 314 150 319 155 304 160 309)(201 242 206 247 211 252 216 257)(202 243 207 248 212 253 217 258)(203 244 208 249 213 254 218 259)(204 245 209 250 214 255 219 260)(205 246 210 251 215 256 220 241)
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), (1,65,279,24,147,250,165,87)(2,72,268,27,148,257,174,90)(3,79,277,30,149,244,163,93)(4,66,266,33,150,251,172,96)(5,73,275,36,151,258,161,99)(6,80,264,39,152,245,170,82)(7,67,273,22,153,252,179,85)(8,74,262,25,154,259,168,88)(9,61,271,28,155,246,177,91)(10,68,280,31,156,253,166,94)(11,75,269,34,157,260,175,97)(12,62,278,37,158,247,164,100)(13,69,267,40,159,254,173,83)(14,76,276,23,160,241,162,86)(15,63,265,26,141,248,171,89)(16,70,274,29,142,255,180,92)(17,77,263,32,143,242,169,95)(18,64,272,35,144,249,178,98)(19,71,261,38,145,256,167,81)(20,78,270,21,146,243,176,84)(41,289,307,195,129,236,114,216)(42,296,316,198,130,223,103,219)(43,283,305,181,131,230,112,202)(44,290,314,184,132,237,101,205)(45,297,303,187,133,224,110,208)(46,284,312,190,134,231,119,211)(47,291,301,193,135,238,108,214)(48,298,310,196,136,225,117,217)(49,285,319,199,137,232,106,220)(50,292,308,182,138,239,115,203)(51,299,317,185,139,226,104,206)(52,286,306,188,140,233,113,209)(53,293,315,191,121,240,102,212)(54,300,304,194,122,227,111,215)(55,287,313,197,123,234,120,218)(56,294,302,200,124,221,109,201)(57,281,311,183,125,228,118,204)(58,288,320,186,126,235,107,207)(59,295,309,189,127,222,116,210)(60,282,318,192,128,229,105,213), (1,103,6,108,11,113,16,118)(2,104,7,109,12,114,17,119)(3,105,8,110,13,115,18,120)(4,106,9,111,14,116,19,101)(5,107,10,112,15,117,20,102)(21,235,26,240,31,225,36,230)(22,236,27,221,32,226,37,231)(23,237,28,222,33,227,38,232)(24,238,29,223,34,228,39,233)(25,239,30,224,35,229,40,234)(41,263,46,268,51,273,56,278)(42,264,47,269,52,274,57,279)(43,265,48,270,53,275,58,280)(44,266,49,271,54,276,59,261)(45,267,50,272,55,277,60,262)(61,189,66,194,71,199,76,184)(62,190,67,195,72,200,77,185)(63,191,68,196,73,181,78,186)(64,192,69,197,74,182,79,187)(65,193,70,198,75,183,80,188)(81,285,86,290,91,295,96,300)(82,286,87,291,92,296,97,281)(83,287,88,292,93,297,98,282)(84,288,89,293,94,298,99,283)(85,289,90,294,95,299,100,284)(121,161,126,166,131,171,136,176)(122,162,127,167,132,172,137,177)(123,163,128,168,133,173,138,178)(124,164,129,169,134,174,139,179)(125,165,130,170,135,175,140,180)(141,310,146,315,151,320,156,305)(142,311,147,316,152,301,157,306)(143,312,148,317,153,302,158,307)(144,313,149,318,154,303,159,308)(145,314,150,319,155,304,160,309)(201,242,206,247,211,252,216,257)(202,243,207,248,212,253,217,258)(203,244,208,249,213,254,218,259)(204,245,209,250,214,255,219,260)(205,246,210,251,215,256,220,241)>;
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), (1,65,279,24,147,250,165,87)(2,72,268,27,148,257,174,90)(3,79,277,30,149,244,163,93)(4,66,266,33,150,251,172,96)(5,73,275,36,151,258,161,99)(6,80,264,39,152,245,170,82)(7,67,273,22,153,252,179,85)(8,74,262,25,154,259,168,88)(9,61,271,28,155,246,177,91)(10,68,280,31,156,253,166,94)(11,75,269,34,157,260,175,97)(12,62,278,37,158,247,164,100)(13,69,267,40,159,254,173,83)(14,76,276,23,160,241,162,86)(15,63,265,26,141,248,171,89)(16,70,274,29,142,255,180,92)(17,77,263,32,143,242,169,95)(18,64,272,35,144,249,178,98)(19,71,261,38,145,256,167,81)(20,78,270,21,146,243,176,84)(41,289,307,195,129,236,114,216)(42,296,316,198,130,223,103,219)(43,283,305,181,131,230,112,202)(44,290,314,184,132,237,101,205)(45,297,303,187,133,224,110,208)(46,284,312,190,134,231,119,211)(47,291,301,193,135,238,108,214)(48,298,310,196,136,225,117,217)(49,285,319,199,137,232,106,220)(50,292,308,182,138,239,115,203)(51,299,317,185,139,226,104,206)(52,286,306,188,140,233,113,209)(53,293,315,191,121,240,102,212)(54,300,304,194,122,227,111,215)(55,287,313,197,123,234,120,218)(56,294,302,200,124,221,109,201)(57,281,311,183,125,228,118,204)(58,288,320,186,126,235,107,207)(59,295,309,189,127,222,116,210)(60,282,318,192,128,229,105,213), (1,103,6,108,11,113,16,118)(2,104,7,109,12,114,17,119)(3,105,8,110,13,115,18,120)(4,106,9,111,14,116,19,101)(5,107,10,112,15,117,20,102)(21,235,26,240,31,225,36,230)(22,236,27,221,32,226,37,231)(23,237,28,222,33,227,38,232)(24,238,29,223,34,228,39,233)(25,239,30,224,35,229,40,234)(41,263,46,268,51,273,56,278)(42,264,47,269,52,274,57,279)(43,265,48,270,53,275,58,280)(44,266,49,271,54,276,59,261)(45,267,50,272,55,277,60,262)(61,189,66,194,71,199,76,184)(62,190,67,195,72,200,77,185)(63,191,68,196,73,181,78,186)(64,192,69,197,74,182,79,187)(65,193,70,198,75,183,80,188)(81,285,86,290,91,295,96,300)(82,286,87,291,92,296,97,281)(83,287,88,292,93,297,98,282)(84,288,89,293,94,298,99,283)(85,289,90,294,95,299,100,284)(121,161,126,166,131,171,136,176)(122,162,127,167,132,172,137,177)(123,163,128,168,133,173,138,178)(124,164,129,169,134,174,139,179)(125,165,130,170,135,175,140,180)(141,310,146,315,151,320,156,305)(142,311,147,316,152,301,157,306)(143,312,148,317,153,302,158,307)(144,313,149,318,154,303,159,308)(145,314,150,319,155,304,160,309)(201,242,206,247,211,252,216,257)(202,243,207,248,212,253,217,258)(203,244,208,249,213,254,218,259)(204,245,209,250,214,255,219,260)(205,246,210,251,215,256,220,241) );
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)], [(1,65,279,24,147,250,165,87),(2,72,268,27,148,257,174,90),(3,79,277,30,149,244,163,93),(4,66,266,33,150,251,172,96),(5,73,275,36,151,258,161,99),(6,80,264,39,152,245,170,82),(7,67,273,22,153,252,179,85),(8,74,262,25,154,259,168,88),(9,61,271,28,155,246,177,91),(10,68,280,31,156,253,166,94),(11,75,269,34,157,260,175,97),(12,62,278,37,158,247,164,100),(13,69,267,40,159,254,173,83),(14,76,276,23,160,241,162,86),(15,63,265,26,141,248,171,89),(16,70,274,29,142,255,180,92),(17,77,263,32,143,242,169,95),(18,64,272,35,144,249,178,98),(19,71,261,38,145,256,167,81),(20,78,270,21,146,243,176,84),(41,289,307,195,129,236,114,216),(42,296,316,198,130,223,103,219),(43,283,305,181,131,230,112,202),(44,290,314,184,132,237,101,205),(45,297,303,187,133,224,110,208),(46,284,312,190,134,231,119,211),(47,291,301,193,135,238,108,214),(48,298,310,196,136,225,117,217),(49,285,319,199,137,232,106,220),(50,292,308,182,138,239,115,203),(51,299,317,185,139,226,104,206),(52,286,306,188,140,233,113,209),(53,293,315,191,121,240,102,212),(54,300,304,194,122,227,111,215),(55,287,313,197,123,234,120,218),(56,294,302,200,124,221,109,201),(57,281,311,183,125,228,118,204),(58,288,320,186,126,235,107,207),(59,295,309,189,127,222,116,210),(60,282,318,192,128,229,105,213)], [(1,103,6,108,11,113,16,118),(2,104,7,109,12,114,17,119),(3,105,8,110,13,115,18,120),(4,106,9,111,14,116,19,101),(5,107,10,112,15,117,20,102),(21,235,26,240,31,225,36,230),(22,236,27,221,32,226,37,231),(23,237,28,222,33,227,38,232),(24,238,29,223,34,228,39,233),(25,239,30,224,35,229,40,234),(41,263,46,268,51,273,56,278),(42,264,47,269,52,274,57,279),(43,265,48,270,53,275,58,280),(44,266,49,271,54,276,59,261),(45,267,50,272,55,277,60,262),(61,189,66,194,71,199,76,184),(62,190,67,195,72,200,77,185),(63,191,68,196,73,181,78,186),(64,192,69,197,74,182,79,187),(65,193,70,198,75,183,80,188),(81,285,86,290,91,295,96,300),(82,286,87,291,92,296,97,281),(83,287,88,292,93,297,98,282),(84,288,89,293,94,298,99,283),(85,289,90,294,95,299,100,284),(121,161,126,166,131,171,136,176),(122,162,127,167,132,172,137,177),(123,163,128,168,133,173,138,178),(124,164,129,169,134,174,139,179),(125,165,130,170,135,175,140,180),(141,310,146,315,151,320,156,305),(142,311,147,316,152,301,157,306),(143,312,148,317,153,302,158,307),(144,313,149,318,154,303,159,308),(145,314,150,319,155,304,160,309),(201,242,206,247,211,252,216,257),(202,243,207,248,212,253,217,258),(203,244,208,249,213,254,218,259),(204,245,209,250,214,255,219,260),(205,246,210,251,215,256,220,241)]])
44 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | ··· | 8P | 10A | 10B | 10C | 20A | 20B | 20C | 20D | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 5 | 5 | 5 | 5 | 10 | 10 | 4 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | ||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D4 | Q8 | SD16 | M4(2) | C8.C4 | F5 | C2×F5 | D5⋊C8 | C22.F5 | C4⋊F5 | C40⋊C4 | D10.Q8 |
| kernel | C20.26M4(2) | C8×Dic5 | C20⋊C8 | C2×C5⋊2C8 | C2×C40 | C5⋊2C8 | C2×Dic5 | C2×Dic5 | Dic5 | C20 | C10 | C2×C8 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 2 | 2 | 2 | 8 | 1 | 1 | 4 | 2 | 4 | 1 | 1 | 2 | 2 | 2 | 4 | 4 |
Matrix representation of C20.26M4(2) ►in GL6(𝔽41)
| 35 | 36 | 0 | 0 | 0 | 0 |
| 32 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 7 | 7 | 34 |
| 0 | 0 | 7 | 0 | 14 | 14 |
| 0 | 0 | 27 | 34 | 27 | 0 |
| 0 | 0 | 0 | 27 | 34 | 27 |
| 0 | 6 | 0 | 0 | 0 | 0 |
| 22 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 12 | 35 | 34 |
| 0 | 0 | 23 | 22 | 29 | 4 |
| 0 | 0 | 7 | 23 | 19 | 1 |
| 0 | 0 | 37 | 19 | 18 | 25 |
| 22 | 22 | 0 | 0 | 0 | 0 |
| 15 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 5 | 5 |
| 0 | 0 | 36 | 3 | 36 | 0 |
| 0 | 0 | 0 | 36 | 3 | 36 |
| 0 | 0 | 5 | 5 | 0 | 8 |
G:=sub<GL(6,GF(41))| [35,32,0,0,0,0,36,6,0,0,0,0,0,0,34,7,27,0,0,0,7,0,34,27,0,0,7,14,27,34,0,0,34,14,0,27],[0,22,0,0,0,0,6,0,0,0,0,0,0,0,16,23,7,37,0,0,12,22,23,19,0,0,35,29,19,18,0,0,34,4,1,25],[22,15,0,0,0,0,22,2,0,0,0,0,0,0,8,36,0,5,0,0,0,3,36,5,0,0,5,36,3,0,0,0,5,0,36,8] >;
C20.26M4(2) in GAP, Magma, Sage, TeX
C_{20}._{26}M_4(2) % in TeX
G:=Group("C20.26M4(2)"); // GroupNames label
G:=SmallGroup(320,221);
// by ID
G=gap.SmallGroup(320,221);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,176,100,1123,136,6278,3156]);
// Polycyclic
G:=Group<a,b,c|a^20=b^8=1,c^2=a^5,b*a*b^-1=a^3,a*c=c*a,c*b*c^-1=a^15*b^5>;
// generators/relations
Export