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G = C25×C10  order 320 = 26·5

Abelian group of type [2,2,2,2,2,10]

direct product, abelian, monomial, 2-elementary

Aliases: C25×C10, SmallGroup(320,1640)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C25×C10
Chief series
C1 — C5 — C10 — C2×C10 — C22×C10 — C23×C10 — C24×C10 — C25×C10
Lower central
C1 — C25×C10
Upper central
C1 — C25×C10

Generators and relations for C25×C10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=e2=f10=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, ef=fe >

Subgroups: 5650, all normal (4 characteristic)
C1, C2, C22, C5, C23, C10, C24, C2×C10, C25, C22×C10, C26, C23×C10, C24×C10, C25×C10
Quotients: C1, C2, C22, C5, C23, C10, C24, C2×C10, C25, C22×C10, C26, C23×C10, C24×C10, C25×C10

Smallest permutation representation of C25×C10
►Regular action on 320 points
Generators in S320
(1 167)(2 168)(3 169)(4 170)(5 161)(6 162)(7 163)(8 164)(9 165)(10 166)(11 171)(12 172)(13 173)(14 174)(15 175)(16 176)(17 177)(18 178)(19 179)(20 180)(21 181)(22 182)(23 183)(24 184)(25 185)(26 186)(27 187)(28 188)(29 189)(30 190)(31 191)(32 192)(33 193)(34 194)(35 195)(36 196)(37 197)(38 198)(39 199)(40 200)(41 201)(42 202)(43 203)(44 204)(45 205)(46 206)(47 207)(48 208)(49 209)(50 210)(51 211)(52 212)(53 213)(54 214)(55 215)(56 216)(57 217)(58 218)(59 219)(60 220)(61 221)(62 222)(63 223)(64 224)(65 225)(66 226)(67 227)(68 228)(69 229)(70 230)(71 231)(72 232)(73 233)(74 234)(75 235)(76 236)(77 237)(78 238)(79 239)(80 240)(81 241)(82 242)(83 243)(84 244)(85 245)(86 246)(87 247)(88 248)(89 249)(90 250)(91 251)(92 252)(93 253)(94 254)(95 255)(96 256)(97 257)(98 258)(99 259)(100 260)(101 261)(102 262)(103 263)(104 264)(105 265)(106 266)(107 267)(108 268)(109 269)(110 270)(111 271)(112 272)(113 273)(114 274)(115 275)(116 276)(117 277)(118 278)(119 279)(120 280)(121 281)(122 282)(123 283)(124 284)(125 285)(126 286)(127 287)(128 288)(129 289)(130 290)(131 291)(132 292)(133 293)(134 294)(135 295)(136 296)(137 297)(138 298)(139 299)(140 300)(141 301)(142 302)(143 303)(144 304)(145 305)(146 306)(147 307)(148 308)(149 309)(150 310)(151 311)(152 312)(153 313)(154 314)(155 315)(156 316)(157 317)(158 318)(159 319)(160 320)

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

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

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

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

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

320 conjugacy classes

class 1 2A···2BK5A5B5C5D10A···10IR
order12···2555510···10
size11···111111···1

320 irreducible representations

dim1111
type++
imageC1C2C5C10
kernelC25×C10C24×C10C26C25
# reps1634252

Matrix representation of C25×C10 ►in GL6(𝔽11)

100000
0100000
0010000
000100
000010
0000010
,
100000
0100000
001000
000100
000010
000001
,
1000000
010000
0010000
000100
000010
000001
,
1000000
010000
0010000
000100
0000100
0000010
,
100000
010000
001000
000100
000010
0000010
,
1000000
080000
0010000
000800
000080
000001

G:=sub<GL(6,GF(11))| [1,0,0,0,0,0,0,10,0,0,0,0,0,0,10,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10],[1,0,0,0,0,0,0,10,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[10,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[10,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,0,0,0,0,10],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10],[10,0,0,0,0,0,0,8,0,0,0,0,0,0,10,0,0,0,0,0,0,8,0,0,0,0,0,0,8,0,0,0,0,0,0,1] >;
 

C25×C10 in GAP, Magma, Sage, TeX 

C_2^5\times C_{10}
 
% in TeX
 
G:=Group("C2^5xC10");
 
// GroupNames label
 
G:=SmallGroup(320,1640);
 
// by ID
 
G=gap.SmallGroup(320,1640);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^2=f^10=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,e*f=f*e>;
 
// generators/relations
 

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