direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic9⋊C4, C23.35D18, C22.4Dic18, C18⋊1(C4⋊C4), C18.7(C2×Q8), (C2×C18).5Q8, (C2×Dic9)⋊4C4, Dic9⋊4(C2×C4), (C2×C18).36D4, (C2×C4).67D18, C18.39(C2×D4), (C22×C4).5D9, (C2×C12).341D6, (C22×C36).4C2, (C2×C6).14Dic6, C2.2(C2×Dic18), C6.34(C2×Dic6), C22.16(C4×D9), C18.18(C22×C4), (C22×C12).10S3, (C2×C36).74C22, (C2×C18).41C23, (C22×C6).135D6, C6.15(Dic3⋊C4), C22.19(C9⋊D4), (C22×Dic9).4C2, C22.20(C22×D9), (C22×C18).33C22, (C2×Dic9).36C22, C9⋊2(C2×C4⋊C4), C6.57(S3×C2×C4), C2.18(C2×C4×D9), C3.(C2×Dic3⋊C4), C2.1(C2×C9⋊D4), (C2×C6).43(C4×S3), C6.86(C2×C3⋊D4), (C2×C18).17(C2×C4), (C2×C6).74(C3⋊D4), (C2×C6).198(C22×S3), SmallGroup(288,133)
Series: Derived ►Chief ►Lower central ►Upper central
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, C2, C3, 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, C2×C12, C22×C6, C2×C4⋊C4, Dic9, Dic9, C36, C2×C18, C2×C18, Dic3⋊C4, C22×Dic3, C22×C12, C2×Dic9, C2×Dic9, C2×C36, C2×C36, C22×C18, C2×Dic3⋊C4, Dic9⋊C4, C22×Dic9, C22×C36, C2×Dic9⋊C4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, Q8, C23, D6, C4⋊C4, C22×C4, C2×D4, C2×Q8, D9, Dic6, C4×S3, C3⋊D4, C22×S3, C2×C4⋊C4, D18, Dic3⋊C4, C2×Dic6, S3×C2×C4, C2×C3⋊D4, Dic18, C4×D9, C9⋊D4, C22×D9, C2×Dic3⋊C4, Dic9⋊C4, C2×Dic18, C2×C4×D9, C2×C9⋊D4, C2×Dic9⋊C4
►Regular action on 288 points
Generators in S288
(1 91)(2 92)(3 93)(4 94)(5 95)(6 96)(7 97)(8 98)(9 99)(10 100)(11 101)(12 102)(13 103)(14 104)(15 105)(16 106)(17 107)(18 108)(19 80)(20 81)(21 82)(22 83)(23 84)(24 85)(25 86)(26 87)(27 88)(28 89)(29 90)(30 73)(31 74)(32 75)(33 76)(34 77)(35 78)(36 79)(37 133)(38 134)(39 135)(40 136)(41 137)(42 138)(43 139)(44 140)(45 141)(46 142)(47 143)(48 144)(49 127)(50 128)(51 129)(52 130)(53 131)(54 132)(55 123)(56 124)(57 125)(58 126)(59 109)(60 110)(61 111)(62 112)(63 113)(64 114)(65 115)(66 116)(67 117)(68 118)(69 119)(70 120)(71 121)(72 122)(145 239)(146 240)(147 241)(148 242)(149 243)(150 244)(151 245)(152 246)(153 247)(154 248)(155 249)(156 250)(157 251)(158 252)(159 235)(160 236)(161 237)(162 238)(163 228)(164 229)(165 230)(166 231)(167 232)(168 233)(169 234)(170 217)(171 218)(172 219)(173 220)(174 221)(175 222)(176 223)(177 224)(178 225)(179 226)(180 227)(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)(199 267)(200 268)(201 269)(202 270)(203 253)(204 254)(205 255)(206 256)(207 257)(208 258)(209 259)(210 260)(211 261)(212 262)(213 263)(214 264)(215 265)(216 266)
(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)
(1 157 10 148)(2 156 11 147)(3 155 12 146)(4 154 13 145)(5 153 14 162)(6 152 15 161)(7 151 16 160)(8 150 17 159)(9 149 18 158)(19 170 28 179)(20 169 29 178)(21 168 30 177)(22 167 31 176)(23 166 32 175)(24 165 33 174)(25 164 34 173)(26 163 35 172)(27 180 36 171)(37 193 46 184)(38 192 47 183)(39 191 48 182)(40 190 49 181)(41 189 50 198)(42 188 51 197)(43 187 52 196)(44 186 53 195)(45 185 54 194)(55 214 64 205)(56 213 65 204)(57 212 66 203)(58 211 67 202)(59 210 68 201)(60 209 69 200)(61 208 70 199)(62 207 71 216)(63 206 72 215)(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)(91 251 100 242)(92 250 101 241)(93 249 102 240)(94 248 103 239)(95 247 104 238)(96 246 105 237)(97 245 106 236)(98 244 107 235)(99 243 108 252)(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 25 122)(2 134 26 123)(3 135 27 124)(4 136 28 125)(5 137 29 126)(6 138 30 109)(7 139 31 110)(8 140 32 111)(9 141 33 112)(10 142 34 113)(11 143 35 114)(12 144 36 115)(13 127 19 116)(14 128 20 117)(15 129 21 118)(16 130 22 119)(17 131 23 120)(18 132 24 121)(37 86 72 91)(38 87 55 92)(39 88 56 93)(40 89 57 94)(41 90 58 95)(42 73 59 96)(43 74 60 97)(44 75 61 98)(45 76 62 99)(46 77 63 100)(47 78 64 101)(48 79 65 102)(49 80 66 103)(50 81 67 104)(51 82 68 105)(52 83 69 106)(53 84 70 107)(54 85 71 108)(145 273 170 262)(146 274 171 263)(147 275 172 264)(148 276 173 265)(149 277 174 266)(150 278 175 267)(151 279 176 268)(152 280 177 269)(153 281 178 270)(154 282 179 253)(155 283 180 254)(156 284 163 255)(157 285 164 256)(158 286 165 257)(159 287 166 258)(160 288 167 259)(161 271 168 260)(162 272 169 261)(181 226 203 248)(182 227 204 249)(183 228 205 250)(184 229 206 251)(185 230 207 252)(186 231 208 235)(187 232 209 236)(188 233 210 237)(189 234 211 238)(190 217 212 239)(191 218 213 240)(192 219 214 241)(193 220 215 242)(194 221 216 243)(195 222 199 244)(196 223 200 245)(197 224 201 246)(198 225 202 247)
G:=sub<Sym(288)| (1,91)(2,92)(3,93)(4,94)(5,95)(6,96)(7,97)(8,98)(9,99)(10,100)(11,101)(12,102)(13,103)(14,104)(15,105)(16,106)(17,107)(18,108)(19,80)(20,81)(21,82)(22,83)(23,84)(24,85)(25,86)(26,87)(27,88)(28,89)(29,90)(30,73)(31,74)(32,75)(33,76)(34,77)(35,78)(36,79)(37,133)(38,134)(39,135)(40,136)(41,137)(42,138)(43,139)(44,140)(45,141)(46,142)(47,143)(48,144)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(55,123)(56,124)(57,125)(58,126)(59,109)(60,110)(61,111)(62,112)(63,113)(64,114)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,121)(72,122)(145,239)(146,240)(147,241)(148,242)(149,243)(150,244)(151,245)(152,246)(153,247)(154,248)(155,249)(156,250)(157,251)(158,252)(159,235)(160,236)(161,237)(162,238)(163,228)(164,229)(165,230)(166,231)(167,232)(168,233)(169,234)(170,217)(171,218)(172,219)(173,220)(174,221)(175,222)(176,223)(177,224)(178,225)(179,226)(180,227)(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)(199,267)(200,268)(201,269)(202,270)(203,253)(204,254)(205,255)(206,256)(207,257)(208,258)(209,259)(210,260)(211,261)(212,262)(213,263)(214,264)(215,265)(216,266), (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), (1,157,10,148)(2,156,11,147)(3,155,12,146)(4,154,13,145)(5,153,14,162)(6,152,15,161)(7,151,16,160)(8,150,17,159)(9,149,18,158)(19,170,28,179)(20,169,29,178)(21,168,30,177)(22,167,31,176)(23,166,32,175)(24,165,33,174)(25,164,34,173)(26,163,35,172)(27,180,36,171)(37,193,46,184)(38,192,47,183)(39,191,48,182)(40,190,49,181)(41,189,50,198)(42,188,51,197)(43,187,52,196)(44,186,53,195)(45,185,54,194)(55,214,64,205)(56,213,65,204)(57,212,66,203)(58,211,67,202)(59,210,68,201)(60,209,69,200)(61,208,70,199)(62,207,71,216)(63,206,72,215)(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)(91,251,100,242)(92,250,101,241)(93,249,102,240)(94,248,103,239)(95,247,104,238)(96,246,105,237)(97,245,106,236)(98,244,107,235)(99,243,108,252)(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), (1,133,25,122)(2,134,26,123)(3,135,27,124)(4,136,28,125)(5,137,29,126)(6,138,30,109)(7,139,31,110)(8,140,32,111)(9,141,33,112)(10,142,34,113)(11,143,35,114)(12,144,36,115)(13,127,19,116)(14,128,20,117)(15,129,21,118)(16,130,22,119)(17,131,23,120)(18,132,24,121)(37,86,72,91)(38,87,55,92)(39,88,56,93)(40,89,57,94)(41,90,58,95)(42,73,59,96)(43,74,60,97)(44,75,61,98)(45,76,62,99)(46,77,63,100)(47,78,64,101)(48,79,65,102)(49,80,66,103)(50,81,67,104)(51,82,68,105)(52,83,69,106)(53,84,70,107)(54,85,71,108)(145,273,170,262)(146,274,171,263)(147,275,172,264)(148,276,173,265)(149,277,174,266)(150,278,175,267)(151,279,176,268)(152,280,177,269)(153,281,178,270)(154,282,179,253)(155,283,180,254)(156,284,163,255)(157,285,164,256)(158,286,165,257)(159,287,166,258)(160,288,167,259)(161,271,168,260)(162,272,169,261)(181,226,203,248)(182,227,204,249)(183,228,205,250)(184,229,206,251)(185,230,207,252)(186,231,208,235)(187,232,209,236)(188,233,210,237)(189,234,211,238)(190,217,212,239)(191,218,213,240)(192,219,214,241)(193,220,215,242)(194,221,216,243)(195,222,199,244)(196,223,200,245)(197,224,201,246)(198,225,202,247)>;
G:=Group( (1,91)(2,92)(3,93)(4,94)(5,95)(6,96)(7,97)(8,98)(9,99)(10,100)(11,101)(12,102)(13,103)(14,104)(15,105)(16,106)(17,107)(18,108)(19,80)(20,81)(21,82)(22,83)(23,84)(24,85)(25,86)(26,87)(27,88)(28,89)(29,90)(30,73)(31,74)(32,75)(33,76)(34,77)(35,78)(36,79)(37,133)(38,134)(39,135)(40,136)(41,137)(42,138)(43,139)(44,140)(45,141)(46,142)(47,143)(48,144)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(55,123)(56,124)(57,125)(58,126)(59,109)(60,110)(61,111)(62,112)(63,113)(64,114)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,121)(72,122)(145,239)(146,240)(147,241)(148,242)(149,243)(150,244)(151,245)(152,246)(153,247)(154,248)(155,249)(156,250)(157,251)(158,252)(159,235)(160,236)(161,237)(162,238)(163,228)(164,229)(165,230)(166,231)(167,232)(168,233)(169,234)(170,217)(171,218)(172,219)(173,220)(174,221)(175,222)(176,223)(177,224)(178,225)(179,226)(180,227)(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)(199,267)(200,268)(201,269)(202,270)(203,253)(204,254)(205,255)(206,256)(207,257)(208,258)(209,259)(210,260)(211,261)(212,262)(213,263)(214,264)(215,265)(216,266), (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), (1,157,10,148)(2,156,11,147)(3,155,12,146)(4,154,13,145)(5,153,14,162)(6,152,15,161)(7,151,16,160)(8,150,17,159)(9,149,18,158)(19,170,28,179)(20,169,29,178)(21,168,30,177)(22,167,31,176)(23,166,32,175)(24,165,33,174)(25,164,34,173)(26,163,35,172)(27,180,36,171)(37,193,46,184)(38,192,47,183)(39,191,48,182)(40,190,49,181)(41,189,50,198)(42,188,51,197)(43,187,52,196)(44,186,53,195)(45,185,54,194)(55,214,64,205)(56,213,65,204)(57,212,66,203)(58,211,67,202)(59,210,68,201)(60,209,69,200)(61,208,70,199)(62,207,71,216)(63,206,72,215)(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)(91,251,100,242)(92,250,101,241)(93,249,102,240)(94,248,103,239)(95,247,104,238)(96,246,105,237)(97,245,106,236)(98,244,107,235)(99,243,108,252)(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), (1,133,25,122)(2,134,26,123)(3,135,27,124)(4,136,28,125)(5,137,29,126)(6,138,30,109)(7,139,31,110)(8,140,32,111)(9,141,33,112)(10,142,34,113)(11,143,35,114)(12,144,36,115)(13,127,19,116)(14,128,20,117)(15,129,21,118)(16,130,22,119)(17,131,23,120)(18,132,24,121)(37,86,72,91)(38,87,55,92)(39,88,56,93)(40,89,57,94)(41,90,58,95)(42,73,59,96)(43,74,60,97)(44,75,61,98)(45,76,62,99)(46,77,63,100)(47,78,64,101)(48,79,65,102)(49,80,66,103)(50,81,67,104)(51,82,68,105)(52,83,69,106)(53,84,70,107)(54,85,71,108)(145,273,170,262)(146,274,171,263)(147,275,172,264)(148,276,173,265)(149,277,174,266)(150,278,175,267)(151,279,176,268)(152,280,177,269)(153,281,178,270)(154,282,179,253)(155,283,180,254)(156,284,163,255)(157,285,164,256)(158,286,165,257)(159,287,166,258)(160,288,167,259)(161,271,168,260)(162,272,169,261)(181,226,203,248)(182,227,204,249)(183,228,205,250)(184,229,206,251)(185,230,207,252)(186,231,208,235)(187,232,209,236)(188,233,210,237)(189,234,211,238)(190,217,212,239)(191,218,213,240)(192,219,214,241)(193,220,215,242)(194,221,216,243)(195,222,199,244)(196,223,200,245)(197,224,201,246)(198,225,202,247) );
G=PermutationGroup([[(1,91),(2,92),(3,93),(4,94),(5,95),(6,96),(7,97),(8,98),(9,99),(10,100),(11,101),(12,102),(13,103),(14,104),(15,105),(16,106),(17,107),(18,108),(19,80),(20,81),(21,82),(22,83),(23,84),(24,85),(25,86),(26,87),(27,88),(28,89),(29,90),(30,73),(31,74),(32,75),(33,76),(34,77),(35,78),(36,79),(37,133),(38,134),(39,135),(40,136),(41,137),(42,138),(43,139),(44,140),(45,141),(46,142),(47,143),(48,144),(49,127),(50,128),(51,129),(52,130),(53,131),(54,132),(55,123),(56,124),(57,125),(58,126),(59,109),(60,110),(61,111),(62,112),(63,113),(64,114),(65,115),(66,116),(67,117),(68,118),(69,119),(70,120),(71,121),(72,122),(145,239),(146,240),(147,241),(148,242),(149,243),(150,244),(151,245),(152,246),(153,247),(154,248),(155,249),(156,250),(157,251),(158,252),(159,235),(160,236),(161,237),(162,238),(163,228),(164,229),(165,230),(166,231),(167,232),(168,233),(169,234),(170,217),(171,218),(172,219),(173,220),(174,221),(175,222),(176,223),(177,224),(178,225),(179,226),(180,227),(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),(199,267),(200,268),(201,269),(202,270),(203,253),(204,254),(205,255),(206,256),(207,257),(208,258),(209,259),(210,260),(211,261),(212,262),(213,263),(214,264),(215,265),(216,266)], [(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)], [(1,157,10,148),(2,156,11,147),(3,155,12,146),(4,154,13,145),(5,153,14,162),(6,152,15,161),(7,151,16,160),(8,150,17,159),(9,149,18,158),(19,170,28,179),(20,169,29,178),(21,168,30,177),(22,167,31,176),(23,166,32,175),(24,165,33,174),(25,164,34,173),(26,163,35,172),(27,180,36,171),(37,193,46,184),(38,192,47,183),(39,191,48,182),(40,190,49,181),(41,189,50,198),(42,188,51,197),(43,187,52,196),(44,186,53,195),(45,185,54,194),(55,214,64,205),(56,213,65,204),(57,212,66,203),(58,211,67,202),(59,210,68,201),(60,209,69,200),(61,208,70,199),(62,207,71,216),(63,206,72,215),(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),(91,251,100,242),(92,250,101,241),(93,249,102,240),(94,248,103,239),(95,247,104,238),(96,246,105,237),(97,245,106,236),(98,244,107,235),(99,243,108,252),(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)], [(1,133,25,122),(2,134,26,123),(3,135,27,124),(4,136,28,125),(5,137,29,126),(6,138,30,109),(7,139,31,110),(8,140,32,111),(9,141,33,112),(10,142,34,113),(11,143,35,114),(12,144,36,115),(13,127,19,116),(14,128,20,117),(15,129,21,118),(16,130,22,119),(17,131,23,120),(18,132,24,121),(37,86,72,91),(38,87,55,92),(39,88,56,93),(40,89,57,94),(41,90,58,95),(42,73,59,96),(43,74,60,97),(44,75,61,98),(45,76,62,99),(46,77,63,100),(47,78,64,101),(48,79,65,102),(49,80,66,103),(50,81,67,104),(51,82,68,105),(52,83,69,106),(53,84,70,107),(54,85,71,108),(145,273,170,262),(146,274,171,263),(147,275,172,264),(148,276,173,265),(149,277,174,266),(150,278,175,267),(151,279,176,268),(152,280,177,269),(153,281,178,270),(154,282,179,253),(155,283,180,254),(156,284,163,255),(157,285,164,256),(158,286,165,257),(159,287,166,258),(160,288,167,259),(161,271,168,260),(162,272,169,261),(181,226,203,248),(182,227,204,249),(183,228,205,250),(184,229,206,251),(185,230,207,252),(186,231,208,235),(187,232,209,236),(188,233,210,237),(189,234,211,238),(190,217,212,239),(191,218,213,240),(192,219,214,241),(193,220,215,242),(194,221,216,243),(195,222,199,244),(196,223,200,245),(197,224,201,246),(198,225,202,247)]])
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