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G = C24×C18  order 288 = 25·32

Abelian group of type [2,2,2,2,18]

direct product, abelian, monomial, 2-elementary

Aliases: C24×C18, SmallGroup(288,840)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C24×C18
Chief series
C1 — C3 — C9 — C18 — C2×C18 — C22×C18 — C23×C18 — C24×C18
Lower central
C1 — C24×C18
Upper central
C1 — C24×C18

Generators and relations for C24×C18
 G = < a,b,c,d,e | a2=b2=c2=d2=e18=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 1122, all normal (6 characteristic)
C1, C2, C3, C22, C6, C23, C9, C2×C6, C24, C18, C22×C6, C25, C2×C18, C23×C6, C22×C18, C24×C6, C23×C18, C24×C18
Quotients: C1, C2, C3, C22, C6, C23, C9, C2×C6, C24, C18, C22×C6, C25, C2×C18, C23×C6, C22×C18, C24×C6, C23×C18, C24×C18

Smallest permutation representation of C24×C18
►Regular action on 288 points
Generators in S288
(1 153)(2 154)(3 155)(4 156)(5 157)(6 158)(7 159)(8 160)(9 161)(10 162)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 151)(18 152)(19 168)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 178)(30 179)(31 180)(32 163)(33 164)(34 165)(35 166)(36 167)(37 181)(38 182)(39 183)(40 184)(41 185)(42 186)(43 187)(44 188)(45 189)(46 190)(47 191)(48 192)(49 193)(50 194)(51 195)(52 196)(53 197)(54 198)(55 207)(56 208)(57 209)(58 210)(59 211)(60 212)(61 213)(62 214)(63 215)(64 216)(65 199)(66 200)(67 201)(68 202)(69 203)(70 204)(71 205)(72 206)(73 227)(74 228)(75 229)(76 230)(77 231)(78 232)(79 233)(80 234)(81 217)(82 218)(83 219)(84 220)(85 221)(86 222)(87 223)(88 224)(89 225)(90 226)(91 250)(92 251)(93 252)(94 235)(95 236)(96 237)(97 238)(98 239)(99 240)(100 241)(101 242)(102 243)(103 244)(104 245)(105 246)(106 247)(107 248)(108 249)(109 266)(110 267)(111 268)(112 269)(113 270)(114 253)(115 254)(116 255)(117 256)(118 257)(119 258)(120 259)(121 260)(122 261)(123 262)(124 263)(125 264)(126 265)(127 286)(128 287)(129 288)(130 271)(131 272)(132 273)(133 274)(134 275)(135 276)(136 277)(137 278)(138 279)(139 280)(140 281)(141 282)(142 283)(143 284)(144 285)

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

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

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

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

288 conjugacy classes

class 1 2A···2AE3A3B6A···6BJ9A···9F18A···18GD
order12···2336···69···918···18
size11···1111···11···11···1

288 irreducible representations

dim111111
type++
imageC1C2C3C6C9C18
kernelC24×C18C23×C18C24×C6C23×C6C25C24
# reps1312626186

Matrix representation of C24×C18 ►in GL5(𝔽19)

180000
01000
00100
00010
000018
,
180000
01000
001800
000180
000018
,
180000
018000
001800
000180
000018
,
180000
018000
001800
000180
00001
,
150000
09000
001500
00050
000014

G:=sub<GL(5,GF(19))| [18,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,18],[18,0,0,0,0,0,1,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,18],[18,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,18],[18,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,1],[15,0,0,0,0,0,9,0,0,0,0,0,15,0,0,0,0,0,5,0,0,0,0,0,14] >;
 

C24×C18 in GAP, Magma, Sage, TeX 

C_2^4\times C_{18}
 
% in TeX
 
G:=Group("C2^4xC18");
 
// GroupNames label
 
G:=SmallGroup(288,840);
 
// by ID
 
G=gap.SmallGroup(288,840);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,166]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^18=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,d*e=e*d>;
 
// generators/relations
 

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