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G = C24×C22order 352 = 25·11

Abelian group of type [2,2,2,2,22]

direct product, abelian, monomial, 2-elementary

Aliases: C24×C22, SmallGroup(352,195)

Series: Derived Chief Lower central Upper central

C1 — C24×C22
C1C11C22C2×C22C22×C22C23×C22 — C24×C22
C1 — C24×C22
C1 — C24×C22

Generators and relations for C24×C22
 G = < a,b,c,d,e | a2=b2=c2=d2=e22=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 748, all normal (4 characteristic)
C1, C2 [×31], C22 [×155], C23 [×155], C11, C24 [×31], C22 [×31], C25, C2×C22 [×155], C22×C22 [×155], C23×C22 [×31], C24×C22
Quotients: C1, C2 [×31], C22 [×155], C23 [×155], C11, C24 [×31], C22 [×31], C25, C2×C22 [×155], C22×C22 [×155], C23×C22 [×31], C24×C22

Smallest permutation representation of C24×C22
Regular action on 352 points
Generators in S352
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 197)(10 198)(11 177)(12 178)(13 179)(14 180)(15 181)(16 182)(17 183)(18 184)(19 185)(20 186)(21 187)(22 188)(23 200)(24 201)(25 202)(26 203)(27 204)(28 205)(29 206)(30 207)(31 208)(32 209)(33 210)(34 211)(35 212)(36 213)(37 214)(38 215)(39 216)(40 217)(41 218)(42 219)(43 220)(44 199)(45 221)(46 222)(47 223)(48 224)(49 225)(50 226)(51 227)(52 228)(53 229)(54 230)(55 231)(56 232)(57 233)(58 234)(59 235)(60 236)(61 237)(62 238)(63 239)(64 240)(65 241)(66 242)(67 246)(68 247)(69 248)(70 249)(71 250)(72 251)(73 252)(74 253)(75 254)(76 255)(77 256)(78 257)(79 258)(80 259)(81 260)(82 261)(83 262)(84 263)(85 264)(86 243)(87 244)(88 245)(89 267)(90 268)(91 269)(92 270)(93 271)(94 272)(95 273)(96 274)(97 275)(98 276)(99 277)(100 278)(101 279)(102 280)(103 281)(104 282)(105 283)(106 284)(107 285)(108 286)(109 265)(110 266)(111 305)(112 306)(113 307)(114 308)(115 287)(116 288)(117 289)(118 290)(119 291)(120 292)(121 293)(122 294)(123 295)(124 296)(125 297)(126 298)(127 299)(128 300)(129 301)(130 302)(131 303)(132 304)(133 311)(134 312)(135 313)(136 314)(137 315)(138 316)(139 317)(140 318)(141 319)(142 320)(143 321)(144 322)(145 323)(146 324)(147 325)(148 326)(149 327)(150 328)(151 329)(152 330)(153 309)(154 310)(155 349)(156 350)(157 351)(158 352)(159 331)(160 332)(161 333)(162 334)(163 335)(164 336)(165 337)(166 338)(167 339)(168 340)(169 341)(170 342)(171 343)(172 344)(173 345)(174 346)(175 347)(176 348)
(1 109)(2 110)(3 89)(4 90)(5 91)(6 92)(7 93)(8 94)(9 95)(10 96)(11 97)(12 98)(13 99)(14 100)(15 101)(16 102)(17 103)(18 104)(19 105)(20 106)(21 107)(22 108)(23 132)(24 111)(25 112)(26 113)(27 114)(28 115)(29 116)(30 117)(31 118)(32 119)(33 120)(34 121)(35 122)(36 123)(37 124)(38 125)(39 126)(40 127)(41 128)(42 129)(43 130)(44 131)(45 152)(46 153)(47 154)(48 133)(49 134)(50 135)(51 136)(52 137)(53 138)(54 139)(55 140)(56 141)(57 142)(58 143)(59 144)(60 145)(61 146)(62 147)(63 148)(64 149)(65 150)(66 151)(67 163)(68 164)(69 165)(70 166)(71 167)(72 168)(73 169)(74 170)(75 171)(76 172)(77 173)(78 174)(79 175)(80 176)(81 155)(82 156)(83 157)(84 158)(85 159)(86 160)(87 161)(88 162)(177 275)(178 276)(179 277)(180 278)(181 279)(182 280)(183 281)(184 282)(185 283)(186 284)(187 285)(188 286)(189 265)(190 266)(191 267)(192 268)(193 269)(194 270)(195 271)(196 272)(197 273)(198 274)(199 303)(200 304)(201 305)(202 306)(203 307)(204 308)(205 287)(206 288)(207 289)(208 290)(209 291)(210 292)(211 293)(212 294)(213 295)(214 296)(215 297)(216 298)(217 299)(218 300)(219 301)(220 302)(221 330)(222 309)(223 310)(224 311)(225 312)(226 313)(227 314)(228 315)(229 316)(230 317)(231 318)(232 319)(233 320)(234 321)(235 322)(236 323)(237 324)(238 325)(239 326)(240 327)(241 328)(242 329)(243 332)(244 333)(245 334)(246 335)(247 336)(248 337)(249 338)(250 339)(251 340)(252 341)(253 342)(254 343)(255 344)(256 345)(257 346)(258 347)(259 348)(260 349)(261 350)(262 351)(263 352)(264 331)
(1 63)(2 64)(3 65)(4 66)(5 45)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 53)(14 54)(15 55)(16 56)(17 57)(18 58)(19 59)(20 60)(21 61)(22 62)(23 82)(24 83)(25 84)(26 85)(27 86)(28 87)(29 88)(30 67)(31 68)(32 69)(33 70)(34 71)(35 72)(36 73)(37 74)(38 75)(39 76)(40 77)(41 78)(42 79)(43 80)(44 81)(89 150)(90 151)(91 152)(92 153)(93 154)(94 133)(95 134)(96 135)(97 136)(98 137)(99 138)(100 139)(101 140)(102 141)(103 142)(104 143)(105 144)(106 145)(107 146)(108 147)(109 148)(110 149)(111 157)(112 158)(113 159)(114 160)(115 161)(116 162)(117 163)(118 164)(119 165)(120 166)(121 167)(122 168)(123 169)(124 170)(125 171)(126 172)(127 173)(128 174)(129 175)(130 176)(131 155)(132 156)(177 227)(178 228)(179 229)(180 230)(181 231)(182 232)(183 233)(184 234)(185 235)(186 236)(187 237)(188 238)(189 239)(190 240)(191 241)(192 242)(193 221)(194 222)(195 223)(196 224)(197 225)(198 226)(199 260)(200 261)(201 262)(202 263)(203 264)(204 243)(205 244)(206 245)(207 246)(208 247)(209 248)(210 249)(211 250)(212 251)(213 252)(214 253)(215 254)(216 255)(217 256)(218 257)(219 258)(220 259)(265 326)(266 327)(267 328)(268 329)(269 330)(270 309)(271 310)(272 311)(273 312)(274 313)(275 314)(276 315)(277 316)(278 317)(279 318)(280 319)(281 320)(282 321)(283 322)(284 323)(285 324)(286 325)(287 333)(288 334)(289 335)(290 336)(291 337)(292 338)(293 339)(294 340)(295 341)(296 342)(297 343)(298 344)(299 345)(300 346)(301 347)(302 348)(303 349)(304 350)(305 351)(306 352)(307 331)(308 332)
(1 42)(2 43)(3 44)(4 23)(5 24)(6 25)(7 26)(8 27)(9 28)(10 29)(11 30)(12 31)(13 32)(14 33)(15 34)(16 35)(17 36)(18 37)(19 38)(20 39)(21 40)(22 41)(45 83)(46 84)(47 85)(48 86)(49 87)(50 88)(51 67)(52 68)(53 69)(54 70)(55 71)(56 72)(57 73)(58 74)(59 75)(60 76)(61 77)(62 78)(63 79)(64 80)(65 81)(66 82)(89 131)(90 132)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(101 121)(102 122)(103 123)(104 124)(105 125)(106 126)(107 127)(108 128)(109 129)(110 130)(133 160)(134 161)(135 162)(136 163)(137 164)(138 165)(139 166)(140 167)(141 168)(142 169)(143 170)(144 171)(145 172)(146 173)(147 174)(148 175)(149 176)(150 155)(151 156)(152 157)(153 158)(154 159)(177 207)(178 208)(179 209)(180 210)(181 211)(182 212)(183 213)(184 214)(185 215)(186 216)(187 217)(188 218)(189 219)(190 220)(191 199)(192 200)(193 201)(194 202)(195 203)(196 204)(197 205)(198 206)(221 262)(222 263)(223 264)(224 243)(225 244)(226 245)(227 246)(228 247)(229 248)(230 249)(231 250)(232 251)(233 252)(234 253)(235 254)(236 255)(237 256)(238 257)(239 258)(240 259)(241 260)(242 261)(265 301)(266 302)(267 303)(268 304)(269 305)(270 306)(271 307)(272 308)(273 287)(274 288)(275 289)(276 290)(277 291)(278 292)(279 293)(280 294)(281 295)(282 296)(283 297)(284 298)(285 299)(286 300)(309 352)(310 331)(311 332)(312 333)(313 334)(314 335)(315 336)(316 337)(317 338)(318 339)(319 340)(320 341)(321 342)(322 343)(323 344)(324 345)(325 346)(326 347)(327 348)(328 349)(329 350)(330 351)
(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)

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

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

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

352 conjugacy classes

class 1 2A···2AE11A···11J22A···22KX
order12···211···1122···22
size11···11···11···1

352 irreducible representations

dim1111
type++
imageC1C2C11C22
kernelC24×C22C23×C22C25C24
# reps13110310

Matrix representation of C24×C22 in GL5(𝔽23)

220000
022000
00100
00010
000022
,
10000
01000
002200
000220
000022
,
10000
022000
002200
00010
000022
,
220000
01000
002200
000220
00001
,
190000
019000
00700
000110
00007

G:=sub<GL(5,GF(23))| [22,0,0,0,0,0,22,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,22],[1,0,0,0,0,0,1,0,0,0,0,0,22,0,0,0,0,0,22,0,0,0,0,0,22],[1,0,0,0,0,0,22,0,0,0,0,0,22,0,0,0,0,0,1,0,0,0,0,0,22],[22,0,0,0,0,0,1,0,0,0,0,0,22,0,0,0,0,0,22,0,0,0,0,0,1],[19,0,0,0,0,0,19,0,0,0,0,0,7,0,0,0,0,0,11,0,0,0,0,0,7] >;

C24×C22 in GAP, Magma, Sage, TeX

C_2^4\times C_{22}
% in TeX

G:=Group("C2^4xC22");
// GroupNames label

G:=SmallGroup(352,195);
// by ID

G=gap.SmallGroup(352,195);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-11]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^22=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

׿
×
𝔽