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G = C5×C23.78C23order 320 = 26·5

Direct product of C5 and C23.78C23

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

Aliases: C5×C23.78C23, (C2×C20)⋊8Q8, (C2×C20).308D4, C10.38(C4⋊Q8), C10.93C22≀C2, C22.71(D4×C10), (C22×Q8).2C10, C22.21(Q8×C10), C10.88(C22⋊Q8), C2.C42.8C10, C23.78(C22×C10), (C22×C20).403C22, (C22×C10).459C23, (C2×C4)⋊1(C5×Q8), C2.4(C5×C4⋊Q8), (C2×C4⋊C4).9C10, (C2×C4).15(C5×D4), (C10×C4⋊C4).38C2, (Q8×C2×C10).12C2, C2.7(C5×C22⋊Q8), C2.7(C5×C22≀C2), (C2×C10).611(C2×D4), (C2×C10).109(C2×Q8), C22.38(C5×C4○D4), (C22×C4).21(C2×C10), (C2×C10).219(C4○D4), (C5×C2.C42).27C2, SmallGroup(320,896)

Series: Derived Chief Lower central Upper central

C1C23 — C5×C23.78C23
C1C2C22C23C22×C10C22×C20Q8×C2×C10 — C5×C23.78C23
C1C23 — C5×C23.78C23
C1C22×C10 — C5×C23.78C23

Generators and relations for C5×C23.78C23
 G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=f2=g2=b, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, 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: 282 in 182 conjugacy classes, 86 normal (14 characteristic)
C1, C2, C2 [×6], C4 [×13], C22, C22 [×6], C5, C2×C4 [×12], C2×C4 [×15], Q8 [×8], C23, C10, C10 [×6], C4⋊C4 [×6], C22×C4, C22×C4 [×6], C2×Q8 [×6], C20 [×13], C2×C10, C2×C10 [×6], C2.C42 [×3], C2×C4⋊C4 [×3], C22×Q8, C2×C20 [×12], C2×C20 [×15], C5×Q8 [×8], C22×C10, C23.78C23, C5×C4⋊C4 [×6], C22×C20, C22×C20 [×6], Q8×C10 [×6], C5×C2.C42 [×3], C10×C4⋊C4 [×3], Q8×C2×C10, C5×C23.78C23
Quotients: C1, C2 [×7], C22 [×7], C5, D4 [×6], Q8 [×6], C23, C10 [×7], C2×D4 [×3], C2×Q8 [×3], C4○D4, C2×C10 [×7], C22≀C2, C22⋊Q8 [×3], C4⋊Q8 [×3], C5×D4 [×6], C5×Q8 [×6], C22×C10, C23.78C23, D4×C10 [×3], Q8×C10 [×3], C5×C4○D4, C5×C22≀C2, C5×C22⋊Q8 [×3], C5×C4⋊Q8 [×3], C5×C23.78C23

Smallest permutation representation of C5×C23.78C23
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)
(1 176 42 201)(2 177 43 202)(3 178 44 203)(4 179 45 204)(5 180 41 205)(6 165 300 140)(7 161 296 136)(8 162 297 137)(9 163 298 138)(10 164 299 139)(11 213 53 184)(12 214 54 185)(13 215 55 181)(14 211 51 182)(15 212 52 183)(16 175 301 141)(17 171 302 142)(18 172 303 143)(19 173 304 144)(20 174 305 145)(21 188 315 155)(22 189 311 151)(23 190 312 152)(24 186 313 153)(25 187 314 154)(26 229 69 191)(27 230 70 192)(28 226 66 193)(29 227 67 194)(30 228 68 195)(31 166 316 156)(32 167 317 157)(33 168 318 158)(34 169 319 159)(35 170 320 160)(36 206 46 196)(37 207 47 197)(38 208 48 198)(39 209 49 199)(40 210 50 200)(56 241 81 216)(57 242 82 217)(58 243 83 218)(59 244 84 219)(60 245 85 220)(61 255 95 221)(62 251 91 222)(63 252 92 223)(64 253 93 224)(65 254 94 225)(71 269 109 231)(72 270 110 232)(73 266 106 233)(74 267 107 234)(75 268 108 235)(76 246 86 236)(77 247 87 237)(78 248 88 238)(79 249 89 239)(80 250 90 240)(96 281 121 256)(97 282 122 257)(98 283 123 258)(99 284 124 259)(100 285 125 260)(101 295 135 261)(102 291 131 262)(103 292 132 263)(104 293 133 264)(105 294 134 265)(111 309 149 271)(112 310 150 272)(113 306 146 273)(114 307 147 274)(115 308 148 275)(116 286 126 276)(117 287 127 277)(118 288 128 278)(119 289 129 279)(120 290 130 280)
(1 96 42 121)(2 97 43 122)(3 98 44 123)(4 99 45 124)(5 100 41 125)(6 220 300 245)(7 216 296 241)(8 217 297 242)(9 218 298 243)(10 219 299 244)(11 133 53 104)(12 134 54 105)(13 135 55 101)(14 131 51 102)(15 132 52 103)(16 221 301 255)(17 222 302 251)(18 223 303 252)(19 224 304 253)(20 225 305 254)(21 235 315 268)(22 231 311 269)(23 232 312 270)(24 233 313 266)(25 234 314 267)(26 149 69 111)(27 150 70 112)(28 146 66 113)(29 147 67 114)(30 148 68 115)(31 236 316 246)(32 237 317 247)(33 238 318 248)(34 239 319 249)(35 240 320 250)(36 126 46 116)(37 127 47 117)(38 128 48 118)(39 129 49 119)(40 130 50 120)(56 161 81 136)(57 162 82 137)(58 163 83 138)(59 164 84 139)(60 165 85 140)(61 175 95 141)(62 171 91 142)(63 172 92 143)(64 173 93 144)(65 174 94 145)(71 189 109 151)(72 190 110 152)(73 186 106 153)(74 187 107 154)(75 188 108 155)(76 166 86 156)(77 167 87 157)(78 168 88 158)(79 169 89 159)(80 170 90 160)(176 256 201 281)(177 257 202 282)(178 258 203 283)(179 259 204 284)(180 260 205 285)(181 261 215 295)(182 262 211 291)(183 263 212 292)(184 264 213 293)(185 265 214 294)(191 271 229 309)(192 272 230 310)(193 273 226 306)(194 274 227 307)(195 275 228 308)(196 276 206 286)(197 277 207 287)(198 278 208 288)(199 279 209 289)(200 280 210 290)
(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), (1,176,42,201)(2,177,43,202)(3,178,44,203)(4,179,45,204)(5,180,41,205)(6,165,300,140)(7,161,296,136)(8,162,297,137)(9,163,298,138)(10,164,299,139)(11,213,53,184)(12,214,54,185)(13,215,55,181)(14,211,51,182)(15,212,52,183)(16,175,301,141)(17,171,302,142)(18,172,303,143)(19,173,304,144)(20,174,305,145)(21,188,315,155)(22,189,311,151)(23,190,312,152)(24,186,313,153)(25,187,314,154)(26,229,69,191)(27,230,70,192)(28,226,66,193)(29,227,67,194)(30,228,68,195)(31,166,316,156)(32,167,317,157)(33,168,318,158)(34,169,319,159)(35,170,320,160)(36,206,46,196)(37,207,47,197)(38,208,48,198)(39,209,49,199)(40,210,50,200)(56,241,81,216)(57,242,82,217)(58,243,83,218)(59,244,84,219)(60,245,85,220)(61,255,95,221)(62,251,91,222)(63,252,92,223)(64,253,93,224)(65,254,94,225)(71,269,109,231)(72,270,110,232)(73,266,106,233)(74,267,107,234)(75,268,108,235)(76,246,86,236)(77,247,87,237)(78,248,88,238)(79,249,89,239)(80,250,90,240)(96,281,121,256)(97,282,122,257)(98,283,123,258)(99,284,124,259)(100,285,125,260)(101,295,135,261)(102,291,131,262)(103,292,132,263)(104,293,133,264)(105,294,134,265)(111,309,149,271)(112,310,150,272)(113,306,146,273)(114,307,147,274)(115,308,148,275)(116,286,126,276)(117,287,127,277)(118,288,128,278)(119,289,129,279)(120,290,130,280), (1,96,42,121)(2,97,43,122)(3,98,44,123)(4,99,45,124)(5,100,41,125)(6,220,300,245)(7,216,296,241)(8,217,297,242)(9,218,298,243)(10,219,299,244)(11,133,53,104)(12,134,54,105)(13,135,55,101)(14,131,51,102)(15,132,52,103)(16,221,301,255)(17,222,302,251)(18,223,303,252)(19,224,304,253)(20,225,305,254)(21,235,315,268)(22,231,311,269)(23,232,312,270)(24,233,313,266)(25,234,314,267)(26,149,69,111)(27,150,70,112)(28,146,66,113)(29,147,67,114)(30,148,68,115)(31,236,316,246)(32,237,317,247)(33,238,318,248)(34,239,319,249)(35,240,320,250)(36,126,46,116)(37,127,47,117)(38,128,48,118)(39,129,49,119)(40,130,50,120)(56,161,81,136)(57,162,82,137)(58,163,83,138)(59,164,84,139)(60,165,85,140)(61,175,95,141)(62,171,91,142)(63,172,92,143)(64,173,93,144)(65,174,94,145)(71,189,109,151)(72,190,110,152)(73,186,106,153)(74,187,107,154)(75,188,108,155)(76,166,86,156)(77,167,87,157)(78,168,88,158)(79,169,89,159)(80,170,90,160)(176,256,201,281)(177,257,202,282)(178,258,203,283)(179,259,204,284)(180,260,205,285)(181,261,215,295)(182,262,211,291)(183,263,212,292)(184,264,213,293)(185,265,214,294)(191,271,229,309)(192,272,230,310)(193,273,226,306)(194,274,227,307)(195,275,228,308)(196,276,206,286)(197,277,207,287)(198,278,208,288)(199,279,209,289)(200,280,210,290), (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), (1,176,42,201)(2,177,43,202)(3,178,44,203)(4,179,45,204)(5,180,41,205)(6,165,300,140)(7,161,296,136)(8,162,297,137)(9,163,298,138)(10,164,299,139)(11,213,53,184)(12,214,54,185)(13,215,55,181)(14,211,51,182)(15,212,52,183)(16,175,301,141)(17,171,302,142)(18,172,303,143)(19,173,304,144)(20,174,305,145)(21,188,315,155)(22,189,311,151)(23,190,312,152)(24,186,313,153)(25,187,314,154)(26,229,69,191)(27,230,70,192)(28,226,66,193)(29,227,67,194)(30,228,68,195)(31,166,316,156)(32,167,317,157)(33,168,318,158)(34,169,319,159)(35,170,320,160)(36,206,46,196)(37,207,47,197)(38,208,48,198)(39,209,49,199)(40,210,50,200)(56,241,81,216)(57,242,82,217)(58,243,83,218)(59,244,84,219)(60,245,85,220)(61,255,95,221)(62,251,91,222)(63,252,92,223)(64,253,93,224)(65,254,94,225)(71,269,109,231)(72,270,110,232)(73,266,106,233)(74,267,107,234)(75,268,108,235)(76,246,86,236)(77,247,87,237)(78,248,88,238)(79,249,89,239)(80,250,90,240)(96,281,121,256)(97,282,122,257)(98,283,123,258)(99,284,124,259)(100,285,125,260)(101,295,135,261)(102,291,131,262)(103,292,132,263)(104,293,133,264)(105,294,134,265)(111,309,149,271)(112,310,150,272)(113,306,146,273)(114,307,147,274)(115,308,148,275)(116,286,126,276)(117,287,127,277)(118,288,128,278)(119,289,129,279)(120,290,130,280), (1,96,42,121)(2,97,43,122)(3,98,44,123)(4,99,45,124)(5,100,41,125)(6,220,300,245)(7,216,296,241)(8,217,297,242)(9,218,298,243)(10,219,299,244)(11,133,53,104)(12,134,54,105)(13,135,55,101)(14,131,51,102)(15,132,52,103)(16,221,301,255)(17,222,302,251)(18,223,303,252)(19,224,304,253)(20,225,305,254)(21,235,315,268)(22,231,311,269)(23,232,312,270)(24,233,313,266)(25,234,314,267)(26,149,69,111)(27,150,70,112)(28,146,66,113)(29,147,67,114)(30,148,68,115)(31,236,316,246)(32,237,317,247)(33,238,318,248)(34,239,319,249)(35,240,320,250)(36,126,46,116)(37,127,47,117)(38,128,48,118)(39,129,49,119)(40,130,50,120)(56,161,81,136)(57,162,82,137)(58,163,83,138)(59,164,84,139)(60,165,85,140)(61,175,95,141)(62,171,91,142)(63,172,92,143)(64,173,93,144)(65,174,94,145)(71,189,109,151)(72,190,110,152)(73,186,106,153)(74,187,107,154)(75,188,108,155)(76,166,86,156)(77,167,87,157)(78,168,88,158)(79,169,89,159)(80,170,90,160)(176,256,201,281)(177,257,202,282)(178,258,203,283)(179,259,204,284)(180,260,205,285)(181,261,215,295)(182,262,211,291)(183,263,212,292)(184,264,213,293)(185,265,214,294)(191,271,229,309)(192,272,230,310)(193,273,226,306)(194,274,227,307)(195,275,228,308)(196,276,206,286)(197,277,207,287)(198,278,208,288)(199,279,209,289)(200,280,210,290), (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)], [(1,176,42,201),(2,177,43,202),(3,178,44,203),(4,179,45,204),(5,180,41,205),(6,165,300,140),(7,161,296,136),(8,162,297,137),(9,163,298,138),(10,164,299,139),(11,213,53,184),(12,214,54,185),(13,215,55,181),(14,211,51,182),(15,212,52,183),(16,175,301,141),(17,171,302,142),(18,172,303,143),(19,173,304,144),(20,174,305,145),(21,188,315,155),(22,189,311,151),(23,190,312,152),(24,186,313,153),(25,187,314,154),(26,229,69,191),(27,230,70,192),(28,226,66,193),(29,227,67,194),(30,228,68,195),(31,166,316,156),(32,167,317,157),(33,168,318,158),(34,169,319,159),(35,170,320,160),(36,206,46,196),(37,207,47,197),(38,208,48,198),(39,209,49,199),(40,210,50,200),(56,241,81,216),(57,242,82,217),(58,243,83,218),(59,244,84,219),(60,245,85,220),(61,255,95,221),(62,251,91,222),(63,252,92,223),(64,253,93,224),(65,254,94,225),(71,269,109,231),(72,270,110,232),(73,266,106,233),(74,267,107,234),(75,268,108,235),(76,246,86,236),(77,247,87,237),(78,248,88,238),(79,249,89,239),(80,250,90,240),(96,281,121,256),(97,282,122,257),(98,283,123,258),(99,284,124,259),(100,285,125,260),(101,295,135,261),(102,291,131,262),(103,292,132,263),(104,293,133,264),(105,294,134,265),(111,309,149,271),(112,310,150,272),(113,306,146,273),(114,307,147,274),(115,308,148,275),(116,286,126,276),(117,287,127,277),(118,288,128,278),(119,289,129,279),(120,290,130,280)], [(1,96,42,121),(2,97,43,122),(3,98,44,123),(4,99,45,124),(5,100,41,125),(6,220,300,245),(7,216,296,241),(8,217,297,242),(9,218,298,243),(10,219,299,244),(11,133,53,104),(12,134,54,105),(13,135,55,101),(14,131,51,102),(15,132,52,103),(16,221,301,255),(17,222,302,251),(18,223,303,252),(19,224,304,253),(20,225,305,254),(21,235,315,268),(22,231,311,269),(23,232,312,270),(24,233,313,266),(25,234,314,267),(26,149,69,111),(27,150,70,112),(28,146,66,113),(29,147,67,114),(30,148,68,115),(31,236,316,246),(32,237,317,247),(33,238,318,248),(34,239,319,249),(35,240,320,250),(36,126,46,116),(37,127,47,117),(38,128,48,118),(39,129,49,119),(40,130,50,120),(56,161,81,136),(57,162,82,137),(58,163,83,138),(59,164,84,139),(60,165,85,140),(61,175,95,141),(62,171,91,142),(63,172,92,143),(64,173,93,144),(65,174,94,145),(71,189,109,151),(72,190,110,152),(73,186,106,153),(74,187,107,154),(75,188,108,155),(76,166,86,156),(77,167,87,157),(78,168,88,158),(79,169,89,159),(80,170,90,160),(176,256,201,281),(177,257,202,282),(178,258,203,283),(179,259,204,284),(180,260,205,285),(181,261,215,295),(182,262,211,291),(183,263,212,292),(184,264,213,293),(185,265,214,294),(191,271,229,309),(192,272,230,310),(193,273,226,306),(194,274,227,307),(195,275,228,308),(196,276,206,286),(197,277,207,287),(198,278,208,288),(199,279,209,289),(200,280,210,290)], [(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···2G4A···4N5A5B5C5D10A···10AB20A···20BD
order12···24···4555510···1020···20
size11···14···411111···14···4

110 irreducible representations

dim11111111222222
type+++++-
imageC1C2C2C2C5C10C10C10D4Q8C4○D4C5×D4C5×Q8C5×C4○D4
kernelC5×C23.78C23C5×C2.C42C10×C4⋊C4Q8×C2×C10C23.78C23C2.C42C2×C4⋊C4C22×Q8C2×C20C2×C20C2×C10C2×C4C2×C4C22
# reps133141212466224248

Matrix representation of C5×C23.78C23 in GL6(𝔽41)

100000
010000
0018000
0001800
0000160
0000016
,
4000000
0400000
0040000
0004000
0000400
0000040
,
100000
010000
001000
000100
0000400
0000040
,
100000
010000
0040000
0004000
0000400
0000040
,
010000
4000000
000100
0040000
00002734
00003414
,
3200000
090000
0032100
00213800
00003414
0000147
,
3200000
0320000
000100
0040000
000001
0000400

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,18,0,0,0,0,0,0,18,0,0,0,0,0,0,16,0,0,0,0,0,0,16],[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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[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],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,27,34,0,0,0,0,34,14],[32,0,0,0,0,0,0,9,0,0,0,0,0,0,3,21,0,0,0,0,21,38,0,0,0,0,0,0,34,14,0,0,0,0,14,7],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;

C5×C23.78C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{78}C_2^3
% in TeX

G:=Group("C5xC2^3.78C2^3");
// GroupNames label

G:=SmallGroup(320,896);
// by ID

G=gap.SmallGroup(320,896);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,280,589,288,1766,1731,226]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=d^2=1,e^2=f^2=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*c=c*b,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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𝔽