metabelian, supersoluble, monomial, A-group
Aliases: C30.3Dic3, (C3×C15)⋊5C8, C15⋊1(C3⋊C8), C3⋊(C15⋊C8), C32⋊4(C5⋊C8), C5⋊(C32⋊4C8), C6.3(C3⋊F5), (C3×C6).3F5, (C3×C30).2C4, C10.(C3⋊Dic3), C2.(C32⋊3F5), (C3×Dic5).8S3, Dic5.2(C3⋊S3), (C32×Dic5).4C2, SmallGroup(360,54)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C15 — C30.Dic3 |
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 >
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)
(1 328 217 359 294 74 16 313 232 344 279 89)(2 317 218 348 295 63 17 302 233 333 280 78)(3 306 219 337 296 82 18 321 234 352 281 67)(4 325 220 356 297 71 19 310 235 341 282 86)(5 314 221 345 298 90 20 329 236 360 283 75)(6 303 222 334 299 79 21 318 237 349 284 64)(7 322 223 353 300 68 22 307 238 338 285 83)(8 311 224 342 271 87 23 326 239 357 286 72)(9 330 225 331 272 76 24 315 240 346 287 61)(10 319 226 350 273 65 25 304 211 335 288 80)(11 308 227 339 274 84 26 323 212 354 289 69)(12 327 228 358 275 73 27 312 213 343 290 88)(13 316 229 347 276 62 28 301 214 332 291 77)(14 305 230 336 277 81 29 320 215 351 292 66)(15 324 231 355 278 70 30 309 216 340 293 85)(31 101 180 209 128 257 46 116 165 194 143 242)(32 120 151 198 129 246 47 105 166 183 144 261)(33 109 152 187 130 265 48 94 167 202 145 250)(34 98 153 206 131 254 49 113 168 191 146 269)(35 117 154 195 132 243 50 102 169 210 147 258)(36 106 155 184 133 262 51 91 170 199 148 247)(37 95 156 203 134 251 52 110 171 188 149 266)(38 114 157 192 135 270 53 99 172 207 150 255)(39 103 158 181 136 259 54 118 173 196 121 244)(40 92 159 200 137 248 55 107 174 185 122 263)(41 111 160 189 138 267 56 96 175 204 123 252)(42 100 161 208 139 256 57 115 176 193 124 241)(43 119 162 197 140 245 58 104 177 182 125 260)(44 108 163 186 141 264 59 93 178 201 126 249)(45 97 164 205 142 253 60 112 179 190 127 268)
(1 111 344 123 16 96 359 138)(2 104 333 140 17 119 348 125)(3 97 352 127 18 112 337 142)(4 120 341 144 19 105 356 129)(5 113 360 131 20 98 345 146)(6 106 349 148 21 91 334 133)(7 99 338 135 22 114 353 150)(8 92 357 122 23 107 342 137)(9 115 346 139 24 100 331 124)(10 108 335 126 25 93 350 141)(11 101 354 143 26 116 339 128)(12 94 343 130 27 109 358 145)(13 117 332 147 28 102 347 132)(14 110 351 134 29 95 336 149)(15 103 340 121 30 118 355 136)(31 274 194 308 46 289 209 323)(32 297 183 325 47 282 198 310)(33 290 202 312 48 275 187 327)(34 283 191 329 49 298 206 314)(35 276 210 316 50 291 195 301)(36 299 199 303 51 284 184 318)(37 292 188 320 52 277 203 305)(38 285 207 307 53 300 192 322)(39 278 196 324 54 293 181 309)(40 271 185 311 55 286 200 326)(41 294 204 328 56 279 189 313)(42 287 193 315 57 272 208 330)(43 280 182 302 58 295 197 317)(44 273 201 319 59 288 186 304)(45 296 190 306 60 281 205 321)(61 161 240 241 76 176 225 256)(62 154 229 258 77 169 214 243)(63 177 218 245 78 162 233 260)(64 170 237 262 79 155 222 247)(65 163 226 249 80 178 211 264)(66 156 215 266 81 171 230 251)(67 179 234 253 82 164 219 268)(68 172 223 270 83 157 238 255)(69 165 212 257 84 180 227 242)(70 158 231 244 85 173 216 259)(71 151 220 261 86 166 235 246)(72 174 239 248 87 159 224 263)(73 167 228 265 88 152 213 250)(74 160 217 252 89 175 232 267)(75 153 236 269 90 168 221 254)
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), (1,328,217,359,294,74,16,313,232,344,279,89)(2,317,218,348,295,63,17,302,233,333,280,78)(3,306,219,337,296,82,18,321,234,352,281,67)(4,325,220,356,297,71,19,310,235,341,282,86)(5,314,221,345,298,90,20,329,236,360,283,75)(6,303,222,334,299,79,21,318,237,349,284,64)(7,322,223,353,300,68,22,307,238,338,285,83)(8,311,224,342,271,87,23,326,239,357,286,72)(9,330,225,331,272,76,24,315,240,346,287,61)(10,319,226,350,273,65,25,304,211,335,288,80)(11,308,227,339,274,84,26,323,212,354,289,69)(12,327,228,358,275,73,27,312,213,343,290,88)(13,316,229,347,276,62,28,301,214,332,291,77)(14,305,230,336,277,81,29,320,215,351,292,66)(15,324,231,355,278,70,30,309,216,340,293,85)(31,101,180,209,128,257,46,116,165,194,143,242)(32,120,151,198,129,246,47,105,166,183,144,261)(33,109,152,187,130,265,48,94,167,202,145,250)(34,98,153,206,131,254,49,113,168,191,146,269)(35,117,154,195,132,243,50,102,169,210,147,258)(36,106,155,184,133,262,51,91,170,199,148,247)(37,95,156,203,134,251,52,110,171,188,149,266)(38,114,157,192,135,270,53,99,172,207,150,255)(39,103,158,181,136,259,54,118,173,196,121,244)(40,92,159,200,137,248,55,107,174,185,122,263)(41,111,160,189,138,267,56,96,175,204,123,252)(42,100,161,208,139,256,57,115,176,193,124,241)(43,119,162,197,140,245,58,104,177,182,125,260)(44,108,163,186,141,264,59,93,178,201,126,249)(45,97,164,205,142,253,60,112,179,190,127,268), (1,111,344,123,16,96,359,138)(2,104,333,140,17,119,348,125)(3,97,352,127,18,112,337,142)(4,120,341,144,19,105,356,129)(5,113,360,131,20,98,345,146)(6,106,349,148,21,91,334,133)(7,99,338,135,22,114,353,150)(8,92,357,122,23,107,342,137)(9,115,346,139,24,100,331,124)(10,108,335,126,25,93,350,141)(11,101,354,143,26,116,339,128)(12,94,343,130,27,109,358,145)(13,117,332,147,28,102,347,132)(14,110,351,134,29,95,336,149)(15,103,340,121,30,118,355,136)(31,274,194,308,46,289,209,323)(32,297,183,325,47,282,198,310)(33,290,202,312,48,275,187,327)(34,283,191,329,49,298,206,314)(35,276,210,316,50,291,195,301)(36,299,199,303,51,284,184,318)(37,292,188,320,52,277,203,305)(38,285,207,307,53,300,192,322)(39,278,196,324,54,293,181,309)(40,271,185,311,55,286,200,326)(41,294,204,328,56,279,189,313)(42,287,193,315,57,272,208,330)(43,280,182,302,58,295,197,317)(44,273,201,319,59,288,186,304)(45,296,190,306,60,281,205,321)(61,161,240,241,76,176,225,256)(62,154,229,258,77,169,214,243)(63,177,218,245,78,162,233,260)(64,170,237,262,79,155,222,247)(65,163,226,249,80,178,211,264)(66,156,215,266,81,171,230,251)(67,179,234,253,82,164,219,268)(68,172,223,270,83,157,238,255)(69,165,212,257,84,180,227,242)(70,158,231,244,85,173,216,259)(71,151,220,261,86,166,235,246)(72,174,239,248,87,159,224,263)(73,167,228,265,88,152,213,250)(74,160,217,252,89,175,232,267)(75,153,236,269,90,168,221,254)>;
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), (1,328,217,359,294,74,16,313,232,344,279,89)(2,317,218,348,295,63,17,302,233,333,280,78)(3,306,219,337,296,82,18,321,234,352,281,67)(4,325,220,356,297,71,19,310,235,341,282,86)(5,314,221,345,298,90,20,329,236,360,283,75)(6,303,222,334,299,79,21,318,237,349,284,64)(7,322,223,353,300,68,22,307,238,338,285,83)(8,311,224,342,271,87,23,326,239,357,286,72)(9,330,225,331,272,76,24,315,240,346,287,61)(10,319,226,350,273,65,25,304,211,335,288,80)(11,308,227,339,274,84,26,323,212,354,289,69)(12,327,228,358,275,73,27,312,213,343,290,88)(13,316,229,347,276,62,28,301,214,332,291,77)(14,305,230,336,277,81,29,320,215,351,292,66)(15,324,231,355,278,70,30,309,216,340,293,85)(31,101,180,209,128,257,46,116,165,194,143,242)(32,120,151,198,129,246,47,105,166,183,144,261)(33,109,152,187,130,265,48,94,167,202,145,250)(34,98,153,206,131,254,49,113,168,191,146,269)(35,117,154,195,132,243,50,102,169,210,147,258)(36,106,155,184,133,262,51,91,170,199,148,247)(37,95,156,203,134,251,52,110,171,188,149,266)(38,114,157,192,135,270,53,99,172,207,150,255)(39,103,158,181,136,259,54,118,173,196,121,244)(40,92,159,200,137,248,55,107,174,185,122,263)(41,111,160,189,138,267,56,96,175,204,123,252)(42,100,161,208,139,256,57,115,176,193,124,241)(43,119,162,197,140,245,58,104,177,182,125,260)(44,108,163,186,141,264,59,93,178,201,126,249)(45,97,164,205,142,253,60,112,179,190,127,268), (1,111,344,123,16,96,359,138)(2,104,333,140,17,119,348,125)(3,97,352,127,18,112,337,142)(4,120,341,144,19,105,356,129)(5,113,360,131,20,98,345,146)(6,106,349,148,21,91,334,133)(7,99,338,135,22,114,353,150)(8,92,357,122,23,107,342,137)(9,115,346,139,24,100,331,124)(10,108,335,126,25,93,350,141)(11,101,354,143,26,116,339,128)(12,94,343,130,27,109,358,145)(13,117,332,147,28,102,347,132)(14,110,351,134,29,95,336,149)(15,103,340,121,30,118,355,136)(31,274,194,308,46,289,209,323)(32,297,183,325,47,282,198,310)(33,290,202,312,48,275,187,327)(34,283,191,329,49,298,206,314)(35,276,210,316,50,291,195,301)(36,299,199,303,51,284,184,318)(37,292,188,320,52,277,203,305)(38,285,207,307,53,300,192,322)(39,278,196,324,54,293,181,309)(40,271,185,311,55,286,200,326)(41,294,204,328,56,279,189,313)(42,287,193,315,57,272,208,330)(43,280,182,302,58,295,197,317)(44,273,201,319,59,288,186,304)(45,296,190,306,60,281,205,321)(61,161,240,241,76,176,225,256)(62,154,229,258,77,169,214,243)(63,177,218,245,78,162,233,260)(64,170,237,262,79,155,222,247)(65,163,226,249,80,178,211,264)(66,156,215,266,81,171,230,251)(67,179,234,253,82,164,219,268)(68,172,223,270,83,157,238,255)(69,165,212,257,84,180,227,242)(70,158,231,244,85,173,216,259)(71,151,220,261,86,166,235,246)(72,174,239,248,87,159,224,263)(73,167,228,265,88,152,213,250)(74,160,217,252,89,175,232,267)(75,153,236,269,90,168,221,254) );
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)], [(1,328,217,359,294,74,16,313,232,344,279,89),(2,317,218,348,295,63,17,302,233,333,280,78),(3,306,219,337,296,82,18,321,234,352,281,67),(4,325,220,356,297,71,19,310,235,341,282,86),(5,314,221,345,298,90,20,329,236,360,283,75),(6,303,222,334,299,79,21,318,237,349,284,64),(7,322,223,353,300,68,22,307,238,338,285,83),(8,311,224,342,271,87,23,326,239,357,286,72),(9,330,225,331,272,76,24,315,240,346,287,61),(10,319,226,350,273,65,25,304,211,335,288,80),(11,308,227,339,274,84,26,323,212,354,289,69),(12,327,228,358,275,73,27,312,213,343,290,88),(13,316,229,347,276,62,28,301,214,332,291,77),(14,305,230,336,277,81,29,320,215,351,292,66),(15,324,231,355,278,70,30,309,216,340,293,85),(31,101,180,209,128,257,46,116,165,194,143,242),(32,120,151,198,129,246,47,105,166,183,144,261),(33,109,152,187,130,265,48,94,167,202,145,250),(34,98,153,206,131,254,49,113,168,191,146,269),(35,117,154,195,132,243,50,102,169,210,147,258),(36,106,155,184,133,262,51,91,170,199,148,247),(37,95,156,203,134,251,52,110,171,188,149,266),(38,114,157,192,135,270,53,99,172,207,150,255),(39,103,158,181,136,259,54,118,173,196,121,244),(40,92,159,200,137,248,55,107,174,185,122,263),(41,111,160,189,138,267,56,96,175,204,123,252),(42,100,161,208,139,256,57,115,176,193,124,241),(43,119,162,197,140,245,58,104,177,182,125,260),(44,108,163,186,141,264,59,93,178,201,126,249),(45,97,164,205,142,253,60,112,179,190,127,268)], [(1,111,344,123,16,96,359,138),(2,104,333,140,17,119,348,125),(3,97,352,127,18,112,337,142),(4,120,341,144,19,105,356,129),(5,113,360,131,20,98,345,146),(6,106,349,148,21,91,334,133),(7,99,338,135,22,114,353,150),(8,92,357,122,23,107,342,137),(9,115,346,139,24,100,331,124),(10,108,335,126,25,93,350,141),(11,101,354,143,26,116,339,128),(12,94,343,130,27,109,358,145),(13,117,332,147,28,102,347,132),(14,110,351,134,29,95,336,149),(15,103,340,121,30,118,355,136),(31,274,194,308,46,289,209,323),(32,297,183,325,47,282,198,310),(33,290,202,312,48,275,187,327),(34,283,191,329,49,298,206,314),(35,276,210,316,50,291,195,301),(36,299,199,303,51,284,184,318),(37,292,188,320,52,277,203,305),(38,285,207,307,53,300,192,322),(39,278,196,324,54,293,181,309),(40,271,185,311,55,286,200,326),(41,294,204,328,56,279,189,313),(42,287,193,315,57,272,208,330),(43,280,182,302,58,295,197,317),(44,273,201,319,59,288,186,304),(45,296,190,306,60,281,205,321),(61,161,240,241,76,176,225,256),(62,154,229,258,77,169,214,243),(63,177,218,245,78,162,233,260),(64,170,237,262,79,155,222,247),(65,163,226,249,80,178,211,264),(66,156,215,266,81,171,230,251),(67,179,234,253,82,164,219,268),(68,172,223,270,83,157,238,255),(69,165,212,257,84,180,227,242),(70,158,231,244,85,173,216,259),(71,151,220,261,86,166,235,246),(72,174,239,248,87,159,224,263),(73,167,228,265,88,152,213,250),(74,160,217,252,89,175,232,267),(75,153,236,269,90,168,221,254)]])
42 conjugacy classes
| class | 1 | 2 | 3A | 3B | 3C | 3D | 4A | 4B | 5 | 6A | 6B | 6C | 6D | 8A | 8B | 8C | 8D | 10 | 12A | ··· | 12H | 15A | ··· | 15H | 30A | ··· | 30H |
| order | 1 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 5 | 6 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | 12 | ··· | 12 | 15 | ··· | 15 | 30 | ··· | 30 |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 5 | 5 | 4 | 2 | 2 | 2 | 2 | 45 | 45 | 45 | 45 | 4 | 10 | ··· | 10 | 4 | ··· | 4 | 4 | ··· | 4 |
42 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | - | + | - | |||||
| image | C1 | C2 | C4 | C8 | S3 | Dic3 | C3⋊C8 | F5 | C5⋊C8 | C3⋊F5 | C15⋊C8 |
| kernel | C30.Dic3 | C32×Dic5 | C3×C30 | C3×C15 | C3×Dic5 | C30 | C15 | C3×C6 | C32 | C6 | C3 |
| # reps | 1 | 1 | 2 | 4 | 4 | 4 | 8 | 1 | 1 | 8 | 8 |
Matrix representation of C30.Dic3 ►in GL8(𝔽241)
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 240 | 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 | 114 | 12 | 0 |
| 0 | 0 | 0 | 0 | 115 | 0 | 126 | 12 |
| 0 | 0 | 0 | 0 | 115 | 229 | 12 | 126 |
| 0 | 0 | 0 | 0 | 127 | 229 | 0 | 12 |
| 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 238 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 43 | 219 | 76 | 174 |
| 0 | 0 | 0 | 0 | 21 | 54 | 9 | 144 |
| 0 | 0 | 0 | 0 | 97 | 228 | 220 | 187 |
| 0 | 0 | 0 | 0 | 30 | 198 | 22 | 165 |
| 71 | 186 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 50 | 56 | 0 | 0 | 0 | 0 |
| 0 | 0 | 149 | 191 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 90 | 21 | 161 | 41 |
| 0 | 0 | 0 | 0 | 131 | 190 | 10 | 62 |
| 0 | 0 | 0 | 0 | 152 | 110 | 51 | 231 |
| 0 | 0 | 0 | 0 | 80 | 200 | 72 | 151 |
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
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