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G = C9×Dic10order 360 = 23·32·5

Direct product of C9 and Dic10

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

Aliases: C9×Dic10, C454Q8, C60.3C6, C36.3D5, C180.4C2, C20.1C18, C18.13D10, C90.18C22, Dic5.1C18, C5⋊(Q8×C9), C4.(C9×D5), C15.(C3×Q8), C12.3(C3×D5), C6.13(C6×D5), C2.3(D5×C18), C3.(C3×Dic10), C30.13(C2×C6), C10.1(C2×C18), (C3×Dic10).C3, (C3×Dic5).2C6, (C9×Dic5).3C2, SmallGroup(360,15)

Series: Derived Chief Lower central Upper central

C1C10 — C9×Dic10
C1C5C15C30C90C9×Dic5 — C9×Dic10
C5C10 — C9×Dic10
C1C18C36

Generators and relations for C9×Dic10
 G = < a,b,c | a9=b20=1, c2=b10, ab=ba, ac=ca, cbc-1=b-1 >

5C4
5C4
5Q8
5C12
5C12
5C3×Q8
5C36
5C36
5Q8×C9

Smallest permutation representation of C9×Dic10
Regular action on 360 points
Generators in S360
(1 105 162 346 329 125 319 267 185)(2 106 163 347 330 126 320 268 186)(3 107 164 348 331 127 301 269 187)(4 108 165 349 332 128 302 270 188)(5 109 166 350 333 129 303 271 189)(6 110 167 351 334 130 304 272 190)(7 111 168 352 335 131 305 273 191)(8 112 169 353 336 132 306 274 192)(9 113 170 354 337 133 307 275 193)(10 114 171 355 338 134 308 276 194)(11 115 172 356 339 135 309 277 195)(12 116 173 357 340 136 310 278 196)(13 117 174 358 321 137 311 279 197)(14 118 175 359 322 138 312 280 198)(15 119 176 360 323 139 313 261 199)(16 120 177 341 324 140 314 262 200)(17 101 178 342 325 121 315 263 181)(18 102 179 343 326 122 316 264 182)(19 103 180 344 327 123 317 265 183)(20 104 161 345 328 124 318 266 184)(21 75 86 292 228 219 47 141 255)(22 76 87 293 229 220 48 142 256)(23 77 88 294 230 201 49 143 257)(24 78 89 295 231 202 50 144 258)(25 79 90 296 232 203 51 145 259)(26 80 91 297 233 204 52 146 260)(27 61 92 298 234 205 53 147 241)(28 62 93 299 235 206 54 148 242)(29 63 94 300 236 207 55 149 243)(30 64 95 281 237 208 56 150 244)(31 65 96 282 238 209 57 151 245)(32 66 97 283 239 210 58 152 246)(33 67 98 284 240 211 59 153 247)(34 68 99 285 221 212 60 154 248)(35 69 100 286 222 213 41 155 249)(36 70 81 287 223 214 42 156 250)(37 71 82 288 224 215 43 157 251)(38 72 83 289 225 216 44 158 252)(39 73 84 290 226 217 45 159 253)(40 74 85 291 227 218 46 160 254)
(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)
(1 33 11 23)(2 32 12 22)(3 31 13 21)(4 30 14 40)(5 29 15 39)(6 28 16 38)(7 27 17 37)(8 26 18 36)(9 25 19 35)(10 24 20 34)(41 307 51 317)(42 306 52 316)(43 305 53 315)(44 304 54 314)(45 303 55 313)(46 302 56 312)(47 301 57 311)(48 320 58 310)(49 319 59 309)(50 318 60 308)(61 101 71 111)(62 120 72 110)(63 119 73 109)(64 118 74 108)(65 117 75 107)(66 116 76 106)(67 115 77 105)(68 114 78 104)(69 113 79 103)(70 112 80 102)(81 169 91 179)(82 168 92 178)(83 167 93 177)(84 166 94 176)(85 165 95 175)(86 164 96 174)(87 163 97 173)(88 162 98 172)(89 161 99 171)(90 180 100 170)(121 215 131 205)(122 214 132 204)(123 213 133 203)(124 212 134 202)(125 211 135 201)(126 210 136 220)(127 209 137 219)(128 208 138 218)(129 207 139 217)(130 206 140 216)(141 269 151 279)(142 268 152 278)(143 267 153 277)(144 266 154 276)(145 265 155 275)(146 264 156 274)(147 263 157 273)(148 262 158 272)(149 261 159 271)(150 280 160 270)(181 251 191 241)(182 250 192 260)(183 249 193 259)(184 248 194 258)(185 247 195 257)(186 246 196 256)(187 245 197 255)(188 244 198 254)(189 243 199 253)(190 242 200 252)(221 338 231 328)(222 337 232 327)(223 336 233 326)(224 335 234 325)(225 334 235 324)(226 333 236 323)(227 332 237 322)(228 331 238 321)(229 330 239 340)(230 329 240 339)(281 359 291 349)(282 358 292 348)(283 357 293 347)(284 356 294 346)(285 355 295 345)(286 354 296 344)(287 353 297 343)(288 352 298 342)(289 351 299 341)(290 350 300 360)

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

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

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

117 conjugacy classes

class 1  2 3A3B4A4B4C5A5B6A6B9A···9F10A10B12A12B12C12D12E12F15A15B15C15D18A···18F20A20B20C20D30A30B30C30D36A···36F36G···36R45A···45L60A···60H90A···90L180A···180X
order123344455669···910101212121212121515151518···18202020203030303036···3636···3645···4560···6090···90180···180
size11112101022111···122221010101022221···1222222222···210···102···22···22···22···2

117 irreducible representations

dim111111111222222222222
type+++-++-
imageC1C2C2C3C6C6C9C18C18Q8D5D10C3×Q8C3×D5Dic10C6×D5Q8×C9C9×D5C3×Dic10D5×C18C9×Dic10
kernelC9×Dic10C9×Dic5C180C3×Dic10C3×Dic5C60Dic10Dic5C20C45C36C18C15C12C9C6C5C4C3C2C1
# reps1212426126122244461281224

Matrix representation of C9×Dic10 in GL2(𝔽19) generated by

60
06
,
1117
100
,
67
1113
G:=sub<GL(2,GF(19))| [6,0,0,6],[11,10,17,0],[6,11,7,13] >;

C9×Dic10 in GAP, Magma, Sage, TeX

C_9\times {\rm Dic}_{10}
% in TeX

G:=Group("C9xDic10");
// GroupNames label

G:=SmallGroup(360,15);
// by ID

G=gap.SmallGroup(360,15);
# by ID

G:=PCGroup([6,-2,-2,-3,-2,-3,-5,72,169,79,122,10373]);
// Polycyclic

G:=Group<a,b,c|a^9=b^20=1,c^2=b^10,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C9×Dic10 in TeX

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