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## G = C2×Dic9⋊C4order 288 = 25·32

### Direct product of C2 and Dic9⋊C4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C18 — C2×Dic9⋊C4
 Chief series C1 — C3 — C9 — C18 — C2×C18 — C2×Dic9 — C22×Dic9 — C2×Dic9⋊C4
 Lower central C9 — C18 — C2×Dic9⋊C4
 Upper central C1 — C23 — C22×C4

Generators and relations for C2×Dic9⋊C4
G = < a,b,c,d | a2=b18=d4=1, c2=b9, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=b9c >

Subgroups: 432 in 138 conjugacy classes, 76 normal (24 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×8], C22, C22 [×6], C6 [×3], C6 [×4], C2×C4 [×2], C2×C4 [×12], C23, C9, Dic3 [×6], C12 [×2], C2×C6, C2×C6 [×6], C4⋊C4 [×4], C22×C4, C22×C4 [×2], C18 [×3], C18 [×4], C2×Dic3 [×10], C2×C12 [×2], C2×C12 [×2], C22×C6, C2×C4⋊C4, Dic9 [×4], Dic9 [×2], C36 [×2], C2×C18, C2×C18 [×6], Dic3⋊C4 [×4], C22×Dic3 [×2], C22×C12, C2×Dic9 [×8], C2×Dic9 [×2], C2×C36 [×2], C2×C36 [×2], C22×C18, C2×Dic3⋊C4, Dic9⋊C4 [×4], C22×Dic9 [×2], C22×C36, C2×Dic9⋊C4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], D4 [×2], Q8 [×2], C23, D6 [×3], C4⋊C4 [×4], C22×C4, C2×D4, C2×Q8, D9, Dic6 [×2], C4×S3 [×2], C3⋊D4 [×2], C22×S3, C2×C4⋊C4, D18 [×3], Dic3⋊C4 [×4], C2×Dic6, S3×C2×C4, C2×C3⋊D4, Dic18 [×2], C4×D9 [×2], C9⋊D4 [×2], C22×D9, C2×Dic3⋊C4, Dic9⋊C4 [×4], C2×Dic18, C2×C4×D9, C2×C9⋊D4, C2×Dic9⋊C4

Smallest permutation representation of C2×Dic9⋊C4
Regular action on 288 points
Generators in S288
(1 103)(2 104)(3 105)(4 106)(5 107)(6 108)(7 91)(8 92)(9 93)(10 94)(11 95)(12 96)(13 97)(14 98)(15 99)(16 100)(17 101)(18 102)(19 74)(20 75)(21 76)(22 77)(23 78)(24 79)(25 80)(26 81)(27 82)(28 83)(29 84)(30 85)(31 86)(32 87)(33 88)(34 89)(35 90)(36 73)(37 135)(38 136)(39 137)(40 138)(41 139)(42 140)(43 141)(44 142)(45 143)(46 144)(47 127)(48 128)(49 129)(50 130)(51 131)(52 132)(53 133)(54 134)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(61 121)(62 122)(63 123)(64 124)(65 125)(66 126)(67 109)(68 110)(69 111)(70 112)(71 113)(72 114)(145 235)(146 236)(147 237)(148 238)(149 239)(150 240)(151 241)(152 242)(153 243)(154 244)(155 245)(156 246)(157 247)(158 248)(159 249)(160 250)(161 251)(162 252)(163 217)(164 218)(165 219)(166 220)(167 221)(168 222)(169 223)(170 224)(171 225)(172 226)(173 227)(174 228)(175 229)(176 230)(177 231)(178 232)(179 233)(180 234)(181 282)(182 283)(183 284)(184 285)(185 286)(186 287)(187 288)(188 271)(189 272)(190 273)(191 274)(192 275)(193 276)(194 277)(195 278)(196 279)(197 280)(198 281)(199 253)(200 254)(201 255)(202 256)(203 257)(204 258)(205 259)(206 260)(207 261)(208 262)(209 263)(210 264)(211 265)(212 266)(213 267)(214 268)(215 269)(216 270)
(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)
(1 150 10 159)(2 149 11 158)(3 148 12 157)(4 147 13 156)(5 146 14 155)(6 145 15 154)(7 162 16 153)(8 161 17 152)(9 160 18 151)(19 179 28 170)(20 178 29 169)(21 177 30 168)(22 176 31 167)(23 175 32 166)(24 174 33 165)(25 173 34 164)(26 172 35 163)(27 171 36 180)(37 191 46 182)(38 190 47 181)(39 189 48 198)(40 188 49 197)(41 187 50 196)(42 186 51 195)(43 185 52 194)(44 184 53 193)(45 183 54 192)(55 200 64 209)(56 199 65 208)(57 216 66 207)(58 215 67 206)(59 214 68 205)(60 213 69 204)(61 212 70 203)(62 211 71 202)(63 210 72 201)(73 234 82 225)(74 233 83 224)(75 232 84 223)(76 231 85 222)(77 230 86 221)(78 229 87 220)(79 228 88 219)(80 227 89 218)(81 226 90 217)(91 252 100 243)(92 251 101 242)(93 250 102 241)(94 249 103 240)(95 248 104 239)(96 247 105 238)(97 246 106 237)(98 245 107 236)(99 244 108 235)(109 260 118 269)(110 259 119 268)(111 258 120 267)(112 257 121 266)(113 256 122 265)(114 255 123 264)(115 254 124 263)(116 253 125 262)(117 270 126 261)(127 282 136 273)(128 281 137 272)(129 280 138 271)(130 279 139 288)(131 278 140 287)(132 277 141 286)(133 276 142 285)(134 275 143 284)(135 274 144 283)
(1 133 30 122)(2 134 31 123)(3 135 32 124)(4 136 33 125)(5 137 34 126)(6 138 35 109)(7 139 36 110)(8 140 19 111)(9 141 20 112)(10 142 21 113)(11 143 22 114)(12 144 23 115)(13 127 24 116)(14 128 25 117)(15 129 26 118)(16 130 27 119)(17 131 28 120)(18 132 29 121)(37 87 64 105)(38 88 65 106)(39 89 66 107)(40 90 67 108)(41 73 68 91)(42 74 69 92)(43 75 70 93)(44 76 71 94)(45 77 72 95)(46 78 55 96)(47 79 56 97)(48 80 57 98)(49 81 58 99)(50 82 59 100)(51 83 60 101)(52 84 61 102)(53 85 62 103)(54 86 63 104)(145 280 163 269)(146 281 164 270)(147 282 165 253)(148 283 166 254)(149 284 167 255)(150 285 168 256)(151 286 169 257)(152 287 170 258)(153 288 171 259)(154 271 172 260)(155 272 173 261)(156 273 174 262)(157 274 175 263)(158 275 176 264)(159 276 177 265)(160 277 178 266)(161 278 179 267)(162 279 180 268)(181 219 199 237)(182 220 200 238)(183 221 201 239)(184 222 202 240)(185 223 203 241)(186 224 204 242)(187 225 205 243)(188 226 206 244)(189 227 207 245)(190 228 208 246)(191 229 209 247)(192 230 210 248)(193 231 211 249)(194 232 212 250)(195 233 213 251)(196 234 214 252)(197 217 215 235)(198 218 216 236)

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

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

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

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 D6 D6 D9 Dic6 C4×S3 C3⋊D4 D18 D18 Dic18 C4×D9 C9⋊D4 kernel C2×Dic9⋊C4 Dic9⋊C4 C22×Dic9 C22×C36 C2×Dic9 C22×C12 C2×C18 C2×C18 C2×C12 C22×C6 C22×C4 C2×C6 C2×C6 C2×C6 C2×C4 C23 C22 C22 C22 # reps 1 4 2 1 8 1 2 2 2 1 3 4 4 4 6 3 12 12 12

Matrix representation of C2×Dic9⋊C4 in GL4(𝔽37) generated by

 36 0 0 0 0 36 0 0 0 0 1 0 0 0 0 1
,
 1 0 0 0 0 1 0 0 0 0 17 6 0 0 31 11
,
 1 0 0 0 0 1 0 0 0 0 9 1 0 0 29 28
,
 6 0 0 0 0 1 0 0 0 0 5 10 0 0 27 32
G:=sub<GL(4,GF(37))| [36,0,0,0,0,36,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,17,31,0,0,6,11],[1,0,0,0,0,1,0,0,0,0,9,29,0,0,1,28],[6,0,0,0,0,1,0,0,0,0,5,27,0,0,10,32] >;

C2×Dic9⋊C4 in GAP, Magma, Sage, TeX

C_2\times {\rm Dic}_9\rtimes C_4
% in TeX

G:=Group("C2xDic9:C4");
// GroupNames label

G:=SmallGroup(288,133);
// by ID

G=gap.SmallGroup(288,133);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,112,422,58,6725,292,9414]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^18=d^4=1,c^2=b^9,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^9*c>;
// generators/relations

׿
×
𝔽