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G = C30.Dic3order 360 = 23·32·5

3rd non-split extension by C30 of Dic3 acting via Dic3/C3=C4

metabelian, supersoluble, monomial, A-group

Aliases: C30.3Dic3, (C3×C15)⋊5C8, C151(C3⋊C8), C3⋊(C15⋊C8), C324(C5⋊C8), C5⋊(C324C8), C6.3(C3⋊F5), (C3×C6).3F5, (C3×C30).2C4, C10.(C3⋊Dic3), C2.(C323F5), (C3×Dic5).8S3, Dic5.2(C3⋊S3), (C32×Dic5).4C2, SmallGroup(360,54)

Series: Derived Chief Lower central Upper central

C1C3×C15 — C30.Dic3
C1C5C15C3×C15C3×C30C32×Dic5 — C30.Dic3
C3×C15 — C30.Dic3
C1C2

Generators and relations for C30.Dic3
 G = < a,b,c | a30=1, b6=a15, c2=a15b3, bab-1=a19, cac-1=a17, cbc-1=b5 >

5C4
45C8
5C12
5C12
5C12
5C12
15C3⋊C8
15C3⋊C8
15C3⋊C8
15C3⋊C8
5C3×C12
9C5⋊C8
5C324C8
3C15⋊C8
3C15⋊C8
3C15⋊C8
3C15⋊C8

Smallest permutation representation of C30.Dic3
Regular action on 360 points
Generators in S360
(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)
(1 233 292 112 136 159 16 218 277 97 121 174)(2 222 293 101 137 178 17 237 278 116 122 163)(3 211 294 120 138 167 18 226 279 105 123 152)(4 230 295 109 139 156 19 215 280 94 124 171)(5 219 296 98 140 175 20 234 281 113 125 160)(6 238 297 117 141 164 21 223 282 102 126 179)(7 227 298 106 142 153 22 212 283 91 127 168)(8 216 299 95 143 172 23 231 284 110 128 157)(9 235 300 114 144 161 24 220 285 99 129 176)(10 224 271 103 145 180 25 239 286 118 130 165)(11 213 272 92 146 169 26 228 287 107 131 154)(12 232 273 111 147 158 27 217 288 96 132 173)(13 221 274 100 148 177 28 236 289 115 133 162)(14 240 275 119 149 166 29 225 290 104 134 151)(15 229 276 108 150 155 30 214 291 93 135 170)(31 268 65 340 198 317 46 253 80 355 183 302)(32 257 66 359 199 306 47 242 81 344 184 321)(33 246 67 348 200 325 48 261 82 333 185 310)(34 265 68 337 201 314 49 250 83 352 186 329)(35 254 69 356 202 303 50 269 84 341 187 318)(36 243 70 345 203 322 51 258 85 360 188 307)(37 262 71 334 204 311 52 247 86 349 189 326)(38 251 72 353 205 330 53 266 87 338 190 315)(39 270 73 342 206 319 54 255 88 357 191 304)(40 259 74 331 207 308 55 244 89 346 192 323)(41 248 75 350 208 327 56 263 90 335 193 312)(42 267 76 339 209 316 57 252 61 354 194 301)(43 256 77 358 210 305 58 241 62 343 195 320)(44 245 78 347 181 324 59 260 63 332 196 309)(45 264 79 336 182 313 60 249 64 351 197 328)
(1 76 97 301 16 61 112 316)(2 69 116 318 17 84 101 303)(3 62 105 305 18 77 120 320)(4 85 94 322 19 70 109 307)(5 78 113 309 20 63 98 324)(6 71 102 326 21 86 117 311)(7 64 91 313 22 79 106 328)(8 87 110 330 23 72 95 315)(9 80 99 317 24 65 114 302)(10 73 118 304 25 88 103 319)(11 66 107 321 26 81 92 306)(12 89 96 308 27 74 111 323)(13 82 115 325 28 67 100 310)(14 75 104 312 29 90 119 327)(15 68 93 329 30 83 108 314)(31 161 355 300 46 176 340 285)(32 154 344 287 47 169 359 272)(33 177 333 274 48 162 348 289)(34 170 352 291 49 155 337 276)(35 163 341 278 50 178 356 293)(36 156 360 295 51 171 345 280)(37 179 349 282 52 164 334 297)(38 172 338 299 53 157 353 284)(39 165 357 286 54 180 342 271)(40 158 346 273 55 173 331 288)(41 151 335 290 56 166 350 275)(42 174 354 277 57 159 339 292)(43 167 343 294 58 152 358 279)(44 160 332 281 59 175 347 296)(45 153 351 298 60 168 336 283)(121 209 218 267 136 194 233 252)(122 202 237 254 137 187 222 269)(123 195 226 241 138 210 211 256)(124 188 215 258 139 203 230 243)(125 181 234 245 140 196 219 260)(126 204 223 262 141 189 238 247)(127 197 212 249 142 182 227 264)(128 190 231 266 143 205 216 251)(129 183 220 253 144 198 235 268)(130 206 239 270 145 191 224 255)(131 199 228 257 146 184 213 242)(132 192 217 244 147 207 232 259)(133 185 236 261 148 200 221 246)(134 208 225 248 149 193 240 263)(135 201 214 265 150 186 229 250)

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

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

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

42 conjugacy classes

class 1  2 3A3B3C3D4A4B 5 6A6B6C6D8A8B8C8D 10 12A···12H15A···15H30A···30H
order123333445666688881012···1215···1530···30
size112222554222245454545410···104···44···4

42 irreducible representations

dim11112224444
type+++-+-
imageC1C2C4C8S3Dic3C3⋊C8F5C5⋊C8C3⋊F5C15⋊C8
kernelC30.Dic3C32×Dic5C3×C30C3×C15C3×Dic5C30C15C3×C6C32C6C3
# reps11244481188

Matrix representation of C30.Dic3 in GL8(𝔽241)

01000000
2401000000
00100000
00010000
0000127114120
0000115012612
000011522912126
0000127229012
,
640000000
064000000
0022380000
0012400000
00004321976174
000021549144
000097228220187
00003019822165
,
71186000000
16170000000
0050560000
001491910000
0000902116141
00001311901062
000015211051231
00008020072151

G:=sub<GL(8,GF(241))| [0,240,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,127,115,115,127,0,0,0,0,114,0,229,229,0,0,0,0,12,126,12,0,0,0,0,0,0,12,126,12],[64,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,238,240,0,0,0,0,0,0,0,0,43,21,97,30,0,0,0,0,219,54,228,198,0,0,0,0,76,9,220,22,0,0,0,0,174,144,187,165],[71,16,0,0,0,0,0,0,186,170,0,0,0,0,0,0,0,0,50,149,0,0,0,0,0,0,56,191,0,0,0,0,0,0,0,0,90,131,152,80,0,0,0,0,21,190,110,200,0,0,0,0,161,10,51,72,0,0,0,0,41,62,231,151] >;

C30.Dic3 in GAP, Magma, Sage, TeX

C_{30}.{\rm Dic}_3
% in TeX

G:=Group("C30.Dic3");
// GroupNames label

G:=SmallGroup(360,54);
// by ID

G=gap.SmallGroup(360,54);
# by ID

G:=PCGroup([6,-2,-2,-2,-3,-3,-5,12,31,387,1444,7781,5195]);
// Polycyclic

G:=Group<a,b,c|a^30=1,b^6=a^15,c^2=a^15*b^3,b*a*b^-1=a^19,c*a*c^-1=a^17,c*b*c^-1=b^5>;
// generators/relations

Export

Subgroup lattice of C30.Dic3 in TeX

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