direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C4⋊Dic9, C23.36D18, C22.15D36, C22.5Dic18, C36⋊7(C2×C4), (C2×C36)⋊5C4, C18⋊2(C4⋊C4), C4⋊2(C2×Dic9), (C2×C4)⋊3Dic9, C2.2(C2×D36), C18.9(C2×Q8), (C2×C18).6Q8, (C2×C18).20D4, (C2×C6).29D12, (C2×C4).85D18, C18.15(C2×D4), C6.44(C2×D12), (C22×C4).8D9, (C2×C12).373D6, (C22×C36).7C2, C6.36(C2×Dic6), (C2×C6).16Dic6, C2.3(C2×Dic18), C18.23(C22×C4), (C2×C36).92C22, (C2×C18).43C23, (C22×C12).19S3, C6.11(C4⋊Dic3), C12.44(C2×Dic3), (C2×C12).15Dic3, (C22×C6).137D6, C2.4(C22×Dic9), (C22×Dic9).5C2, C22.14(C2×Dic9), C6.24(C22×Dic3), C22.21(C22×D9), (C22×C18).35C22, (C2×Dic9).37C22, C9⋊3(C2×C4⋊C4), C3.(C2×C4⋊Dic3), (C2×C18).34(C2×C4), (C2×C6).39(C2×Dic3), (C2×C6).200(C22×S3), SmallGroup(288,135)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C4⋊Dic9
G = < a,b,c,d | a2=b4=c18=1, d2=c9, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 432 in 138 conjugacy classes, 92 normal (22 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C2×C4, C2×C4, C23, C9, Dic3, C12, C2×C6, C2×C6, C4⋊C4, C22×C4, C22×C4, C18, C18, C2×Dic3, C2×C12, C22×C6, C2×C4⋊C4, Dic9, C36, C2×C18, C2×C18, C4⋊Dic3, C22×Dic3, C22×C12, C2×Dic9, C2×Dic9, C2×C36, C22×C18, C2×C4⋊Dic3, C4⋊Dic9, C22×Dic9, C22×C36, C2×C4⋊Dic9
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, Q8, C23, Dic3, D6, C4⋊C4, C22×C4, C2×D4, C2×Q8, D9, Dic6, D12, C2×Dic3, C22×S3, C2×C4⋊C4, Dic9, D18, C4⋊Dic3, C2×Dic6, C2×D12, C22×Dic3, Dic18, D36, C2×Dic9, C22×D9, C2×C4⋊Dic3, C4⋊Dic9, C2×Dic18, C2×D36, C22×Dic9, C2×C4⋊Dic9
►Regular action on 288 points
Generators in S288
(1 147)(2 148)(3 149)(4 150)(5 151)(6 152)(7 153)(8 154)(9 155)(10 156)(11 157)(12 158)(13 159)(14 160)(15 161)(16 162)(17 145)(18 146)(19 268)(20 269)(21 270)(22 253)(23 254)(24 255)(25 256)(26 257)(27 258)(28 259)(29 260)(30 261)(31 262)(32 263)(33 264)(34 265)(35 266)(36 267)(37 224)(38 225)(39 226)(40 227)(41 228)(42 229)(43 230)(44 231)(45 232)(46 233)(47 234)(48 217)(49 218)(50 219)(51 220)(52 221)(53 222)(54 223)(55 128)(56 129)(57 130)(58 131)(59 132)(60 133)(61 134)(62 135)(63 136)(64 137)(65 138)(66 139)(67 140)(68 141)(69 142)(70 143)(71 144)(72 127)(73 105)(74 106)(75 107)(76 108)(77 91)(78 92)(79 93)(80 94)(81 95)(82 96)(83 97)(84 98)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(109 187)(110 188)(111 189)(112 190)(113 191)(114 192)(115 193)(116 194)(117 195)(118 196)(119 197)(120 198)(121 181)(122 182)(123 183)(124 184)(125 185)(126 186)(163 213)(164 214)(165 215)(166 216)(167 199)(168 200)(169 201)(170 202)(171 203)(172 204)(173 205)(174 206)(175 207)(176 208)(177 209)(178 210)(179 211)(180 212)(235 283)(236 284)(237 285)(238 286)(239 287)(240 288)(241 271)(242 272)(243 273)(244 274)(245 275)(246 276)(247 277)(248 278)(249 279)(250 280)(251 281)(252 282)
(1 179 226 126)(2 180 227 109)(3 163 228 110)(4 164 229 111)(5 165 230 112)(6 166 231 113)(7 167 232 114)(8 168 233 115)(9 169 234 116)(10 170 217 117)(11 171 218 118)(12 172 219 119)(13 173 220 120)(14 174 221 121)(15 175 222 122)(16 176 223 123)(17 177 224 124)(18 178 225 125)(19 139 101 245)(20 140 102 246)(21 141 103 247)(22 142 104 248)(23 143 105 249)(24 144 106 250)(25 127 107 251)(26 128 108 252)(27 129 91 235)(28 130 92 236)(29 131 93 237)(30 132 94 238)(31 133 95 239)(32 134 96 240)(33 135 97 241)(34 136 98 242)(35 137 99 243)(36 138 100 244)(37 184 145 209)(38 185 146 210)(39 186 147 211)(40 187 148 212)(41 188 149 213)(42 189 150 214)(43 190 151 215)(44 191 152 216)(45 192 153 199)(46 193 154 200)(47 194 155 201)(48 195 156 202)(49 196 157 203)(50 197 158 204)(51 198 159 205)(52 181 160 206)(53 182 161 207)(54 183 162 208)(55 76 282 257)(56 77 283 258)(57 78 284 259)(58 79 285 260)(59 80 286 261)(60 81 287 262)(61 82 288 263)(62 83 271 264)(63 84 272 265)(64 85 273 266)(65 86 274 267)(66 87 275 268)(67 88 276 269)(68 89 277 270)(69 90 278 253)(70 73 279 254)(71 74 280 255)(72 75 281 256)
(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)
(1 261 10 270)(2 260 11 269)(3 259 12 268)(4 258 13 267)(5 257 14 266)(6 256 15 265)(7 255 16 264)(8 254 17 263)(9 253 18 262)(19 149 28 158)(20 148 29 157)(21 147 30 156)(22 146 31 155)(23 145 32 154)(24 162 33 153)(25 161 34 152)(26 160 35 151)(27 159 36 150)(37 96 46 105)(38 95 47 104)(39 94 48 103)(40 93 49 102)(41 92 50 101)(42 91 51 100)(43 108 52 99)(44 107 53 98)(45 106 54 97)(55 121 64 112)(56 120 65 111)(57 119 66 110)(58 118 67 109)(59 117 68 126)(60 116 69 125)(61 115 70 124)(62 114 71 123)(63 113 72 122)(73 224 82 233)(74 223 83 232)(75 222 84 231)(76 221 85 230)(77 220 86 229)(78 219 87 228)(79 218 88 227)(80 217 89 226)(81 234 90 225)(127 182 136 191)(128 181 137 190)(129 198 138 189)(130 197 139 188)(131 196 140 187)(132 195 141 186)(133 194 142 185)(134 193 143 184)(135 192 144 183)(163 284 172 275)(164 283 173 274)(165 282 174 273)(166 281 175 272)(167 280 176 271)(168 279 177 288)(169 278 178 287)(170 277 179 286)(171 276 180 285)(199 250 208 241)(200 249 209 240)(201 248 210 239)(202 247 211 238)(203 246 212 237)(204 245 213 236)(205 244 214 235)(206 243 215 252)(207 242 216 251)
G:=sub<Sym(288)| (1,147)(2,148)(3,149)(4,150)(5,151)(6,152)(7,153)(8,154)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,145)(18,146)(19,268)(20,269)(21,270)(22,253)(23,254)(24,255)(25,256)(26,257)(27,258)(28,259)(29,260)(30,261)(31,262)(32,263)(33,264)(34,265)(35,266)(36,267)(37,224)(38,225)(39,226)(40,227)(41,228)(42,229)(43,230)(44,231)(45,232)(46,233)(47,234)(48,217)(49,218)(50,219)(51,220)(52,221)(53,222)(54,223)(55,128)(56,129)(57,130)(58,131)(59,132)(60,133)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,141)(69,142)(70,143)(71,144)(72,127)(73,105)(74,106)(75,107)(76,108)(77,91)(78,92)(79,93)(80,94)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(109,187)(110,188)(111,189)(112,190)(113,191)(114,192)(115,193)(116,194)(117,195)(118,196)(119,197)(120,198)(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(163,213)(164,214)(165,215)(166,216)(167,199)(168,200)(169,201)(170,202)(171,203)(172,204)(173,205)(174,206)(175,207)(176,208)(177,209)(178,210)(179,211)(180,212)(235,283)(236,284)(237,285)(238,286)(239,287)(240,288)(241,271)(242,272)(243,273)(244,274)(245,275)(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)(252,282), (1,179,226,126)(2,180,227,109)(3,163,228,110)(4,164,229,111)(5,165,230,112)(6,166,231,113)(7,167,232,114)(8,168,233,115)(9,169,234,116)(10,170,217,117)(11,171,218,118)(12,172,219,119)(13,173,220,120)(14,174,221,121)(15,175,222,122)(16,176,223,123)(17,177,224,124)(18,178,225,125)(19,139,101,245)(20,140,102,246)(21,141,103,247)(22,142,104,248)(23,143,105,249)(24,144,106,250)(25,127,107,251)(26,128,108,252)(27,129,91,235)(28,130,92,236)(29,131,93,237)(30,132,94,238)(31,133,95,239)(32,134,96,240)(33,135,97,241)(34,136,98,242)(35,137,99,243)(36,138,100,244)(37,184,145,209)(38,185,146,210)(39,186,147,211)(40,187,148,212)(41,188,149,213)(42,189,150,214)(43,190,151,215)(44,191,152,216)(45,192,153,199)(46,193,154,200)(47,194,155,201)(48,195,156,202)(49,196,157,203)(50,197,158,204)(51,198,159,205)(52,181,160,206)(53,182,161,207)(54,183,162,208)(55,76,282,257)(56,77,283,258)(57,78,284,259)(58,79,285,260)(59,80,286,261)(60,81,287,262)(61,82,288,263)(62,83,271,264)(63,84,272,265)(64,85,273,266)(65,86,274,267)(66,87,275,268)(67,88,276,269)(68,89,277,270)(69,90,278,253)(70,73,279,254)(71,74,280,255)(72,75,281,256), (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), (1,261,10,270)(2,260,11,269)(3,259,12,268)(4,258,13,267)(5,257,14,266)(6,256,15,265)(7,255,16,264)(8,254,17,263)(9,253,18,262)(19,149,28,158)(20,148,29,157)(21,147,30,156)(22,146,31,155)(23,145,32,154)(24,162,33,153)(25,161,34,152)(26,160,35,151)(27,159,36,150)(37,96,46,105)(38,95,47,104)(39,94,48,103)(40,93,49,102)(41,92,50,101)(42,91,51,100)(43,108,52,99)(44,107,53,98)(45,106,54,97)(55,121,64,112)(56,120,65,111)(57,119,66,110)(58,118,67,109)(59,117,68,126)(60,116,69,125)(61,115,70,124)(62,114,71,123)(63,113,72,122)(73,224,82,233)(74,223,83,232)(75,222,84,231)(76,221,85,230)(77,220,86,229)(78,219,87,228)(79,218,88,227)(80,217,89,226)(81,234,90,225)(127,182,136,191)(128,181,137,190)(129,198,138,189)(130,197,139,188)(131,196,140,187)(132,195,141,186)(133,194,142,185)(134,193,143,184)(135,192,144,183)(163,284,172,275)(164,283,173,274)(165,282,174,273)(166,281,175,272)(167,280,176,271)(168,279,177,288)(169,278,178,287)(170,277,179,286)(171,276,180,285)(199,250,208,241)(200,249,209,240)(201,248,210,239)(202,247,211,238)(203,246,212,237)(204,245,213,236)(205,244,214,235)(206,243,215,252)(207,242,216,251)>;
G:=Group( (1,147)(2,148)(3,149)(4,150)(5,151)(6,152)(7,153)(8,154)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,145)(18,146)(19,268)(20,269)(21,270)(22,253)(23,254)(24,255)(25,256)(26,257)(27,258)(28,259)(29,260)(30,261)(31,262)(32,263)(33,264)(34,265)(35,266)(36,267)(37,224)(38,225)(39,226)(40,227)(41,228)(42,229)(43,230)(44,231)(45,232)(46,233)(47,234)(48,217)(49,218)(50,219)(51,220)(52,221)(53,222)(54,223)(55,128)(56,129)(57,130)(58,131)(59,132)(60,133)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,141)(69,142)(70,143)(71,144)(72,127)(73,105)(74,106)(75,107)(76,108)(77,91)(78,92)(79,93)(80,94)(81,95)(82,96)(83,97)(84,98)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(109,187)(110,188)(111,189)(112,190)(113,191)(114,192)(115,193)(116,194)(117,195)(118,196)(119,197)(120,198)(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(163,213)(164,214)(165,215)(166,216)(167,199)(168,200)(169,201)(170,202)(171,203)(172,204)(173,205)(174,206)(175,207)(176,208)(177,209)(178,210)(179,211)(180,212)(235,283)(236,284)(237,285)(238,286)(239,287)(240,288)(241,271)(242,272)(243,273)(244,274)(245,275)(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)(252,282), (1,179,226,126)(2,180,227,109)(3,163,228,110)(4,164,229,111)(5,165,230,112)(6,166,231,113)(7,167,232,114)(8,168,233,115)(9,169,234,116)(10,170,217,117)(11,171,218,118)(12,172,219,119)(13,173,220,120)(14,174,221,121)(15,175,222,122)(16,176,223,123)(17,177,224,124)(18,178,225,125)(19,139,101,245)(20,140,102,246)(21,141,103,247)(22,142,104,248)(23,143,105,249)(24,144,106,250)(25,127,107,251)(26,128,108,252)(27,129,91,235)(28,130,92,236)(29,131,93,237)(30,132,94,238)(31,133,95,239)(32,134,96,240)(33,135,97,241)(34,136,98,242)(35,137,99,243)(36,138,100,244)(37,184,145,209)(38,185,146,210)(39,186,147,211)(40,187,148,212)(41,188,149,213)(42,189,150,214)(43,190,151,215)(44,191,152,216)(45,192,153,199)(46,193,154,200)(47,194,155,201)(48,195,156,202)(49,196,157,203)(50,197,158,204)(51,198,159,205)(52,181,160,206)(53,182,161,207)(54,183,162,208)(55,76,282,257)(56,77,283,258)(57,78,284,259)(58,79,285,260)(59,80,286,261)(60,81,287,262)(61,82,288,263)(62,83,271,264)(63,84,272,265)(64,85,273,266)(65,86,274,267)(66,87,275,268)(67,88,276,269)(68,89,277,270)(69,90,278,253)(70,73,279,254)(71,74,280,255)(72,75,281,256), (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), (1,261,10,270)(2,260,11,269)(3,259,12,268)(4,258,13,267)(5,257,14,266)(6,256,15,265)(7,255,16,264)(8,254,17,263)(9,253,18,262)(19,149,28,158)(20,148,29,157)(21,147,30,156)(22,146,31,155)(23,145,32,154)(24,162,33,153)(25,161,34,152)(26,160,35,151)(27,159,36,150)(37,96,46,105)(38,95,47,104)(39,94,48,103)(40,93,49,102)(41,92,50,101)(42,91,51,100)(43,108,52,99)(44,107,53,98)(45,106,54,97)(55,121,64,112)(56,120,65,111)(57,119,66,110)(58,118,67,109)(59,117,68,126)(60,116,69,125)(61,115,70,124)(62,114,71,123)(63,113,72,122)(73,224,82,233)(74,223,83,232)(75,222,84,231)(76,221,85,230)(77,220,86,229)(78,219,87,228)(79,218,88,227)(80,217,89,226)(81,234,90,225)(127,182,136,191)(128,181,137,190)(129,198,138,189)(130,197,139,188)(131,196,140,187)(132,195,141,186)(133,194,142,185)(134,193,143,184)(135,192,144,183)(163,284,172,275)(164,283,173,274)(165,282,174,273)(166,281,175,272)(167,280,176,271)(168,279,177,288)(169,278,178,287)(170,277,179,286)(171,276,180,285)(199,250,208,241)(200,249,209,240)(201,248,210,239)(202,247,211,238)(203,246,212,237)(204,245,213,236)(205,244,214,235)(206,243,215,252)(207,242,216,251) );
G=PermutationGroup([[(1,147),(2,148),(3,149),(4,150),(5,151),(6,152),(7,153),(8,154),(9,155),(10,156),(11,157),(12,158),(13,159),(14,160),(15,161),(16,162),(17,145),(18,146),(19,268),(20,269),(21,270),(22,253),(23,254),(24,255),(25,256),(26,257),(27,258),(28,259),(29,260),(30,261),(31,262),(32,263),(33,264),(34,265),(35,266),(36,267),(37,224),(38,225),(39,226),(40,227),(41,228),(42,229),(43,230),(44,231),(45,232),(46,233),(47,234),(48,217),(49,218),(50,219),(51,220),(52,221),(53,222),(54,223),(55,128),(56,129),(57,130),(58,131),(59,132),(60,133),(61,134),(62,135),(63,136),(64,137),(65,138),(66,139),(67,140),(68,141),(69,142),(70,143),(71,144),(72,127),(73,105),(74,106),(75,107),(76,108),(77,91),(78,92),(79,93),(80,94),(81,95),(82,96),(83,97),(84,98),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(109,187),(110,188),(111,189),(112,190),(113,191),(114,192),(115,193),(116,194),(117,195),(118,196),(119,197),(120,198),(121,181),(122,182),(123,183),(124,184),(125,185),(126,186),(163,213),(164,214),(165,215),(166,216),(167,199),(168,200),(169,201),(170,202),(171,203),(172,204),(173,205),(174,206),(175,207),(176,208),(177,209),(178,210),(179,211),(180,212),(235,283),(236,284),(237,285),(238,286),(239,287),(240,288),(241,271),(242,272),(243,273),(244,274),(245,275),(246,276),(247,277),(248,278),(249,279),(250,280),(251,281),(252,282)], [(1,179,226,126),(2,180,227,109),(3,163,228,110),(4,164,229,111),(5,165,230,112),(6,166,231,113),(7,167,232,114),(8,168,233,115),(9,169,234,116),(10,170,217,117),(11,171,218,118),(12,172,219,119),(13,173,220,120),(14,174,221,121),(15,175,222,122),(16,176,223,123),(17,177,224,124),(18,178,225,125),(19,139,101,245),(20,140,102,246),(21,141,103,247),(22,142,104,248),(23,143,105,249),(24,144,106,250),(25,127,107,251),(26,128,108,252),(27,129,91,235),(28,130,92,236),(29,131,93,237),(30,132,94,238),(31,133,95,239),(32,134,96,240),(33,135,97,241),(34,136,98,242),(35,137,99,243),(36,138,100,244),(37,184,145,209),(38,185,146,210),(39,186,147,211),(40,187,148,212),(41,188,149,213),(42,189,150,214),(43,190,151,215),(44,191,152,216),(45,192,153,199),(46,193,154,200),(47,194,155,201),(48,195,156,202),(49,196,157,203),(50,197,158,204),(51,198,159,205),(52,181,160,206),(53,182,161,207),(54,183,162,208),(55,76,282,257),(56,77,283,258),(57,78,284,259),(58,79,285,260),(59,80,286,261),(60,81,287,262),(61,82,288,263),(62,83,271,264),(63,84,272,265),(64,85,273,266),(65,86,274,267),(66,87,275,268),(67,88,276,269),(68,89,277,270),(69,90,278,253),(70,73,279,254),(71,74,280,255),(72,75,281,256)], [(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)], [(1,261,10,270),(2,260,11,269),(3,259,12,268),(4,258,13,267),(5,257,14,266),(6,256,15,265),(7,255,16,264),(8,254,17,263),(9,253,18,262),(19,149,28,158),(20,148,29,157),(21,147,30,156),(22,146,31,155),(23,145,32,154),(24,162,33,153),(25,161,34,152),(26,160,35,151),(27,159,36,150),(37,96,46,105),(38,95,47,104),(39,94,48,103),(40,93,49,102),(41,92,50,101),(42,91,51,100),(43,108,52,99),(44,107,53,98),(45,106,54,97),(55,121,64,112),(56,120,65,111),(57,119,66,110),(58,118,67,109),(59,117,68,126),(60,116,69,125),(61,115,70,124),(62,114,71,123),(63,113,72,122),(73,224,82,233),(74,223,83,232),(75,222,84,231),(76,221,85,230),(77,220,86,229),(78,219,87,228),(79,218,88,227),(80,217,89,226),(81,234,90,225),(127,182,136,191),(128,181,137,190),(129,198,138,189),(130,197,139,188),(131,196,140,187),(132,195,141,186),(133,194,142,185),(134,193,143,184),(135,192,144,183),(163,284,172,275),(164,283,173,274),(165,282,174,273),(166,281,175,272),(167,280,176,271),(168,279,177,288),(169,278,178,287),(170,277,179,286),(171,276,180,285),(199,250,208,241),(200,249,209,240),(201,248,210,239),(202,247,211,238),(203,246,212,237),(204,245,213,236),(205,244,214,235),(206,243,215,252),(207,242,216,251)]])
84 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 6A | ··· | 6G | 9A | 9B | 9C | 12A | ··· | 12H | 18A | ··· | 18U | 36A | ··· | 36X |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 9 | 9 | 9 | 12 | ··· | 12 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 18 | ··· | 18 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | - | + | + | + | - | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C4 | S3 | D4 | Q8 | Dic3 | D6 | D6 | D9 | Dic6 | D12 | Dic9 | D18 | D18 | Dic18 | D36 |
| kernel | C2×C4⋊Dic9 | C4⋊Dic9 | C22×Dic9 | C22×C36 | C2×C36 | C22×C12 | C2×C18 | C2×C18 | C2×C12 | C2×C12 | C22×C6 | C22×C4 | C2×C6 | C2×C6 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 4 | 4 | 12 | 6 | 3 | 12 | 12 |
Matrix representation of C2×C4⋊Dic9 ►in GL5(𝔽37)
| 36 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 0 | 36 |
| 36 | 0 | 0 | 0 | 0 |
| 0 | 36 | 0 | 0 | 0 |
| 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 0 | 32 | 27 |
| 0 | 0 | 0 | 10 | 5 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 26 | 20 | 0 | 0 |
| 0 | 17 | 6 | 0 | 0 |
| 0 | 0 | 0 | 31 | 11 |
| 0 | 0 | 0 | 26 | 20 |
| 36 | 0 | 0 | 0 | 0 |
| 0 | 30 | 7 | 0 | 0 |
| 0 | 14 | 7 | 0 | 0 |
| 0 | 0 | 0 | 8 | 9 |
| 0 | 0 | 0 | 1 | 29 |
G:=sub<GL(5,GF(37))| [36,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,36,0,0,0,0,0,36],[36,0,0,0,0,0,36,0,0,0,0,0,36,0,0,0,0,0,32,10,0,0,0,27,5],[1,0,0,0,0,0,26,17,0,0,0,20,6,0,0,0,0,0,31,26,0,0,0,11,20],[36,0,0,0,0,0,30,14,0,0,0,7,7,0,0,0,0,0,8,1,0,0,0,9,29] >;
C2×C4⋊Dic9 in GAP, Magma, Sage, TeX
C_2\times C_4\rtimes {\rm Dic}_9 % in TeX
G:=Group("C2xC4:Dic9"); // GroupNames label
G:=SmallGroup(288,135);
// by ID
G=gap.SmallGroup(288,135);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,56,422,100,6725,292,9414]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^18=1,d^2=c^9,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations