direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C7×Dic13, C91⋊4C4, C13⋊2C28, C26.C14, C182.2C2, C14.2D13, C2.(C7×D13), SmallGroup(364,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C7×Dic13 |
Generators and relations for C7×Dic13
G = < a,b,c | a7=b26=1, c2=b13, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C7×Dic13
►Regular action on 364 points
Generators in S364
(1 176 131 105 95 58 46)(2 177 132 106 96 59 47)(3 178 133 107 97 60 48)(4 179 134 108 98 61 49)(5 180 135 109 99 62 50)(6 181 136 110 100 63 51)(7 182 137 111 101 64 52)(8 157 138 112 102 65 27)(9 158 139 113 103 66 28)(10 159 140 114 104 67 29)(11 160 141 115 79 68 30)(12 161 142 116 80 69 31)(13 162 143 117 81 70 32)(14 163 144 118 82 71 33)(15 164 145 119 83 72 34)(16 165 146 120 84 73 35)(17 166 147 121 85 74 36)(18 167 148 122 86 75 37)(19 168 149 123 87 76 38)(20 169 150 124 88 77 39)(21 170 151 125 89 78 40)(22 171 152 126 90 53 41)(23 172 153 127 91 54 42)(24 173 154 128 92 55 43)(25 174 155 129 93 56 44)(26 175 156 130 94 57 45)(183 339 326 287 274 235 209)(184 340 327 288 275 236 210)(185 341 328 289 276 237 211)(186 342 329 290 277 238 212)(187 343 330 291 278 239 213)(188 344 331 292 279 240 214)(189 345 332 293 280 241 215)(190 346 333 294 281 242 216)(191 347 334 295 282 243 217)(192 348 335 296 283 244 218)(193 349 336 297 284 245 219)(194 350 337 298 285 246 220)(195 351 338 299 286 247 221)(196 352 313 300 261 248 222)(197 353 314 301 262 249 223)(198 354 315 302 263 250 224)(199 355 316 303 264 251 225)(200 356 317 304 265 252 226)(201 357 318 305 266 253 227)(202 358 319 306 267 254 228)(203 359 320 307 268 255 229)(204 360 321 308 269 256 230)(205 361 322 309 270 257 231)(206 362 323 310 271 258 232)(207 363 324 311 272 259 233)(208 364 325 312 273 260 234)
(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)
(1 196 14 183)(2 195 15 208)(3 194 16 207)(4 193 17 206)(5 192 18 205)(6 191 19 204)(7 190 20 203)(8 189 21 202)(9 188 22 201)(10 187 23 200)(11 186 24 199)(12 185 25 198)(13 184 26 197)(27 215 40 228)(28 214 41 227)(29 213 42 226)(30 212 43 225)(31 211 44 224)(32 210 45 223)(33 209 46 222)(34 234 47 221)(35 233 48 220)(36 232 49 219)(37 231 50 218)(38 230 51 217)(39 229 52 216)(53 253 66 240)(54 252 67 239)(55 251 68 238)(56 250 69 237)(57 249 70 236)(58 248 71 235)(59 247 72 260)(60 246 73 259)(61 245 74 258)(62 244 75 257)(63 243 76 256)(64 242 77 255)(65 241 78 254)(79 277 92 264)(80 276 93 263)(81 275 94 262)(82 274 95 261)(83 273 96 286)(84 272 97 285)(85 271 98 284)(86 270 99 283)(87 269 100 282)(88 268 101 281)(89 267 102 280)(90 266 103 279)(91 265 104 278)(105 300 118 287)(106 299 119 312)(107 298 120 311)(108 297 121 310)(109 296 122 309)(110 295 123 308)(111 294 124 307)(112 293 125 306)(113 292 126 305)(114 291 127 304)(115 290 128 303)(116 289 129 302)(117 288 130 301)(131 313 144 326)(132 338 145 325)(133 337 146 324)(134 336 147 323)(135 335 148 322)(136 334 149 321)(137 333 150 320)(138 332 151 319)(139 331 152 318)(140 330 153 317)(141 329 154 316)(142 328 155 315)(143 327 156 314)(157 345 170 358)(158 344 171 357)(159 343 172 356)(160 342 173 355)(161 341 174 354)(162 340 175 353)(163 339 176 352)(164 364 177 351)(165 363 178 350)(166 362 179 349)(167 361 180 348)(168 360 181 347)(169 359 182 346)
G:=sub<Sym(364)| (1,176,131,105,95,58,46)(2,177,132,106,96,59,47)(3,178,133,107,97,60,48)(4,179,134,108,98,61,49)(5,180,135,109,99,62,50)(6,181,136,110,100,63,51)(7,182,137,111,101,64,52)(8,157,138,112,102,65,27)(9,158,139,113,103,66,28)(10,159,140,114,104,67,29)(11,160,141,115,79,68,30)(12,161,142,116,80,69,31)(13,162,143,117,81,70,32)(14,163,144,118,82,71,33)(15,164,145,119,83,72,34)(16,165,146,120,84,73,35)(17,166,147,121,85,74,36)(18,167,148,122,86,75,37)(19,168,149,123,87,76,38)(20,169,150,124,88,77,39)(21,170,151,125,89,78,40)(22,171,152,126,90,53,41)(23,172,153,127,91,54,42)(24,173,154,128,92,55,43)(25,174,155,129,93,56,44)(26,175,156,130,94,57,45)(183,339,326,287,274,235,209)(184,340,327,288,275,236,210)(185,341,328,289,276,237,211)(186,342,329,290,277,238,212)(187,343,330,291,278,239,213)(188,344,331,292,279,240,214)(189,345,332,293,280,241,215)(190,346,333,294,281,242,216)(191,347,334,295,282,243,217)(192,348,335,296,283,244,218)(193,349,336,297,284,245,219)(194,350,337,298,285,246,220)(195,351,338,299,286,247,221)(196,352,313,300,261,248,222)(197,353,314,301,262,249,223)(198,354,315,302,263,250,224)(199,355,316,303,264,251,225)(200,356,317,304,265,252,226)(201,357,318,305,266,253,227)(202,358,319,306,267,254,228)(203,359,320,307,268,255,229)(204,360,321,308,269,256,230)(205,361,322,309,270,257,231)(206,362,323,310,271,258,232)(207,363,324,311,272,259,233)(208,364,325,312,273,260,234), (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), (1,196,14,183)(2,195,15,208)(3,194,16,207)(4,193,17,206)(5,192,18,205)(6,191,19,204)(7,190,20,203)(8,189,21,202)(9,188,22,201)(10,187,23,200)(11,186,24,199)(12,185,25,198)(13,184,26,197)(27,215,40,228)(28,214,41,227)(29,213,42,226)(30,212,43,225)(31,211,44,224)(32,210,45,223)(33,209,46,222)(34,234,47,221)(35,233,48,220)(36,232,49,219)(37,231,50,218)(38,230,51,217)(39,229,52,216)(53,253,66,240)(54,252,67,239)(55,251,68,238)(56,250,69,237)(57,249,70,236)(58,248,71,235)(59,247,72,260)(60,246,73,259)(61,245,74,258)(62,244,75,257)(63,243,76,256)(64,242,77,255)(65,241,78,254)(79,277,92,264)(80,276,93,263)(81,275,94,262)(82,274,95,261)(83,273,96,286)(84,272,97,285)(85,271,98,284)(86,270,99,283)(87,269,100,282)(88,268,101,281)(89,267,102,280)(90,266,103,279)(91,265,104,278)(105,300,118,287)(106,299,119,312)(107,298,120,311)(108,297,121,310)(109,296,122,309)(110,295,123,308)(111,294,124,307)(112,293,125,306)(113,292,126,305)(114,291,127,304)(115,290,128,303)(116,289,129,302)(117,288,130,301)(131,313,144,326)(132,338,145,325)(133,337,146,324)(134,336,147,323)(135,335,148,322)(136,334,149,321)(137,333,150,320)(138,332,151,319)(139,331,152,318)(140,330,153,317)(141,329,154,316)(142,328,155,315)(143,327,156,314)(157,345,170,358)(158,344,171,357)(159,343,172,356)(160,342,173,355)(161,341,174,354)(162,340,175,353)(163,339,176,352)(164,364,177,351)(165,363,178,350)(166,362,179,349)(167,361,180,348)(168,360,181,347)(169,359,182,346)>;
G:=Group( (1,176,131,105,95,58,46)(2,177,132,106,96,59,47)(3,178,133,107,97,60,48)(4,179,134,108,98,61,49)(5,180,135,109,99,62,50)(6,181,136,110,100,63,51)(7,182,137,111,101,64,52)(8,157,138,112,102,65,27)(9,158,139,113,103,66,28)(10,159,140,114,104,67,29)(11,160,141,115,79,68,30)(12,161,142,116,80,69,31)(13,162,143,117,81,70,32)(14,163,144,118,82,71,33)(15,164,145,119,83,72,34)(16,165,146,120,84,73,35)(17,166,147,121,85,74,36)(18,167,148,122,86,75,37)(19,168,149,123,87,76,38)(20,169,150,124,88,77,39)(21,170,151,125,89,78,40)(22,171,152,126,90,53,41)(23,172,153,127,91,54,42)(24,173,154,128,92,55,43)(25,174,155,129,93,56,44)(26,175,156,130,94,57,45)(183,339,326,287,274,235,209)(184,340,327,288,275,236,210)(185,341,328,289,276,237,211)(186,342,329,290,277,238,212)(187,343,330,291,278,239,213)(188,344,331,292,279,240,214)(189,345,332,293,280,241,215)(190,346,333,294,281,242,216)(191,347,334,295,282,243,217)(192,348,335,296,283,244,218)(193,349,336,297,284,245,219)(194,350,337,298,285,246,220)(195,351,338,299,286,247,221)(196,352,313,300,261,248,222)(197,353,314,301,262,249,223)(198,354,315,302,263,250,224)(199,355,316,303,264,251,225)(200,356,317,304,265,252,226)(201,357,318,305,266,253,227)(202,358,319,306,267,254,228)(203,359,320,307,268,255,229)(204,360,321,308,269,256,230)(205,361,322,309,270,257,231)(206,362,323,310,271,258,232)(207,363,324,311,272,259,233)(208,364,325,312,273,260,234), (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), (1,196,14,183)(2,195,15,208)(3,194,16,207)(4,193,17,206)(5,192,18,205)(6,191,19,204)(7,190,20,203)(8,189,21,202)(9,188,22,201)(10,187,23,200)(11,186,24,199)(12,185,25,198)(13,184,26,197)(27,215,40,228)(28,214,41,227)(29,213,42,226)(30,212,43,225)(31,211,44,224)(32,210,45,223)(33,209,46,222)(34,234,47,221)(35,233,48,220)(36,232,49,219)(37,231,50,218)(38,230,51,217)(39,229,52,216)(53,253,66,240)(54,252,67,239)(55,251,68,238)(56,250,69,237)(57,249,70,236)(58,248,71,235)(59,247,72,260)(60,246,73,259)(61,245,74,258)(62,244,75,257)(63,243,76,256)(64,242,77,255)(65,241,78,254)(79,277,92,264)(80,276,93,263)(81,275,94,262)(82,274,95,261)(83,273,96,286)(84,272,97,285)(85,271,98,284)(86,270,99,283)(87,269,100,282)(88,268,101,281)(89,267,102,280)(90,266,103,279)(91,265,104,278)(105,300,118,287)(106,299,119,312)(107,298,120,311)(108,297,121,310)(109,296,122,309)(110,295,123,308)(111,294,124,307)(112,293,125,306)(113,292,126,305)(114,291,127,304)(115,290,128,303)(116,289,129,302)(117,288,130,301)(131,313,144,326)(132,338,145,325)(133,337,146,324)(134,336,147,323)(135,335,148,322)(136,334,149,321)(137,333,150,320)(138,332,151,319)(139,331,152,318)(140,330,153,317)(141,329,154,316)(142,328,155,315)(143,327,156,314)(157,345,170,358)(158,344,171,357)(159,343,172,356)(160,342,173,355)(161,341,174,354)(162,340,175,353)(163,339,176,352)(164,364,177,351)(165,363,178,350)(166,362,179,349)(167,361,180,348)(168,360,181,347)(169,359,182,346) );
G=PermutationGroup([[(1,176,131,105,95,58,46),(2,177,132,106,96,59,47),(3,178,133,107,97,60,48),(4,179,134,108,98,61,49),(5,180,135,109,99,62,50),(6,181,136,110,100,63,51),(7,182,137,111,101,64,52),(8,157,138,112,102,65,27),(9,158,139,113,103,66,28),(10,159,140,114,104,67,29),(11,160,141,115,79,68,30),(12,161,142,116,80,69,31),(13,162,143,117,81,70,32),(14,163,144,118,82,71,33),(15,164,145,119,83,72,34),(16,165,146,120,84,73,35),(17,166,147,121,85,74,36),(18,167,148,122,86,75,37),(19,168,149,123,87,76,38),(20,169,150,124,88,77,39),(21,170,151,125,89,78,40),(22,171,152,126,90,53,41),(23,172,153,127,91,54,42),(24,173,154,128,92,55,43),(25,174,155,129,93,56,44),(26,175,156,130,94,57,45),(183,339,326,287,274,235,209),(184,340,327,288,275,236,210),(185,341,328,289,276,237,211),(186,342,329,290,277,238,212),(187,343,330,291,278,239,213),(188,344,331,292,279,240,214),(189,345,332,293,280,241,215),(190,346,333,294,281,242,216),(191,347,334,295,282,243,217),(192,348,335,296,283,244,218),(193,349,336,297,284,245,219),(194,350,337,298,285,246,220),(195,351,338,299,286,247,221),(196,352,313,300,261,248,222),(197,353,314,301,262,249,223),(198,354,315,302,263,250,224),(199,355,316,303,264,251,225),(200,356,317,304,265,252,226),(201,357,318,305,266,253,227),(202,358,319,306,267,254,228),(203,359,320,307,268,255,229),(204,360,321,308,269,256,230),(205,361,322,309,270,257,231),(206,362,323,310,271,258,232),(207,363,324,311,272,259,233),(208,364,325,312,273,260,234)], [(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)], [(1,196,14,183),(2,195,15,208),(3,194,16,207),(4,193,17,206),(5,192,18,205),(6,191,19,204),(7,190,20,203),(8,189,21,202),(9,188,22,201),(10,187,23,200),(11,186,24,199),(12,185,25,198),(13,184,26,197),(27,215,40,228),(28,214,41,227),(29,213,42,226),(30,212,43,225),(31,211,44,224),(32,210,45,223),(33,209,46,222),(34,234,47,221),(35,233,48,220),(36,232,49,219),(37,231,50,218),(38,230,51,217),(39,229,52,216),(53,253,66,240),(54,252,67,239),(55,251,68,238),(56,250,69,237),(57,249,70,236),(58,248,71,235),(59,247,72,260),(60,246,73,259),(61,245,74,258),(62,244,75,257),(63,243,76,256),(64,242,77,255),(65,241,78,254),(79,277,92,264),(80,276,93,263),(81,275,94,262),(82,274,95,261),(83,273,96,286),(84,272,97,285),(85,271,98,284),(86,270,99,283),(87,269,100,282),(88,268,101,281),(89,267,102,280),(90,266,103,279),(91,265,104,278),(105,300,118,287),(106,299,119,312),(107,298,120,311),(108,297,121,310),(109,296,122,309),(110,295,123,308),(111,294,124,307),(112,293,125,306),(113,292,126,305),(114,291,127,304),(115,290,128,303),(116,289,129,302),(117,288,130,301),(131,313,144,326),(132,338,145,325),(133,337,146,324),(134,336,147,323),(135,335,148,322),(136,334,149,321),(137,333,150,320),(138,332,151,319),(139,331,152,318),(140,330,153,317),(141,329,154,316),(142,328,155,315),(143,327,156,314),(157,345,170,358),(158,344,171,357),(159,343,172,356),(160,342,173,355),(161,341,174,354),(162,340,175,353),(163,339,176,352),(164,364,177,351),(165,363,178,350),(166,362,179,349),(167,361,180,348),(168,360,181,347),(169,359,182,346)]])
112 conjugacy classes
| class | 1 | 2 | 4A | 4B | 7A | ··· | 7F | 13A | ··· | 13F | 14A | ··· | 14F | 26A | ··· | 26F | 28A | ··· | 28L | 91A | ··· | 91AJ | 182A | ··· | 182AJ |
| order | 1 | 2 | 4 | 4 | 7 | ··· | 7 | 13 | ··· | 13 | 14 | ··· | 14 | 26 | ··· | 26 | 28 | ··· | 28 | 91 | ··· | 91 | 182 | ··· | 182 |
| size | 1 | 1 | 13 | 13 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 13 | ··· | 13 | 2 | ··· | 2 | 2 | ··· | 2 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C7 | C14 | C28 | D13 | Dic13 | C7×D13 | C7×Dic13 |
| kernel | C7×Dic13 | C182 | C91 | Dic13 | C26 | C13 | C14 | C7 | C2 | C1 |
| # reps | 1 | 1 | 2 | 6 | 6 | 12 | 6 | 6 | 36 | 36 |
Matrix representation of C7×Dic13 ►in GL4(𝔽1093) generated by
| 3 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1092 | 0 | 0 |
| 0 | 0 | 1092 | 1 |
| 0 | 0 | 699 | 393 |
| 1092 | 0 | 0 | 0 |
| 0 | 563 | 0 | 0 |
| 0 | 0 | 267 | 367 |
| 0 | 0 | 592 | 826 |
G:=sub<GL(4,GF(1093))| [3,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1092,0,0,0,0,1092,699,0,0,1,393],[1092,0,0,0,0,563,0,0,0,0,267,592,0,0,367,826] >;
C7×Dic13 in GAP, Magma, Sage, TeX
C_7\times {\rm Dic}_{13} % in TeX
G:=Group("C7xDic13"); // GroupNames label
G:=SmallGroup(364,2);
// by ID
G=gap.SmallGroup(364,2);
# by ID
G:=PCGroup([4,-2,-7,-2,-13,56,5379]);
// Polycyclic
G:=Group<a,b,c|a^7=b^26=1,c^2=b^13,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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