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G = C42.147D10order 320 = 26·5

147th non-split extension by C42 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C42.147D10, C10.272- 1+4, C4⋊C4.110D10, C42.C2.7D5, (C4×C20).223C22, (C2×C10).230C24, (C2×C20).187C23, C5⋊(C22.58C24), C4.Dic10.14C2, C20.6Q8.12C2, C4⋊Dic5.237C22, Dic5.Q8.3C2, C22.251(C23×D5), (C4×Dic5).146C22, (C2×Dic5).120C23, C10.D4.85C22, C2.56(D4.10D10), C2.28(Q8.10D10), (C5×C42.C2).6C2, (C5×C4⋊C4).185C22, (C2×C4).202(C22×D5), SmallGroup(320,1358)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C42.147D10
C1C5C10C2×C10C2×Dic5C4×Dic5Dic5.Q8 — C42.147D10
C5C2×C10 — C42.147D10
C1C22C42.C2

Generators and relations for C42.147D10
 G = < a,b,c,d | a4=b4=1, c10=a2, d2=a2b2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c9 >

Subgroups: 470 in 172 conjugacy classes, 91 normal (13 characteristic)
C1, C2, C2 [×2], C4 [×15], C22, C5, C2×C4, C2×C4 [×6], C2×C4 [×8], C10, C10 [×2], C42, C42 [×4], C4⋊C4 [×6], C4⋊C4 [×24], Dic5 [×8], C20 [×7], C2×C10, C42.C2, C42.C2 [×14], C2×Dic5 [×8], C2×C20, C2×C20 [×6], C22.58C24, C4×Dic5 [×4], C10.D4 [×16], C4⋊Dic5 [×8], C4×C20, C5×C4⋊C4 [×6], C20.6Q8 [×2], Dic5.Q8 [×8], C4.Dic10 [×4], C5×C42.C2, C42.147D10
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C24, D10 [×7], 2- 1+4 [×3], C22×D5 [×7], C22.58C24, C23×D5, Q8.10D10, D4.10D10 [×2], C42.147D10

Smallest permutation representation of C42.147D10
Regular action on 320 points
Generators in S320
(1 300 11 290)(2 34 12 24)(3 282 13 292)(4 36 14 26)(5 284 15 294)(6 38 16 28)(7 286 17 296)(8 40 18 30)(9 288 19 298)(10 22 20 32)(21 124 31 134)(23 126 33 136)(25 128 35 138)(27 130 37 140)(29 132 39 122)(41 101 51 111)(42 209 52 219)(43 103 53 113)(44 211 54 201)(45 105 55 115)(46 213 56 203)(47 107 57 117)(48 215 58 205)(49 109 59 119)(50 217 60 207)(61 234 71 224)(62 193 72 183)(63 236 73 226)(64 195 74 185)(65 238 75 228)(66 197 76 187)(67 240 77 230)(68 199 78 189)(69 222 79 232)(70 181 80 191)(81 208 91 218)(82 102 92 112)(83 210 93 220)(84 104 94 114)(85 212 95 202)(86 106 96 116)(87 214 97 204)(88 108 98 118)(89 216 99 206)(90 110 100 120)(121 295 131 285)(123 297 133 287)(125 299 135 289)(127 281 137 291)(129 283 139 293)(141 264 151 274)(142 313 152 303)(143 266 153 276)(144 315 154 305)(145 268 155 278)(146 317 156 307)(147 270 157 280)(148 319 158 309)(149 272 159 262)(150 301 160 311)(161 239 171 229)(162 198 172 188)(163 221 173 231)(164 200 174 190)(165 223 175 233)(166 182 176 192)(167 225 177 235)(168 184 178 194)(169 227 179 237)(170 186 180 196)(241 269 251 279)(242 318 252 308)(243 271 253 261)(244 320 254 310)(245 273 255 263)(246 302 256 312)(247 275 257 265)(248 304 258 314)(249 277 259 267)(250 306 260 316)
(1 315 136 277)(2 278 137 316)(3 317 138 279)(4 280 139 318)(5 319 140 261)(6 262 121 320)(7 301 122 263)(8 264 123 302)(9 303 124 265)(10 266 125 304)(11 305 126 267)(12 268 127 306)(13 307 128 269)(14 270 129 308)(15 309 130 271)(16 272 131 310)(17 311 132 273)(18 274 133 312)(19 313 134 275)(20 276 135 314)(21 257 298 152)(22 153 299 258)(23 259 300 154)(24 155 281 260)(25 241 282 156)(26 157 283 242)(27 243 284 158)(28 159 285 244)(29 245 286 160)(30 141 287 246)(31 247 288 142)(32 143 289 248)(33 249 290 144)(34 145 291 250)(35 251 292 146)(36 147 293 252)(37 253 294 148)(38 149 295 254)(39 255 296 150)(40 151 297 256)(41 198 91 230)(42 231 92 199)(43 200 93 232)(44 233 94 181)(45 182 95 234)(46 235 96 183)(47 184 97 236)(48 237 98 185)(49 186 99 238)(50 239 100 187)(51 188 81 240)(52 221 82 189)(53 190 83 222)(54 223 84 191)(55 192 85 224)(56 225 86 193)(57 194 87 226)(58 227 88 195)(59 196 89 228)(60 229 90 197)(61 115 166 212)(62 213 167 116)(63 117 168 214)(64 215 169 118)(65 119 170 216)(66 217 171 120)(67 101 172 218)(68 219 173 102)(69 103 174 220)(70 201 175 104)(71 105 176 202)(72 203 177 106)(73 107 178 204)(74 205 179 108)(75 109 180 206)(76 207 161 110)(77 111 162 208)(78 209 163 112)(79 113 164 210)(80 211 165 114)
(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)
(1 218 126 111)(2 207 127 120)(3 216 128 109)(4 205 129 118)(5 214 130 107)(6 203 131 116)(7 212 132 105)(8 201 133 114)(9 210 134 103)(10 219 135 112)(11 208 136 101)(12 217 137 110)(13 206 138 119)(14 215 139 108)(15 204 140 117)(16 213 121 106)(17 202 122 115)(18 211 123 104)(19 220 124 113)(20 209 125 102)(21 43 288 83)(22 52 289 92)(23 41 290 81)(24 50 291 90)(25 59 292 99)(26 48 293 88)(27 57 294 97)(28 46 295 86)(29 55 296 95)(30 44 297 84)(31 53 298 93)(32 42 299 82)(33 51 300 91)(34 60 281 100)(35 49 282 89)(36 58 283 98)(37 47 284 87)(38 56 285 96)(39 45 286 85)(40 54 287 94)(61 301 176 273)(62 310 177 262)(63 319 178 271)(64 308 179 280)(65 317 180 269)(66 306 161 278)(67 315 162 267)(68 304 163 276)(69 313 164 265)(70 302 165 274)(71 311 166 263)(72 320 167 272)(73 309 168 261)(74 318 169 270)(75 307 170 279)(76 316 171 268)(77 305 172 277)(78 314 173 266)(79 303 174 275)(80 312 175 264)(141 191 256 233)(142 200 257 222)(143 189 258 231)(144 198 259 240)(145 187 260 229)(146 196 241 238)(147 185 242 227)(148 194 243 236)(149 183 244 225)(150 192 245 234)(151 181 246 223)(152 190 247 232)(153 199 248 221)(154 188 249 230)(155 197 250 239)(156 186 251 228)(157 195 252 237)(158 184 253 226)(159 193 254 235)(160 182 255 224)

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

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

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

47 conjugacy classes

class 1 2A2B2C4A···4G4H···4O5A5B10A···10F20A···20L20M···20T
order12224···44···45510···1020···2020···20
size11114···420···20222···24···48···8

47 irreducible representations

dim11111222444
type++++++++--
imageC1C2C2C2C2D5D10D102- 1+4Q8.10D10D4.10D10
kernelC42.147D10C20.6Q8Dic5.Q8C4.Dic10C5×C42.C2C42.C2C42C4⋊C4C10C2C2
# reps128412212348

Matrix representation of C42.147D10 in GL8(𝔽41)

00100000
00010000
400000000
040000000
000000213
0000002839
0000392800
000013200
,
241000000
4017000000
002410000
0040170000
00000010
00000001
000040000
000004000
,
34348330000
718230000
833770000
82334400000
00006351010
00006113129
00001010356
000031293530
,
2325000000
2818000000
0018160000
0013230000
0000002320
0000003518
0000232000
0000351800

G:=sub<GL(8,GF(41))| [0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,39,13,0,0,0,0,0,0,28,2,0,0,0,0,2,28,0,0,0,0,0,0,13,39,0,0],[24,40,0,0,0,0,0,0,1,17,0,0,0,0,0,0,0,0,24,40,0,0,0,0,0,0,1,17,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[34,7,8,8,0,0,0,0,34,1,33,23,0,0,0,0,8,8,7,34,0,0,0,0,33,23,7,40,0,0,0,0,0,0,0,0,6,6,10,31,0,0,0,0,35,11,10,29,0,0,0,0,10,31,35,35,0,0,0,0,10,29,6,30],[23,28,0,0,0,0,0,0,25,18,0,0,0,0,0,0,0,0,18,13,0,0,0,0,0,0,16,23,0,0,0,0,0,0,0,0,0,0,23,35,0,0,0,0,0,0,20,18,0,0,0,0,23,35,0,0,0,0,0,0,20,18,0,0] >;

C42.147D10 in GAP, Magma, Sage, TeX

C_4^2._{147}D_{10}
% in TeX

G:=Group("C4^2.147D10");
// GroupNames label

G:=SmallGroup(320,1358);
// by ID

G=gap.SmallGroup(320,1358);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,758,555,100,675,570,136,12550]);
// Polycyclic

G:=Group<a,b,c,d|a^4=b^4=1,c^10=a^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^9>;
// generators/relations

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