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## G = C5×C23.84C23order 320 = 26·5

### Direct product of C5 and C23.84C23

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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C23 — C5×C23.84C23
 Chief series C1 — C2 — C22 — C23 — C22×C10 — C22×C20 — C5×C2.C42 — C5×C23.84C23
 Lower central C1 — C23 — C5×C23.84C23
 Upper central C1 — C22×C10 — C5×C23.84C23

Generators and relations for C5×C23.84C23
G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=bcd, f2=cb=bc, g2=b, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bd=db, fef-1=be=eb, bf=fb, bg=gb, cd=dc, geg-1=ce=ec, cf=fc, cg=gc, de=ed, gfg-1=df=fd, dg=gd >

Subgroups: 202 in 118 conjugacy classes, 62 normal (6 characteristic)
C1, C2, C4, C22, C5, C2×C4, C23, C10, C22×C4, C20, C2×C10, C2.C42, C2×C20, C22×C10, C23.84C23, C22×C20, C5×C2.C42, C5×C23.84C23
Quotients: C1, C2, C22, C5, C23, C10, C4○D4, C2×C10, C422C2, C22×C10, C23.84C23, C5×C4○D4, C5×C422C2, C5×C23.84C23

Smallest permutation representation of C5×C23.84C23
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 42)(2 43)(3 44)(4 45)(5 41)(6 300)(7 296)(8 297)(9 298)(10 299)(11 53)(12 54)(13 55)(14 51)(15 52)(16 301)(17 302)(18 303)(19 304)(20 305)(21 315)(22 311)(23 312)(24 313)(25 314)(26 69)(27 70)(28 66)(29 67)(30 68)(31 316)(32 317)(33 318)(34 319)(35 320)(36 46)(37 47)(38 48)(39 49)(40 50)(56 81)(57 82)(58 83)(59 84)(60 85)(61 95)(62 91)(63 92)(64 93)(65 94)(71 109)(72 110)(73 106)(74 107)(75 108)(76 86)(77 87)(78 88)(79 89)(80 90)(96 121)(97 122)(98 123)(99 124)(100 125)(101 135)(102 131)(103 132)(104 133)(105 134)(111 149)(112 150)(113 146)(114 147)(115 148)(116 126)(117 127)(118 128)(119 129)(120 130)(136 161)(137 162)(138 163)(139 164)(140 165)(141 175)(142 171)(143 172)(144 173)(145 174)(151 189)(152 190)(153 186)(154 187)(155 188)(156 166)(157 167)(158 168)(159 169)(160 170)(176 201)(177 202)(178 203)(179 204)(180 205)(181 215)(182 211)(183 212)(184 213)(185 214)(191 229)(192 230)(193 226)(194 227)(195 228)(196 206)(197 207)(198 208)(199 209)(200 210)(216 241)(217 242)(218 243)(219 244)(220 245)(221 255)(222 251)(223 252)(224 253)(225 254)(231 269)(232 270)(233 266)(234 267)(235 268)(236 246)(237 247)(238 248)(239 249)(240 250)(256 281)(257 282)(258 283)(259 284)(260 285)(261 295)(262 291)(263 292)(264 293)(265 294)(271 309)(272 310)(273 306)(274 307)(275 308)(276 286)(277 287)(278 288)(279 289)(280 290)
(1 66)(2 67)(3 68)(4 69)(5 70)(6 23)(7 24)(8 25)(9 21)(10 22)(11 36)(12 37)(13 38)(14 39)(15 40)(16 33)(17 34)(18 35)(19 31)(20 32)(26 45)(27 41)(28 42)(29 43)(30 44)(46 53)(47 54)(48 55)(49 51)(50 52)(56 73)(57 74)(58 75)(59 71)(60 72)(61 78)(62 79)(63 80)(64 76)(65 77)(81 106)(82 107)(83 108)(84 109)(85 110)(86 93)(87 94)(88 95)(89 91)(90 92)(96 113)(97 114)(98 115)(99 111)(100 112)(101 118)(102 119)(103 120)(104 116)(105 117)(121 146)(122 147)(123 148)(124 149)(125 150)(126 133)(127 134)(128 135)(129 131)(130 132)(136 153)(137 154)(138 155)(139 151)(140 152)(141 158)(142 159)(143 160)(144 156)(145 157)(161 186)(162 187)(163 188)(164 189)(165 190)(166 173)(167 174)(168 175)(169 171)(170 172)(176 193)(177 194)(178 195)(179 191)(180 192)(181 198)(182 199)(183 200)(184 196)(185 197)(201 226)(202 227)(203 228)(204 229)(205 230)(206 213)(207 214)(208 215)(209 211)(210 212)(216 233)(217 234)(218 235)(219 231)(220 232)(221 238)(222 239)(223 240)(224 236)(225 237)(241 266)(242 267)(243 268)(244 269)(245 270)(246 253)(247 254)(248 255)(249 251)(250 252)(256 273)(257 274)(258 275)(259 271)(260 272)(261 278)(262 279)(263 280)(264 276)(265 277)(281 306)(282 307)(283 308)(284 309)(285 310)(286 293)(287 294)(288 295)(289 291)(290 292)(296 313)(297 314)(298 315)(299 311)(300 312)(301 318)(302 319)(303 320)(304 316)(305 317)
(1 12)(2 13)(3 14)(4 15)(5 11)(6 304)(7 305)(8 301)(9 302)(10 303)(16 297)(17 298)(18 299)(19 300)(20 296)(21 319)(22 320)(23 316)(24 317)(25 318)(26 50)(27 46)(28 47)(29 48)(30 49)(31 312)(32 313)(33 314)(34 315)(35 311)(36 70)(37 66)(38 67)(39 68)(40 69)(41 53)(42 54)(43 55)(44 51)(45 52)(56 94)(57 95)(58 91)(59 92)(60 93)(61 82)(62 83)(63 84)(64 85)(65 81)(71 90)(72 86)(73 87)(74 88)(75 89)(76 110)(77 106)(78 107)(79 108)(80 109)(96 134)(97 135)(98 131)(99 132)(100 133)(101 122)(102 123)(103 124)(104 125)(105 121)(111 130)(112 126)(113 127)(114 128)(115 129)(116 150)(117 146)(118 147)(119 148)(120 149)(136 174)(137 175)(138 171)(139 172)(140 173)(141 162)(142 163)(143 164)(144 165)(145 161)(151 170)(152 166)(153 167)(154 168)(155 169)(156 190)(157 186)(158 187)(159 188)(160 189)(176 214)(177 215)(178 211)(179 212)(180 213)(181 202)(182 203)(183 204)(184 205)(185 201)(191 210)(192 206)(193 207)(194 208)(195 209)(196 230)(197 226)(198 227)(199 228)(200 229)(216 254)(217 255)(218 251)(219 252)(220 253)(221 242)(222 243)(223 244)(224 245)(225 241)(231 250)(232 246)(233 247)(234 248)(235 249)(236 270)(237 266)(238 267)(239 268)(240 269)(256 294)(257 295)(258 291)(259 292)(260 293)(261 282)(262 283)(263 284)(264 285)(265 281)(271 290)(272 286)(273 287)(274 288)(275 289)(276 310)(277 306)(278 307)(279 308)(280 309)
(1 207 47 201)(2 208 48 202)(3 209 49 203)(4 210 50 204)(5 206 46 205)(6 165 31 166)(7 161 32 167)(8 162 33 168)(9 163 34 169)(10 164 35 170)(11 192 27 184)(12 193 28 185)(13 194 29 181)(14 195 30 182)(15 191 26 183)(16 175 25 187)(17 171 21 188)(18 172 22 189)(19 173 23 190)(20 174 24 186)(36 180 41 196)(37 176 42 197)(38 177 43 198)(39 178 44 199)(40 179 45 200)(51 228 68 211)(52 229 69 212)(53 230 70 213)(54 226 66 214)(55 227 67 215)(56 237 77 216)(57 238 78 217)(58 239 79 218)(59 240 80 219)(60 236 76 220)(61 234 74 221)(62 235 75 222)(63 231 71 223)(64 232 72 224)(65 233 73 225)(81 247 87 241)(82 248 88 242)(83 249 89 243)(84 250 90 244)(85 246 86 245)(91 268 108 251)(92 269 109 252)(93 270 110 253)(94 266 106 254)(95 267 107 255)(96 277 117 256)(97 278 118 257)(98 279 119 258)(99 280 120 259)(100 276 116 260)(101 274 114 261)(102 275 115 262)(103 271 111 263)(104 272 112 264)(105 273 113 265)(121 287 127 281)(122 288 128 282)(123 289 129 283)(124 290 130 284)(125 286 126 285)(131 308 148 291)(132 309 149 292)(133 310 150 293)(134 306 146 294)(135 307 147 295)(136 317 157 296)(137 318 158 297)(138 319 159 298)(139 320 160 299)(140 316 156 300)(141 314 154 301)(142 315 155 302)(143 311 151 303)(144 312 152 304)(145 313 153 305)
(1 113 28 121)(2 114 29 122)(3 115 30 123)(4 111 26 124)(5 112 27 125)(6 220 312 270)(7 216 313 266)(8 217 314 267)(9 218 315 268)(10 219 311 269)(11 126 46 104)(12 127 47 105)(13 128 48 101)(14 129 49 102)(15 130 50 103)(16 221 318 248)(17 222 319 249)(18 223 320 250)(19 224 316 246)(20 225 317 247)(21 235 298 243)(22 231 299 244)(23 232 300 245)(24 233 296 241)(25 234 297 242)(31 236 304 253)(32 237 305 254)(33 238 301 255)(34 239 302 251)(35 240 303 252)(36 133 53 116)(37 134 54 117)(38 135 55 118)(39 131 51 119)(40 132 52 120)(41 150 70 100)(42 146 66 96)(43 147 67 97)(44 148 68 98)(45 149 69 99)(56 186 106 136)(57 187 107 137)(58 188 108 138)(59 189 109 139)(60 190 110 140)(61 168 88 141)(62 169 89 142)(63 170 90 143)(64 166 86 144)(65 167 87 145)(71 164 84 151)(72 165 85 152)(73 161 81 153)(74 162 82 154)(75 163 83 155)(76 173 93 156)(77 174 94 157)(78 175 95 158)(79 171 91 159)(80 172 92 160)(176 273 226 281)(177 274 227 282)(178 275 228 283)(179 271 229 284)(180 272 230 285)(181 278 208 295)(182 279 209 291)(183 280 210 292)(184 276 206 293)(185 277 207 294)(191 259 204 309)(192 260 205 310)(193 256 201 306)(194 257 202 307)(195 258 203 308)(196 264 213 286)(197 265 214 287)(198 261 215 288)(199 262 211 289)(200 263 212 290)
(1 56 42 81)(2 57 43 82)(3 58 44 83)(4 59 45 84)(5 60 41 85)(6 276 300 286)(7 277 296 287)(8 278 297 288)(9 279 298 289)(10 280 299 290)(11 93 53 64)(12 94 54 65)(13 95 55 61)(14 91 51 62)(15 92 52 63)(16 274 301 307)(17 275 302 308)(18 271 303 309)(19 272 304 310)(20 273 305 306)(21 262 315 291)(22 263 311 292)(23 264 312 293)(24 265 313 294)(25 261 314 295)(26 109 69 71)(27 110 70 72)(28 106 66 73)(29 107 67 74)(30 108 68 75)(31 260 316 285)(32 256 317 281)(33 257 318 282)(34 258 319 283)(35 259 320 284)(36 86 46 76)(37 87 47 77)(38 88 48 78)(39 89 49 79)(40 90 50 80)(96 145 121 174)(97 141 122 175)(98 142 123 171)(99 143 124 172)(100 144 125 173)(101 137 135 162)(102 138 131 163)(103 139 132 164)(104 140 133 165)(105 136 134 161)(111 160 149 170)(112 156 150 166)(113 157 146 167)(114 158 147 168)(115 159 148 169)(116 152 126 190)(117 153 127 186)(118 154 128 187)(119 155 129 188)(120 151 130 189)(176 266 201 233)(177 267 202 234)(178 268 203 235)(179 269 204 231)(180 270 205 232)(181 248 215 238)(182 249 211 239)(183 250 212 240)(184 246 213 236)(185 247 214 237)(191 244 229 219)(192 245 230 220)(193 241 226 216)(194 242 227 217)(195 243 228 218)(196 253 206 224)(197 254 207 225)(198 255 208 221)(199 251 209 222)(200 252 210 223)

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

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

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

110 conjugacy classes

 class 1 2A ··· 2G 4A ··· 4N 5A 5B 5C 5D 10A ··· 10AB 20A ··· 20BD order 1 2 ··· 2 4 ··· 4 5 5 5 5 10 ··· 10 20 ··· 20 size 1 1 ··· 1 4 ··· 4 1 1 1 1 1 ··· 1 4 ··· 4

110 irreducible representations

 dim 1 1 1 1 2 2 type + + image C1 C2 C5 C10 C4○D4 C5×C4○D4 kernel C5×C23.84C23 C5×C2.C42 C23.84C23 C2.C42 C2×C10 C22 # reps 1 7 4 28 14 56

Matrix representation of C5×C23.84C23 in GL6(𝔽41)

 16 0 0 0 0 0 0 16 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
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 12 12 0 0 0 0 12 29 0 0 0 0 0 0 10 39 0 0 0 0 30 31 0 0 0 0 0 0 0 32 0 0 0 0 9 0
,
 0 32 0 0 0 0 9 0 0 0 0 0 0 0 26 34 0 0 0 0 32 15 0 0 0 0 0 0 32 0 0 0 0 0 0 9
,
 0 1 0 0 0 0 40 0 0 0 0 0 0 0 40 39 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 40 0

G:=sub<GL(6,GF(41))| [16,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[12,12,0,0,0,0,12,29,0,0,0,0,0,0,10,30,0,0,0,0,39,31,0,0,0,0,0,0,0,9,0,0,0,0,32,0],[0,9,0,0,0,0,32,0,0,0,0,0,0,0,26,32,0,0,0,0,34,15,0,0,0,0,0,0,32,0,0,0,0,0,0,9],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,40,1,0,0,0,0,39,1,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;

C5×C23.84C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{84}C_2^3
% in TeX

G:=Group("C5xC2^3.84C2^3");
// GroupNames label

G:=SmallGroup(320,902);
// by ID

G=gap.SmallGroup(320,902);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,1960,589,848,1766,1731,226]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=d^2=1,e^2=b*c*d,f^2=c*b=b*c,g^2=b,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*d=d*b,f*e*f^-1=b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,g*e*g^-1=c*e=e*c,c*f=f*c,c*g=g*c,d*e=e*d,g*f*g^-1=d*f=f*d,d*g=g*d>;
// generators/relations

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