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G = C5×C22.58C24  order 320 = 26·5

Direct product of C5 and C22.58C24

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C5×C22.58C24, C10.1252- 1+4, C42.56(C2×C10), C42.C2.7C10, (C2×C20).685C23, (C2×C10).384C24, (C4×C20).297C22, C22.58(C23×C10), C2.17(C5×2- 1+4), C4⋊C4.36(C2×C10), (C5×C4⋊C4).253C22, (C2×C4).44(C22×C10), (C5×C42.C2).14C2, SmallGroup(320,1566)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C22 — C5×C22.58C24
Chief series
C1 — C2 — C22 — C2×C10 — C2×C20 — C5×C4⋊C4 — C5×C42.C2 — C5×C22.58C24
Lower central
C1 — C22 — C5×C22.58C24
Upper central
C1 — C2×C10 — C5×C22.58C24

Generators and relations for C5×C22.58C24
 G = < a,b,c,d,e,f,g | a5=b2=c2=1, d2=g2=b, e2=f2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, ede-1=bd=db, geg-1=be=eb, bf=fb, bg=gb, fdf-1=cd=dc, ce=ec, cf=fc, cg=gc, gdg-1=bcd, fef-1=bce, fg=gf >

Subgroups: 202 in 172 conjugacy classes, 142 normal (6 characteristic)
C1, C2, C4, C22, C5, C2×C4, C10, C42, C4⋊C4, C20, C2×C10, C42.C2, C2×C20, C22.58C24, C4×C20, C5×C4⋊C4, C5×C42.C2, C5×C22.58C24
Quotients: C1, C2, C22, C5, C23, C10, C24, C2×C10, 2- 1+4, C22×C10, C22.58C24, C23×C10, C5×2- 1+4, C5×C22.58C24

Smallest permutation representation of C5×C22.58C24
►Regular action on 320 points
Generators in S320
(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)

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

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

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

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

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

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

95 conjugacy classes

class 1 2A2B2C4A···4O5A5B5C5D10A···10L20A···20BH
order12224···4555510···1020···20
size11114···411111···14···4

95 irreducible representations

dim111144
type++-
imageC1C2C5C102- 1+4C5×2- 1+4
kernelC5×C22.58C24C5×C42.C2C22.58C24C42.C2C10C2
# reps115460312

Matrix representation of C5×C22.58C24 ►in GL8(𝔽41)

10000000
01000000
00100000
00010000
000037000
000003700
000000370
000000037
,
10000000
01000000
00100000
00010000
000040000
000004000
000000400
000000040
,
400000000
040000000
004000000
000400000
00001000
00000100
00000010
00000001
,
17439150000
243629120000
361139150000
12138310000
000030353721
00003511214
000037213035
00002143511
,
18273610000
035220000
202736130000
211611340000
000020184036
00001821361
0000152123
00005402320
,
4003900000
00110000
10100000
40404000000
00000010
00000001
00001000
00000100
,
4039000000
01000000
01010000
040100000
00000100
000040000
00000001
000000400

G:=sub<GL(8,GF(41))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,37,0,0,0,0,0,0,0,0,37,0,0,0,0,0,0,0,0,37,0,0,0,0,0,0,0,0,37],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[17,24,36,12,0,0,0,0,4,36,11,1,0,0,0,0,39,29,39,38,0,0,0,0,15,12,15,31,0,0,0,0,0,0,0,0,30,35,37,21,0,0,0,0,35,11,21,4,0,0,0,0,37,21,30,35,0,0,0,0,21,4,35,11],[18,0,20,21,0,0,0,0,27,35,27,16,0,0,0,0,36,2,36,11,0,0,0,0,1,2,13,34,0,0,0,0,0,0,0,0,20,18,1,5,0,0,0,0,18,21,5,40,0,0,0,0,40,36,21,23,0,0,0,0,36,1,23,20],[40,0,1,40,0,0,0,0,0,0,0,40,0,0,0,0,39,1,1,40,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[40,0,0,0,0,0,0,0,39,1,1,40,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0] >;
 

C5×C22.58C24 in GAP, Magma, Sage, TeX 

C_5\times C_2^2._{58}C_2^4
 
% in TeX
 
G:=Group("C5xC2^2.58C2^4");
 
// GroupNames label
 
G:=SmallGroup(320,1566);
 
// by ID
 
G=gap.SmallGroup(320,1566);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-2,560,1149,1128,3446,2571,856,6947,1242,304]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=1,d^2=g^2=b,e^2=f^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,e*d*e^-1=b*d=d*b,g*e*g^-1=b*e=e*b,b*f=f*b,b*g=g*b,f*d*f^-1=c*d=d*c,c*e=e*c,c*f=f*c,c*g=g*c,g*d*g^-1=b*c*d,f*e*f^-1=b*c*e,f*g=g*f>;
 
// generators/relations
 

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