Copied to
clipboard

G = C5×Dic18order 360 = 23·32·5

Direct product of C5 and Dic18

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

Aliases: C5×Dic18, C453Q8, C60.8S3, C20.3D9, C180.3C2, C36.1C10, C30.56D6, Dic9.C10, C10.13D18, C15.3Dic6, C90.13C22, C9⋊(C5×Q8), C4.(C5×D9), C3.(C5×Dic6), C6.6(S3×C10), C12.1(C5×S3), C2.3(C10×D9), C18.1(C2×C10), (C5×Dic9).2C2, SmallGroup(360,20)

Series: Derived Chief Lower central Upper central

C1C18 — C5×Dic18
C1C3C9C18C90C5×Dic9 — C5×Dic18
C9C18 — C5×Dic18
C1C10C20

Generators and relations for C5×Dic18
 G = < a,b,c | a5=b36=1, c2=b18, ab=ba, ac=ca, cbc-1=b-1 >

9C4
9C4
9Q8
3Dic3
3Dic3
9C20
9C20
3Dic6
9C5×Q8
3C5×Dic3
3C5×Dic3
3C5×Dic6

Smallest permutation representation of C5×Dic18
Regular action on 360 points
Generators in S360
(1 277 166 54 118)(2 278 167 55 119)(3 279 168 56 120)(4 280 169 57 121)(5 281 170 58 122)(6 282 171 59 123)(7 283 172 60 124)(8 284 173 61 125)(9 285 174 62 126)(10 286 175 63 127)(11 287 176 64 128)(12 288 177 65 129)(13 253 178 66 130)(14 254 179 67 131)(15 255 180 68 132)(16 256 145 69 133)(17 257 146 70 134)(18 258 147 71 135)(19 259 148 72 136)(20 260 149 37 137)(21 261 150 38 138)(22 262 151 39 139)(23 263 152 40 140)(24 264 153 41 141)(25 265 154 42 142)(26 266 155 43 143)(27 267 156 44 144)(28 268 157 45 109)(29 269 158 46 110)(30 270 159 47 111)(31 271 160 48 112)(32 272 161 49 113)(33 273 162 50 114)(34 274 163 51 115)(35 275 164 52 116)(36 276 165 53 117)(73 227 300 327 188)(74 228 301 328 189)(75 229 302 329 190)(76 230 303 330 191)(77 231 304 331 192)(78 232 305 332 193)(79 233 306 333 194)(80 234 307 334 195)(81 235 308 335 196)(82 236 309 336 197)(83 237 310 337 198)(84 238 311 338 199)(85 239 312 339 200)(86 240 313 340 201)(87 241 314 341 202)(88 242 315 342 203)(89 243 316 343 204)(90 244 317 344 205)(91 245 318 345 206)(92 246 319 346 207)(93 247 320 347 208)(94 248 321 348 209)(95 249 322 349 210)(96 250 323 350 211)(97 251 324 351 212)(98 252 289 352 213)(99 217 290 353 214)(100 218 291 354 215)(101 219 292 355 216)(102 220 293 356 181)(103 221 294 357 182)(104 222 295 358 183)(105 223 296 359 184)(106 224 297 360 185)(107 225 298 325 186)(108 226 299 326 187)
(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)
(1 333 19 351)(2 332 20 350)(3 331 21 349)(4 330 22 348)(5 329 23 347)(6 328 24 346)(7 327 25 345)(8 326 26 344)(9 325 27 343)(10 360 28 342)(11 359 29 341)(12 358 30 340)(13 357 31 339)(14 356 32 338)(15 355 33 337)(16 354 34 336)(17 353 35 335)(18 352 36 334)(37 250 55 232)(38 249 56 231)(39 248 57 230)(40 247 58 229)(41 246 59 228)(42 245 60 227)(43 244 61 226)(44 243 62 225)(45 242 63 224)(46 241 64 223)(47 240 65 222)(48 239 66 221)(49 238 67 220)(50 237 68 219)(51 236 69 218)(52 235 70 217)(53 234 71 252)(54 233 72 251)(73 154 91 172)(74 153 92 171)(75 152 93 170)(76 151 94 169)(77 150 95 168)(78 149 96 167)(79 148 97 166)(80 147 98 165)(81 146 99 164)(82 145 100 163)(83 180 101 162)(84 179 102 161)(85 178 103 160)(86 177 104 159)(87 176 105 158)(88 175 106 157)(89 174 107 156)(90 173 108 155)(109 315 127 297)(110 314 128 296)(111 313 129 295)(112 312 130 294)(113 311 131 293)(114 310 132 292)(115 309 133 291)(116 308 134 290)(117 307 135 289)(118 306 136 324)(119 305 137 323)(120 304 138 322)(121 303 139 321)(122 302 140 320)(123 301 141 319)(124 300 142 318)(125 299 143 317)(126 298 144 316)(181 272 199 254)(182 271 200 253)(183 270 201 288)(184 269 202 287)(185 268 203 286)(186 267 204 285)(187 266 205 284)(188 265 206 283)(189 264 207 282)(190 263 208 281)(191 262 209 280)(192 261 210 279)(193 260 211 278)(194 259 212 277)(195 258 213 276)(196 257 214 275)(197 256 215 274)(198 255 216 273)

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

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

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

105 conjugacy classes

class 1  2  3 4A4B4C5A5B5C5D 6 9A9B9C10A10B10C10D12A12B15A15B15C15D18A18B18C20A20B20C20D20E···20L30A30B30C30D36A···36F45A···45L60A···60H90A···90L180A···180X
order12344455556999101010101212151515151818182020202020···203030303036···3645···4560···6090···90180···180
size11221818111122221111222222222222218···1822222···22···22···22···22···2

105 irreducible representations

dim11111122222222222222
type++++-++-+-
imageC1C2C2C5C10C10S3Q8D6D9Dic6C5×S3D18C5×Q8S3×C10Dic18C5×D9C5×Dic6C10×D9C5×Dic18
kernelC5×Dic18C5×Dic9C180Dic18Dic9C36C60C45C30C20C15C12C10C9C6C5C4C3C2C1
# reps12148411132434461281224

Matrix representation of C5×Dic18 in GL2(𝔽181) generated by

590
059
,
58144
3795
,
69158
89112
G:=sub<GL(2,GF(181))| [59,0,0,59],[58,37,144,95],[69,89,158,112] >;

C5×Dic18 in GAP, Magma, Sage, TeX

C_5\times {\rm Dic}_{18}
% in TeX

G:=Group("C5xDic18");
// GroupNames label

G:=SmallGroup(360,20);
// by ID

G=gap.SmallGroup(360,20);
# by ID

G:=PCGroup([6,-2,-2,-5,-2,-3,-3,120,265,127,6004,208,8645]);
// Polycyclic

G:=Group<a,b,c|a^5=b^36=1,c^2=b^18,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C5×Dic18 in TeX

׿
×
𝔽