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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, (C4×C20).297C22, (C2×C10).384C24, 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

Subgroups: 202 in 172 conjugacy classes, 142 normal (6 characteristic)
C1, C2 [×3], C4 [×15], C22, C5, C2×C4 [×15], C10 [×3], C42 [×5], C4⋊C4 [×30], C20 [×15], C2×C10, C42.C2 [×15], C2×C20 [×15], C22.58C24, C4×C20 [×5], C5×C4⋊C4 [×30], C5×C42.C2 [×15], C5×C22.58C24

Quotients:
C1, C2 [×15], C22 [×35], C5, C23 [×15], C10 [×15], C24, C2×C10 [×35], 2- (1+4) [×3], C22×C10 [×15], C22.58C24, C23×C10, C5×2- (1+4) [×3], C5×C22.58C24

Generators and relations
 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 >

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

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

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

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

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

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

Matrix representation ►G ⊆ 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] >;
 

95 conjugacy classes

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

95 irreducible representations

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

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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