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G = C7×Dic13order 364 = 22·7·13

Direct product of C7 and Dic13

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C7×Dic13, C914C4, C132C28, C26.C14, C182.2C2, C14.2D13, C2.(C7×D13), SmallGroup(364,2)

Series: Derived Chief Lower central Upper central

C1C13 — C7×Dic13
C1C13C26C182 — C7×Dic13
C13 — C7×Dic13
C1C14

Generators and relations for C7×Dic13
 G = < a,b,c | a7=b26=1, c2=b13, ab=ba, ac=ca, cbc-1=b-1 >

13C4
13C28

Smallest permutation representation of C7×Dic13
Regular action on 364 points
Generators in S364
(1 181 140 110 83 76 32)(2 182 141 111 84 77 33)(3 157 142 112 85 78 34)(4 158 143 113 86 53 35)(5 159 144 114 87 54 36)(6 160 145 115 88 55 37)(7 161 146 116 89 56 38)(8 162 147 117 90 57 39)(9 163 148 118 91 58 40)(10 164 149 119 92 59 41)(11 165 150 120 93 60 42)(12 166 151 121 94 61 43)(13 167 152 122 95 62 44)(14 168 153 123 96 63 45)(15 169 154 124 97 64 46)(16 170 155 125 98 65 47)(17 171 156 126 99 66 48)(18 172 131 127 100 67 49)(19 173 132 128 101 68 50)(20 174 133 129 102 69 51)(21 175 134 130 103 70 52)(22 176 135 105 104 71 27)(23 177 136 106 79 72 28)(24 178 137 107 80 73 29)(25 179 138 108 81 74 30)(26 180 139 109 82 75 31)(183 339 313 300 261 248 209)(184 340 314 301 262 249 210)(185 341 315 302 263 250 211)(186 342 316 303 264 251 212)(187 343 317 304 265 252 213)(188 344 318 305 266 253 214)(189 345 319 306 267 254 215)(190 346 320 307 268 255 216)(191 347 321 308 269 256 217)(192 348 322 309 270 257 218)(193 349 323 310 271 258 219)(194 350 324 311 272 259 220)(195 351 325 312 273 260 221)(196 352 326 287 274 235 222)(197 353 327 288 275 236 223)(198 354 328 289 276 237 224)(199 355 329 290 277 238 225)(200 356 330 291 278 239 226)(201 357 331 292 279 240 227)(202 358 332 293 280 241 228)(203 359 333 294 281 242 229)(204 360 334 295 282 243 230)(205 361 335 296 283 244 231)(206 362 336 297 284 245 232)(207 363 337 298 285 246 233)(208 364 338 299 286 247 234)
(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)(27 227 40 214)(28 226 41 213)(29 225 42 212)(30 224 43 211)(31 223 44 210)(32 222 45 209)(33 221 46 234)(34 220 47 233)(35 219 48 232)(36 218 49 231)(37 217 50 230)(38 216 51 229)(39 215 52 228)(53 258 66 245)(54 257 67 244)(55 256 68 243)(56 255 69 242)(57 254 70 241)(58 253 71 240)(59 252 72 239)(60 251 73 238)(61 250 74 237)(62 249 75 236)(63 248 76 235)(64 247 77 260)(65 246 78 259)(79 278 92 265)(80 277 93 264)(81 276 94 263)(82 275 95 262)(83 274 96 261)(84 273 97 286)(85 272 98 285)(86 271 99 284)(87 270 100 283)(88 269 101 282)(89 268 102 281)(90 267 103 280)(91 266 104 279)(105 292 118 305)(106 291 119 304)(107 290 120 303)(108 289 121 302)(109 288 122 301)(110 287 123 300)(111 312 124 299)(112 311 125 298)(113 310 126 297)(114 309 127 296)(115 308 128 295)(116 307 129 294)(117 306 130 293)(131 335 144 322)(132 334 145 321)(133 333 146 320)(134 332 147 319)(135 331 148 318)(136 330 149 317)(137 329 150 316)(138 328 151 315)(139 327 152 314)(140 326 153 313)(141 325 154 338)(142 324 155 337)(143 323 156 336)(157 350 170 363)(158 349 171 362)(159 348 172 361)(160 347 173 360)(161 346 174 359)(162 345 175 358)(163 344 176 357)(164 343 177 356)(165 342 178 355)(166 341 179 354)(167 340 180 353)(168 339 181 352)(169 364 182 351)

G:=sub<Sym(364)| (1,181,140,110,83,76,32)(2,182,141,111,84,77,33)(3,157,142,112,85,78,34)(4,158,143,113,86,53,35)(5,159,144,114,87,54,36)(6,160,145,115,88,55,37)(7,161,146,116,89,56,38)(8,162,147,117,90,57,39)(9,163,148,118,91,58,40)(10,164,149,119,92,59,41)(11,165,150,120,93,60,42)(12,166,151,121,94,61,43)(13,167,152,122,95,62,44)(14,168,153,123,96,63,45)(15,169,154,124,97,64,46)(16,170,155,125,98,65,47)(17,171,156,126,99,66,48)(18,172,131,127,100,67,49)(19,173,132,128,101,68,50)(20,174,133,129,102,69,51)(21,175,134,130,103,70,52)(22,176,135,105,104,71,27)(23,177,136,106,79,72,28)(24,178,137,107,80,73,29)(25,179,138,108,81,74,30)(26,180,139,109,82,75,31)(183,339,313,300,261,248,209)(184,340,314,301,262,249,210)(185,341,315,302,263,250,211)(186,342,316,303,264,251,212)(187,343,317,304,265,252,213)(188,344,318,305,266,253,214)(189,345,319,306,267,254,215)(190,346,320,307,268,255,216)(191,347,321,308,269,256,217)(192,348,322,309,270,257,218)(193,349,323,310,271,258,219)(194,350,324,311,272,259,220)(195,351,325,312,273,260,221)(196,352,326,287,274,235,222)(197,353,327,288,275,236,223)(198,354,328,289,276,237,224)(199,355,329,290,277,238,225)(200,356,330,291,278,239,226)(201,357,331,292,279,240,227)(202,358,332,293,280,241,228)(203,359,333,294,281,242,229)(204,360,334,295,282,243,230)(205,361,335,296,283,244,231)(206,362,336,297,284,245,232)(207,363,337,298,285,246,233)(208,364,338,299,286,247,234), (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)(27,227,40,214)(28,226,41,213)(29,225,42,212)(30,224,43,211)(31,223,44,210)(32,222,45,209)(33,221,46,234)(34,220,47,233)(35,219,48,232)(36,218,49,231)(37,217,50,230)(38,216,51,229)(39,215,52,228)(53,258,66,245)(54,257,67,244)(55,256,68,243)(56,255,69,242)(57,254,70,241)(58,253,71,240)(59,252,72,239)(60,251,73,238)(61,250,74,237)(62,249,75,236)(63,248,76,235)(64,247,77,260)(65,246,78,259)(79,278,92,265)(80,277,93,264)(81,276,94,263)(82,275,95,262)(83,274,96,261)(84,273,97,286)(85,272,98,285)(86,271,99,284)(87,270,100,283)(88,269,101,282)(89,268,102,281)(90,267,103,280)(91,266,104,279)(105,292,118,305)(106,291,119,304)(107,290,120,303)(108,289,121,302)(109,288,122,301)(110,287,123,300)(111,312,124,299)(112,311,125,298)(113,310,126,297)(114,309,127,296)(115,308,128,295)(116,307,129,294)(117,306,130,293)(131,335,144,322)(132,334,145,321)(133,333,146,320)(134,332,147,319)(135,331,148,318)(136,330,149,317)(137,329,150,316)(138,328,151,315)(139,327,152,314)(140,326,153,313)(141,325,154,338)(142,324,155,337)(143,323,156,336)(157,350,170,363)(158,349,171,362)(159,348,172,361)(160,347,173,360)(161,346,174,359)(162,345,175,358)(163,344,176,357)(164,343,177,356)(165,342,178,355)(166,341,179,354)(167,340,180,353)(168,339,181,352)(169,364,182,351)>;

G:=Group( (1,181,140,110,83,76,32)(2,182,141,111,84,77,33)(3,157,142,112,85,78,34)(4,158,143,113,86,53,35)(5,159,144,114,87,54,36)(6,160,145,115,88,55,37)(7,161,146,116,89,56,38)(8,162,147,117,90,57,39)(9,163,148,118,91,58,40)(10,164,149,119,92,59,41)(11,165,150,120,93,60,42)(12,166,151,121,94,61,43)(13,167,152,122,95,62,44)(14,168,153,123,96,63,45)(15,169,154,124,97,64,46)(16,170,155,125,98,65,47)(17,171,156,126,99,66,48)(18,172,131,127,100,67,49)(19,173,132,128,101,68,50)(20,174,133,129,102,69,51)(21,175,134,130,103,70,52)(22,176,135,105,104,71,27)(23,177,136,106,79,72,28)(24,178,137,107,80,73,29)(25,179,138,108,81,74,30)(26,180,139,109,82,75,31)(183,339,313,300,261,248,209)(184,340,314,301,262,249,210)(185,341,315,302,263,250,211)(186,342,316,303,264,251,212)(187,343,317,304,265,252,213)(188,344,318,305,266,253,214)(189,345,319,306,267,254,215)(190,346,320,307,268,255,216)(191,347,321,308,269,256,217)(192,348,322,309,270,257,218)(193,349,323,310,271,258,219)(194,350,324,311,272,259,220)(195,351,325,312,273,260,221)(196,352,326,287,274,235,222)(197,353,327,288,275,236,223)(198,354,328,289,276,237,224)(199,355,329,290,277,238,225)(200,356,330,291,278,239,226)(201,357,331,292,279,240,227)(202,358,332,293,280,241,228)(203,359,333,294,281,242,229)(204,360,334,295,282,243,230)(205,361,335,296,283,244,231)(206,362,336,297,284,245,232)(207,363,337,298,285,246,233)(208,364,338,299,286,247,234), (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)(27,227,40,214)(28,226,41,213)(29,225,42,212)(30,224,43,211)(31,223,44,210)(32,222,45,209)(33,221,46,234)(34,220,47,233)(35,219,48,232)(36,218,49,231)(37,217,50,230)(38,216,51,229)(39,215,52,228)(53,258,66,245)(54,257,67,244)(55,256,68,243)(56,255,69,242)(57,254,70,241)(58,253,71,240)(59,252,72,239)(60,251,73,238)(61,250,74,237)(62,249,75,236)(63,248,76,235)(64,247,77,260)(65,246,78,259)(79,278,92,265)(80,277,93,264)(81,276,94,263)(82,275,95,262)(83,274,96,261)(84,273,97,286)(85,272,98,285)(86,271,99,284)(87,270,100,283)(88,269,101,282)(89,268,102,281)(90,267,103,280)(91,266,104,279)(105,292,118,305)(106,291,119,304)(107,290,120,303)(108,289,121,302)(109,288,122,301)(110,287,123,300)(111,312,124,299)(112,311,125,298)(113,310,126,297)(114,309,127,296)(115,308,128,295)(116,307,129,294)(117,306,130,293)(131,335,144,322)(132,334,145,321)(133,333,146,320)(134,332,147,319)(135,331,148,318)(136,330,149,317)(137,329,150,316)(138,328,151,315)(139,327,152,314)(140,326,153,313)(141,325,154,338)(142,324,155,337)(143,323,156,336)(157,350,170,363)(158,349,171,362)(159,348,172,361)(160,347,173,360)(161,346,174,359)(162,345,175,358)(163,344,176,357)(164,343,177,356)(165,342,178,355)(166,341,179,354)(167,340,180,353)(168,339,181,352)(169,364,182,351) );

G=PermutationGroup([(1,181,140,110,83,76,32),(2,182,141,111,84,77,33),(3,157,142,112,85,78,34),(4,158,143,113,86,53,35),(5,159,144,114,87,54,36),(6,160,145,115,88,55,37),(7,161,146,116,89,56,38),(8,162,147,117,90,57,39),(9,163,148,118,91,58,40),(10,164,149,119,92,59,41),(11,165,150,120,93,60,42),(12,166,151,121,94,61,43),(13,167,152,122,95,62,44),(14,168,153,123,96,63,45),(15,169,154,124,97,64,46),(16,170,155,125,98,65,47),(17,171,156,126,99,66,48),(18,172,131,127,100,67,49),(19,173,132,128,101,68,50),(20,174,133,129,102,69,51),(21,175,134,130,103,70,52),(22,176,135,105,104,71,27),(23,177,136,106,79,72,28),(24,178,137,107,80,73,29),(25,179,138,108,81,74,30),(26,180,139,109,82,75,31),(183,339,313,300,261,248,209),(184,340,314,301,262,249,210),(185,341,315,302,263,250,211),(186,342,316,303,264,251,212),(187,343,317,304,265,252,213),(188,344,318,305,266,253,214),(189,345,319,306,267,254,215),(190,346,320,307,268,255,216),(191,347,321,308,269,256,217),(192,348,322,309,270,257,218),(193,349,323,310,271,258,219),(194,350,324,311,272,259,220),(195,351,325,312,273,260,221),(196,352,326,287,274,235,222),(197,353,327,288,275,236,223),(198,354,328,289,276,237,224),(199,355,329,290,277,238,225),(200,356,330,291,278,239,226),(201,357,331,292,279,240,227),(202,358,332,293,280,241,228),(203,359,333,294,281,242,229),(204,360,334,295,282,243,230),(205,361,335,296,283,244,231),(206,362,336,297,284,245,232),(207,363,337,298,285,246,233),(208,364,338,299,286,247,234)], [(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),(27,227,40,214),(28,226,41,213),(29,225,42,212),(30,224,43,211),(31,223,44,210),(32,222,45,209),(33,221,46,234),(34,220,47,233),(35,219,48,232),(36,218,49,231),(37,217,50,230),(38,216,51,229),(39,215,52,228),(53,258,66,245),(54,257,67,244),(55,256,68,243),(56,255,69,242),(57,254,70,241),(58,253,71,240),(59,252,72,239),(60,251,73,238),(61,250,74,237),(62,249,75,236),(63,248,76,235),(64,247,77,260),(65,246,78,259),(79,278,92,265),(80,277,93,264),(81,276,94,263),(82,275,95,262),(83,274,96,261),(84,273,97,286),(85,272,98,285),(86,271,99,284),(87,270,100,283),(88,269,101,282),(89,268,102,281),(90,267,103,280),(91,266,104,279),(105,292,118,305),(106,291,119,304),(107,290,120,303),(108,289,121,302),(109,288,122,301),(110,287,123,300),(111,312,124,299),(112,311,125,298),(113,310,126,297),(114,309,127,296),(115,308,128,295),(116,307,129,294),(117,306,130,293),(131,335,144,322),(132,334,145,321),(133,333,146,320),(134,332,147,319),(135,331,148,318),(136,330,149,317),(137,329,150,316),(138,328,151,315),(139,327,152,314),(140,326,153,313),(141,325,154,338),(142,324,155,337),(143,323,156,336),(157,350,170,363),(158,349,171,362),(159,348,172,361),(160,347,173,360),(161,346,174,359),(162,345,175,358),(163,344,176,357),(164,343,177,356),(165,342,178,355),(166,341,179,354),(167,340,180,353),(168,339,181,352),(169,364,182,351)])

112 conjugacy classes

class 1  2 4A4B7A···7F13A···13F14A···14F26A···26F28A···28L91A···91AJ182A···182AJ
order12447···713···1314···1426···2628···2891···91182···182
size1113131···12···21···12···213···132···22···2

112 irreducible representations

dim1111112222
type+++-
imageC1C2C4C7C14C28D13Dic13C7×D13C7×Dic13
kernelC7×Dic13C182C91Dic13C26C13C14C7C2C1
# reps1126612663636

Matrix representation of C7×Dic13 in GL4(𝔽1093) generated by

3000
0100
0010
0001
,
1000
0109200
0010921
00699393
,
1092000
056300
00267367
00592826
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

Export

Subgroup lattice of C7×Dic13 in TeX

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