Copied to
clipboard

G = C13×Dic7order 364 = 22·7·13

Direct product of C13 and Dic7

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

Aliases: C13×Dic7, C7⋊C52, C915C4, C14.C26, C26.2D7, C182.3C2, C2.(C13×D7), SmallGroup(364,1)

Series: Derived Chief Lower central Upper central

C1C7 — C13×Dic7
C1C7C14C182 — C13×Dic7
C7 — C13×Dic7
C1C26

Generators and relations for C13×Dic7
 G = < a,b,c | a13=b14=1, c2=b7, ab=ba, ac=ca, cbc-1=b-1 >

7C4
7C52

Smallest permutation representation of C13×Dic7
Regular action on 364 points
Generators in S364
(1 169 168 153 131 113 102 94 75 70 47 38 18)(2 170 155 154 132 114 103 95 76 57 48 39 19)(3 171 156 141 133 115 104 96 77 58 49 40 20)(4 172 157 142 134 116 105 97 78 59 50 41 21)(5 173 158 143 135 117 106 98 79 60 51 42 22)(6 174 159 144 136 118 107 85 80 61 52 29 23)(7 175 160 145 137 119 108 86 81 62 53 30 24)(8 176 161 146 138 120 109 87 82 63 54 31 25)(9 177 162 147 139 121 110 88 83 64 55 32 26)(10 178 163 148 140 122 111 89 84 65 56 33 27)(11 179 164 149 127 123 112 90 71 66 43 34 28)(12 180 165 150 128 124 99 91 72 67 44 35 15)(13 181 166 151 129 125 100 92 73 68 45 36 16)(14 182 167 152 130 126 101 93 74 69 46 37 17)(183 351 337 323 309 295 281 267 260 246 232 211 197)(184 352 338 324 310 296 282 268 261 247 233 212 198)(185 353 339 325 311 297 283 269 262 248 234 213 199)(186 354 340 326 312 298 284 270 263 249 235 214 200)(187 355 341 327 313 299 285 271 264 250 236 215 201)(188 356 342 328 314 300 286 272 265 251 237 216 202)(189 357 343 329 315 301 287 273 266 252 238 217 203)(190 358 344 330 316 302 288 274 253 239 225 218 204)(191 359 345 331 317 303 289 275 254 240 226 219 205)(192 360 346 332 318 304 290 276 255 241 227 220 206)(193 361 347 333 319 305 291 277 256 242 228 221 207)(194 362 348 334 320 306 292 278 257 243 229 222 208)(195 363 349 335 321 307 293 279 258 244 230 223 209)(196 364 350 336 322 308 294 280 259 245 231 224 210)
(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)
(1 190 8 183)(2 189 9 196)(3 188 10 195)(4 187 11 194)(5 186 12 193)(6 185 13 192)(7 184 14 191)(15 207 22 200)(16 206 23 199)(17 205 24 198)(18 204 25 197)(19 203 26 210)(20 202 27 209)(21 201 28 208)(29 213 36 220)(30 212 37 219)(31 211 38 218)(32 224 39 217)(33 223 40 216)(34 222 41 215)(35 221 42 214)(43 229 50 236)(44 228 51 235)(45 227 52 234)(46 226 53 233)(47 225 54 232)(48 238 55 231)(49 237 56 230)(57 252 64 245)(58 251 65 244)(59 250 66 243)(60 249 67 242)(61 248 68 241)(62 247 69 240)(63 246 70 239)(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)(85 269 92 276)(86 268 93 275)(87 267 94 274)(88 280 95 273)(89 279 96 272)(90 278 97 271)(91 277 98 270)(99 291 106 284)(100 290 107 283)(101 289 108 282)(102 288 109 281)(103 287 110 294)(104 286 111 293)(105 285 112 292)(113 302 120 295)(114 301 121 308)(115 300 122 307)(116 299 123 306)(117 298 124 305)(118 297 125 304)(119 296 126 303)(127 320 134 313)(128 319 135 312)(129 318 136 311)(130 317 137 310)(131 316 138 309)(132 315 139 322)(133 314 140 321)(141 328 148 335)(142 327 149 334)(143 326 150 333)(144 325 151 332)(145 324 152 331)(146 323 153 330)(147 336 154 329)(155 343 162 350)(156 342 163 349)(157 341 164 348)(158 340 165 347)(159 339 166 346)(160 338 167 345)(161 337 168 344)(169 358 176 351)(170 357 177 364)(171 356 178 363)(172 355 179 362)(173 354 180 361)(174 353 181 360)(175 352 182 359)

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

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

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

130 conjugacy classes

class 1  2 4A4B7A7B7C13A···13L14A14B14C26A···26L52A···52X91A···91AJ182A···182AJ
order124477713···1314141426···2652···5291···91182···182
size11772221···12221···17···72···22···2

130 irreducible representations

dim1111112222
type+++-
imageC1C2C4C13C26C52D7Dic7C13×D7C13×Dic7
kernelC13×Dic7C182C91Dic7C14C7C26C13C2C1
# reps112121224333636

Matrix representation of C13×Dic7 in GL3(𝔽1093) generated by

100
04320
00432
,
109200
001
01092252
,
56300
025114
0965842
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

Export

Subgroup lattice of C13×Dic7 in TeX

׿
×
𝔽