direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C13×Dic7, C7⋊C52, C91⋊5C4, C14.C26, C26.2D7, C182.3C2, C2.(C13×D7), SmallGroup(364,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C13×Dic7 |
Generators and relations for C13×Dic7
G = < a,b,c | a13=b14=1, c2=b7, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C13×Dic7
►Regular action on 364 points
Generators in S364
(1 169 158 153 127 125 103 89 75 61 51 37 28)(2 170 159 154 128 126 104 90 76 62 52 38 15)(3 171 160 141 129 113 105 91 77 63 53 39 16)(4 172 161 142 130 114 106 92 78 64 54 40 17)(5 173 162 143 131 115 107 93 79 65 55 41 18)(6 174 163 144 132 116 108 94 80 66 56 42 19)(7 175 164 145 133 117 109 95 81 67 43 29 20)(8 176 165 146 134 118 110 96 82 68 44 30 21)(9 177 166 147 135 119 111 97 83 69 45 31 22)(10 178 167 148 136 120 112 98 84 70 46 32 23)(11 179 168 149 137 121 99 85 71 57 47 33 24)(12 180 155 150 138 122 100 86 72 58 48 34 25)(13 181 156 151 139 123 101 87 73 59 49 35 26)(14 182 157 152 140 124 102 88 74 60 50 36 27)(183 351 337 323 316 302 281 274 253 239 225 218 204)(184 352 338 324 317 303 282 275 254 240 226 219 205)(185 353 339 325 318 304 283 276 255 241 227 220 206)(186 354 340 326 319 305 284 277 256 242 228 221 207)(187 355 341 327 320 306 285 278 257 243 229 222 208)(188 356 342 328 321 307 286 279 258 244 230 223 209)(189 357 343 329 322 308 287 280 259 245 231 224 210)(190 358 344 330 309 295 288 267 260 246 232 211 197)(191 359 345 331 310 296 289 268 261 247 233 212 198)(192 360 346 332 311 297 290 269 262 248 234 213 199)(193 361 347 333 312 298 291 270 263 249 235 214 200)(194 362 348 334 313 299 292 271 264 250 236 215 201)(195 363 349 335 314 300 293 272 265 251 237 216 202)(196 364 350 336 315 301 294 273 266 252 238 217 203)
(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)(309 310 311 312 313 314 315 316 317 318 319 320 321 322)(323 324 325 326 327 328 329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344 345 346 347 348 349 350)(351 352 353 354 355 356 357 358 359 360 361 362 363 364)
(1 183 8 190)(2 196 9 189)(3 195 10 188)(4 194 11 187)(5 193 12 186)(6 192 13 185)(7 191 14 184)(15 203 22 210)(16 202 23 209)(17 201 24 208)(18 200 25 207)(19 199 26 206)(20 198 27 205)(21 197 28 204)(29 212 36 219)(30 211 37 218)(31 224 38 217)(32 223 39 216)(33 222 40 215)(34 221 41 214)(35 220 42 213)(43 233 50 226)(44 232 51 225)(45 231 52 238)(46 230 53 237)(47 229 54 236)(48 228 55 235)(49 227 56 234)(57 243 64 250)(58 242 65 249)(59 241 66 248)(60 240 67 247)(61 239 68 246)(62 252 69 245)(63 251 70 244)(71 257 78 264)(72 256 79 263)(73 255 80 262)(74 254 81 261)(75 253 82 260)(76 266 83 259)(77 265 84 258)(85 278 92 271)(86 277 93 270)(87 276 94 269)(88 275 95 268)(89 274 96 267)(90 273 97 280)(91 272 98 279)(99 285 106 292)(100 284 107 291)(101 283 108 290)(102 282 109 289)(103 281 110 288)(104 294 111 287)(105 293 112 286)(113 300 120 307)(114 299 121 306)(115 298 122 305)(116 297 123 304)(117 296 124 303)(118 295 125 302)(119 308 126 301)(127 316 134 309)(128 315 135 322)(129 314 136 321)(130 313 137 320)(131 312 138 319)(132 311 139 318)(133 310 140 317)(141 335 148 328)(142 334 149 327)(143 333 150 326)(144 332 151 325)(145 331 152 324)(146 330 153 323)(147 329 154 336)(155 340 162 347)(156 339 163 346)(157 338 164 345)(158 337 165 344)(159 350 166 343)(160 349 167 342)(161 348 168 341)(169 351 176 358)(170 364 177 357)(171 363 178 356)(172 362 179 355)(173 361 180 354)(174 360 181 353)(175 359 182 352)
G:=sub<Sym(364)| (1,169,158,153,127,125,103,89,75,61,51,37,28)(2,170,159,154,128,126,104,90,76,62,52,38,15)(3,171,160,141,129,113,105,91,77,63,53,39,16)(4,172,161,142,130,114,106,92,78,64,54,40,17)(5,173,162,143,131,115,107,93,79,65,55,41,18)(6,174,163,144,132,116,108,94,80,66,56,42,19)(7,175,164,145,133,117,109,95,81,67,43,29,20)(8,176,165,146,134,118,110,96,82,68,44,30,21)(9,177,166,147,135,119,111,97,83,69,45,31,22)(10,178,167,148,136,120,112,98,84,70,46,32,23)(11,179,168,149,137,121,99,85,71,57,47,33,24)(12,180,155,150,138,122,100,86,72,58,48,34,25)(13,181,156,151,139,123,101,87,73,59,49,35,26)(14,182,157,152,140,124,102,88,74,60,50,36,27)(183,351,337,323,316,302,281,274,253,239,225,218,204)(184,352,338,324,317,303,282,275,254,240,226,219,205)(185,353,339,325,318,304,283,276,255,241,227,220,206)(186,354,340,326,319,305,284,277,256,242,228,221,207)(187,355,341,327,320,306,285,278,257,243,229,222,208)(188,356,342,328,321,307,286,279,258,244,230,223,209)(189,357,343,329,322,308,287,280,259,245,231,224,210)(190,358,344,330,309,295,288,267,260,246,232,211,197)(191,359,345,331,310,296,289,268,261,247,233,212,198)(192,360,346,332,311,297,290,269,262,248,234,213,199)(193,361,347,333,312,298,291,270,263,249,235,214,200)(194,362,348,334,313,299,292,271,264,250,236,215,201)(195,363,349,335,314,300,293,272,265,251,237,216,202)(196,364,350,336,315,301,294,273,266,252,238,217,203), (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)(309,310,311,312,313,314,315,316,317,318,319,320,321,322)(323,324,325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348,349,350)(351,352,353,354,355,356,357,358,359,360,361,362,363,364), (1,183,8,190)(2,196,9,189)(3,195,10,188)(4,194,11,187)(5,193,12,186)(6,192,13,185)(7,191,14,184)(15,203,22,210)(16,202,23,209)(17,201,24,208)(18,200,25,207)(19,199,26,206)(20,198,27,205)(21,197,28,204)(29,212,36,219)(30,211,37,218)(31,224,38,217)(32,223,39,216)(33,222,40,215)(34,221,41,214)(35,220,42,213)(43,233,50,226)(44,232,51,225)(45,231,52,238)(46,230,53,237)(47,229,54,236)(48,228,55,235)(49,227,56,234)(57,243,64,250)(58,242,65,249)(59,241,66,248)(60,240,67,247)(61,239,68,246)(62,252,69,245)(63,251,70,244)(71,257,78,264)(72,256,79,263)(73,255,80,262)(74,254,81,261)(75,253,82,260)(76,266,83,259)(77,265,84,258)(85,278,92,271)(86,277,93,270)(87,276,94,269)(88,275,95,268)(89,274,96,267)(90,273,97,280)(91,272,98,279)(99,285,106,292)(100,284,107,291)(101,283,108,290)(102,282,109,289)(103,281,110,288)(104,294,111,287)(105,293,112,286)(113,300,120,307)(114,299,121,306)(115,298,122,305)(116,297,123,304)(117,296,124,303)(118,295,125,302)(119,308,126,301)(127,316,134,309)(128,315,135,322)(129,314,136,321)(130,313,137,320)(131,312,138,319)(132,311,139,318)(133,310,140,317)(141,335,148,328)(142,334,149,327)(143,333,150,326)(144,332,151,325)(145,331,152,324)(146,330,153,323)(147,329,154,336)(155,340,162,347)(156,339,163,346)(157,338,164,345)(158,337,165,344)(159,350,166,343)(160,349,167,342)(161,348,168,341)(169,351,176,358)(170,364,177,357)(171,363,178,356)(172,362,179,355)(173,361,180,354)(174,360,181,353)(175,359,182,352)>;
G:=Group( (1,169,158,153,127,125,103,89,75,61,51,37,28)(2,170,159,154,128,126,104,90,76,62,52,38,15)(3,171,160,141,129,113,105,91,77,63,53,39,16)(4,172,161,142,130,114,106,92,78,64,54,40,17)(5,173,162,143,131,115,107,93,79,65,55,41,18)(6,174,163,144,132,116,108,94,80,66,56,42,19)(7,175,164,145,133,117,109,95,81,67,43,29,20)(8,176,165,146,134,118,110,96,82,68,44,30,21)(9,177,166,147,135,119,111,97,83,69,45,31,22)(10,178,167,148,136,120,112,98,84,70,46,32,23)(11,179,168,149,137,121,99,85,71,57,47,33,24)(12,180,155,150,138,122,100,86,72,58,48,34,25)(13,181,156,151,139,123,101,87,73,59,49,35,26)(14,182,157,152,140,124,102,88,74,60,50,36,27)(183,351,337,323,316,302,281,274,253,239,225,218,204)(184,352,338,324,317,303,282,275,254,240,226,219,205)(185,353,339,325,318,304,283,276,255,241,227,220,206)(186,354,340,326,319,305,284,277,256,242,228,221,207)(187,355,341,327,320,306,285,278,257,243,229,222,208)(188,356,342,328,321,307,286,279,258,244,230,223,209)(189,357,343,329,322,308,287,280,259,245,231,224,210)(190,358,344,330,309,295,288,267,260,246,232,211,197)(191,359,345,331,310,296,289,268,261,247,233,212,198)(192,360,346,332,311,297,290,269,262,248,234,213,199)(193,361,347,333,312,298,291,270,263,249,235,214,200)(194,362,348,334,313,299,292,271,264,250,236,215,201)(195,363,349,335,314,300,293,272,265,251,237,216,202)(196,364,350,336,315,301,294,273,266,252,238,217,203), (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)(309,310,311,312,313,314,315,316,317,318,319,320,321,322)(323,324,325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348,349,350)(351,352,353,354,355,356,357,358,359,360,361,362,363,364), (1,183,8,190)(2,196,9,189)(3,195,10,188)(4,194,11,187)(5,193,12,186)(6,192,13,185)(7,191,14,184)(15,203,22,210)(16,202,23,209)(17,201,24,208)(18,200,25,207)(19,199,26,206)(20,198,27,205)(21,197,28,204)(29,212,36,219)(30,211,37,218)(31,224,38,217)(32,223,39,216)(33,222,40,215)(34,221,41,214)(35,220,42,213)(43,233,50,226)(44,232,51,225)(45,231,52,238)(46,230,53,237)(47,229,54,236)(48,228,55,235)(49,227,56,234)(57,243,64,250)(58,242,65,249)(59,241,66,248)(60,240,67,247)(61,239,68,246)(62,252,69,245)(63,251,70,244)(71,257,78,264)(72,256,79,263)(73,255,80,262)(74,254,81,261)(75,253,82,260)(76,266,83,259)(77,265,84,258)(85,278,92,271)(86,277,93,270)(87,276,94,269)(88,275,95,268)(89,274,96,267)(90,273,97,280)(91,272,98,279)(99,285,106,292)(100,284,107,291)(101,283,108,290)(102,282,109,289)(103,281,110,288)(104,294,111,287)(105,293,112,286)(113,300,120,307)(114,299,121,306)(115,298,122,305)(116,297,123,304)(117,296,124,303)(118,295,125,302)(119,308,126,301)(127,316,134,309)(128,315,135,322)(129,314,136,321)(130,313,137,320)(131,312,138,319)(132,311,139,318)(133,310,140,317)(141,335,148,328)(142,334,149,327)(143,333,150,326)(144,332,151,325)(145,331,152,324)(146,330,153,323)(147,329,154,336)(155,340,162,347)(156,339,163,346)(157,338,164,345)(158,337,165,344)(159,350,166,343)(160,349,167,342)(161,348,168,341)(169,351,176,358)(170,364,177,357)(171,363,178,356)(172,362,179,355)(173,361,180,354)(174,360,181,353)(175,359,182,352) );
G=PermutationGroup([[(1,169,158,153,127,125,103,89,75,61,51,37,28),(2,170,159,154,128,126,104,90,76,62,52,38,15),(3,171,160,141,129,113,105,91,77,63,53,39,16),(4,172,161,142,130,114,106,92,78,64,54,40,17),(5,173,162,143,131,115,107,93,79,65,55,41,18),(6,174,163,144,132,116,108,94,80,66,56,42,19),(7,175,164,145,133,117,109,95,81,67,43,29,20),(8,176,165,146,134,118,110,96,82,68,44,30,21),(9,177,166,147,135,119,111,97,83,69,45,31,22),(10,178,167,148,136,120,112,98,84,70,46,32,23),(11,179,168,149,137,121,99,85,71,57,47,33,24),(12,180,155,150,138,122,100,86,72,58,48,34,25),(13,181,156,151,139,123,101,87,73,59,49,35,26),(14,182,157,152,140,124,102,88,74,60,50,36,27),(183,351,337,323,316,302,281,274,253,239,225,218,204),(184,352,338,324,317,303,282,275,254,240,226,219,205),(185,353,339,325,318,304,283,276,255,241,227,220,206),(186,354,340,326,319,305,284,277,256,242,228,221,207),(187,355,341,327,320,306,285,278,257,243,229,222,208),(188,356,342,328,321,307,286,279,258,244,230,223,209),(189,357,343,329,322,308,287,280,259,245,231,224,210),(190,358,344,330,309,295,288,267,260,246,232,211,197),(191,359,345,331,310,296,289,268,261,247,233,212,198),(192,360,346,332,311,297,290,269,262,248,234,213,199),(193,361,347,333,312,298,291,270,263,249,235,214,200),(194,362,348,334,313,299,292,271,264,250,236,215,201),(195,363,349,335,314,300,293,272,265,251,237,216,202),(196,364,350,336,315,301,294,273,266,252,238,217,203)], [(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),(309,310,311,312,313,314,315,316,317,318,319,320,321,322),(323,324,325,326,327,328,329,330,331,332,333,334,335,336),(337,338,339,340,341,342,343,344,345,346,347,348,349,350),(351,352,353,354,355,356,357,358,359,360,361,362,363,364)], [(1,183,8,190),(2,196,9,189),(3,195,10,188),(4,194,11,187),(5,193,12,186),(6,192,13,185),(7,191,14,184),(15,203,22,210),(16,202,23,209),(17,201,24,208),(18,200,25,207),(19,199,26,206),(20,198,27,205),(21,197,28,204),(29,212,36,219),(30,211,37,218),(31,224,38,217),(32,223,39,216),(33,222,40,215),(34,221,41,214),(35,220,42,213),(43,233,50,226),(44,232,51,225),(45,231,52,238),(46,230,53,237),(47,229,54,236),(48,228,55,235),(49,227,56,234),(57,243,64,250),(58,242,65,249),(59,241,66,248),(60,240,67,247),(61,239,68,246),(62,252,69,245),(63,251,70,244),(71,257,78,264),(72,256,79,263),(73,255,80,262),(74,254,81,261),(75,253,82,260),(76,266,83,259),(77,265,84,258),(85,278,92,271),(86,277,93,270),(87,276,94,269),(88,275,95,268),(89,274,96,267),(90,273,97,280),(91,272,98,279),(99,285,106,292),(100,284,107,291),(101,283,108,290),(102,282,109,289),(103,281,110,288),(104,294,111,287),(105,293,112,286),(113,300,120,307),(114,299,121,306),(115,298,122,305),(116,297,123,304),(117,296,124,303),(118,295,125,302),(119,308,126,301),(127,316,134,309),(128,315,135,322),(129,314,136,321),(130,313,137,320),(131,312,138,319),(132,311,139,318),(133,310,140,317),(141,335,148,328),(142,334,149,327),(143,333,150,326),(144,332,151,325),(145,331,152,324),(146,330,153,323),(147,329,154,336),(155,340,162,347),(156,339,163,346),(157,338,164,345),(158,337,165,344),(159,350,166,343),(160,349,167,342),(161,348,168,341),(169,351,176,358),(170,364,177,357),(171,363,178,356),(172,362,179,355),(173,361,180,354),(174,360,181,353),(175,359,182,352)]])
130 conjugacy classes
| class | 1 | 2 | 4A | 4B | 7A | 7B | 7C | 13A | ··· | 13L | 14A | 14B | 14C | 26A | ··· | 26L | 52A | ··· | 52X | 91A | ··· | 91AJ | 182A | ··· | 182AJ |
| order | 1 | 2 | 4 | 4 | 7 | 7 | 7 | 13 | ··· | 13 | 14 | 14 | 14 | 26 | ··· | 26 | 52 | ··· | 52 | 91 | ··· | 91 | 182 | ··· | 182 |
| size | 1 | 1 | 7 | 7 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 1 | ··· | 1 | 7 | ··· | 7 | 2 | ··· | 2 | 2 | ··· | 2 |
130 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C13 | C26 | C52 | D7 | Dic7 | C13×D7 | C13×Dic7 |
| kernel | C13×Dic7 | C182 | C91 | Dic7 | C14 | C7 | C26 | C13 | C2 | C1 |
| # reps | 1 | 1 | 2 | 12 | 12 | 24 | 3 | 3 | 36 | 36 |
Matrix representation of C13×Dic7 ►in GL3(𝔽1093) generated by
| 1 | 0 | 0 |
| 0 | 432 | 0 |
| 0 | 0 | 432 |
| 1092 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 1092 | 252 |
| 563 | 0 | 0 |
| 0 | 251 | 14 |
| 0 | 965 | 842 |
G:=sub<GL(3,GF(1093))| [1,0,0,0,432,0,0,0,432],[1092,0,0,0,0,1092,0,1,252],[563,0,0,0,251,965,0,14,842] >;
C13×Dic7 in GAP, Magma, Sage, TeX
C_{13}\times {\rm Dic}_7 % in TeX
G:=Group("C13xDic7"); // GroupNames label
G:=SmallGroup(364,1);
// by ID
G=gap.SmallGroup(364,1);
# by ID
G:=PCGroup([4,-2,-13,-2,-7,104,4995]);
// Polycyclic
G:=Group<a,b,c|a^13=b^14=1,c^2=b^7,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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