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G = C206(C4⋊C4)  order 320 = 26·5

3rd semidirect product of C20 and C4⋊C4 acting via C4⋊C4/C22=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C206(C4⋊C4), C4⋊C46Dic5, C41(C4⋊Dic5), C2.5(C20⋊Q8), (C2×C20).20Q8, C10.34(C4×Q8), C2.7(D4×Dic5), C2.4(Q8×Dic5), (C2×C20).140D4, C10.119(C4×D4), (C2×C4).142D20, C10.23(C4⋊Q8), C22.25(Q8×D5), C2.3(C4⋊D20), (C2×Dic5).25Q8, (C2×C4).31Dic10, C22.109(D4×D5), C22.46(C2×D20), C10.52(C4⋊D4), C2.4(D102Q8), (C2×Dic5).154D4, (C22×C4).102D10, C10.48(C22⋊Q8), C2.5(C4.Dic10), (C22×C20).66C22, C10.24(C42.C2), C22.29(C2×Dic10), C23.294(C22×D5), C22.58(D42D5), (C22×C10).349C23, C56(C23.65C23), C22.26(Q82D5), C22.42(C22×Dic5), C10.10C42.29C2, (C22×Dic5).214C22, (C5×C4⋊C4)⋊16C4, C10.61(C2×C4⋊C4), (C2×C4⋊C4).22D5, (C10×C4⋊C4).15C2, C2.8(C2×C4⋊Dic5), (C2×C4×Dic5).8C2, (C2×C10).38(C2×Q8), (C2×C20).218(C2×C4), (C2×C10).333(C2×D4), (C2×C4⋊Dic5).36C2, (C2×C4).18(C2×Dic5), (C2×C10).187(C4○D4), (C2×C10).282(C22×C4), SmallGroup(320,612)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C206(C4⋊C4)
C1C5C10C2×C10C22×C10C22×Dic5C2×C4×Dic5 — C206(C4⋊C4)
C5C2×C10 — C206(C4⋊C4)
C1C23C2×C4⋊C4

Generators and relations for C206(C4⋊C4)
 G = < a,b,c | a20=b4=c4=1, bab-1=a11, cac-1=a9, cbc-1=b-1 >

Subgroups: 510 in 170 conjugacy classes, 91 normal (41 characteristic)
C1, C2 [×7], C4 [×4], C4 [×10], C22 [×7], C5, C2×C4 [×10], C2×C4 [×18], C23, C10 [×7], C42 [×2], C4⋊C4 [×4], C4⋊C4 [×6], C22×C4, C22×C4 [×2], C22×C4 [×4], Dic5 [×6], C20 [×4], C20 [×4], C2×C10 [×7], C2.C42 [×2], C2×C42, C2×C4⋊C4, C2×C4⋊C4 [×3], C2×Dic5 [×4], C2×Dic5 [×10], C2×C20 [×10], C2×C20 [×4], C22×C10, C23.65C23, C4×Dic5 [×2], C4⋊Dic5 [×6], C5×C4⋊C4 [×4], C22×Dic5 [×2], C22×Dic5 [×2], C22×C20, C22×C20 [×2], C10.10C42 [×2], C2×C4×Dic5, C2×C4⋊Dic5, C2×C4⋊Dic5 [×2], C10×C4⋊C4, C206(C4⋊C4)
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], Q8 [×4], C23, D5, C4⋊C4 [×4], C22×C4, C2×D4 [×2], C2×Q8 [×2], C4○D4 [×2], Dic5 [×4], D10 [×3], C2×C4⋊C4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C42.C2, C4⋊Q8, Dic10 [×2], D20 [×2], C2×Dic5 [×6], C22×D5, C23.65C23, C4⋊Dic5 [×4], C2×Dic10, C2×D20, D4×D5, D42D5, Q8×D5, Q82D5, C22×Dic5, C20⋊Q8, C4.Dic10, C4⋊D20, D102Q8, C2×C4⋊Dic5, D4×Dic5, Q8×Dic5, C206(C4⋊C4)

Smallest permutation representation of C206(C4⋊C4)
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)
(1 282 141 235)(2 293 142 226)(3 284 143 237)(4 295 144 228)(5 286 145 239)(6 297 146 230)(7 288 147 221)(8 299 148 232)(9 290 149 223)(10 281 150 234)(11 292 151 225)(12 283 152 236)(13 294 153 227)(14 285 154 238)(15 296 155 229)(16 287 156 240)(17 298 157 231)(18 289 158 222)(19 300 159 233)(20 291 160 224)(21 100 276 248)(22 91 277 259)(23 82 278 250)(24 93 279 241)(25 84 280 252)(26 95 261 243)(27 86 262 254)(28 97 263 245)(29 88 264 256)(30 99 265 247)(31 90 266 258)(32 81 267 249)(33 92 268 260)(34 83 269 251)(35 94 270 242)(36 85 271 253)(37 96 272 244)(38 87 273 255)(39 98 274 246)(40 89 275 257)(41 103 214 188)(42 114 215 199)(43 105 216 190)(44 116 217 181)(45 107 218 192)(46 118 219 183)(47 109 220 194)(48 120 201 185)(49 111 202 196)(50 102 203 187)(51 113 204 198)(52 104 205 189)(53 115 206 200)(54 106 207 191)(55 117 208 182)(56 108 209 193)(57 119 210 184)(58 110 211 195)(59 101 212 186)(60 112 213 197)(61 302 133 176)(62 313 134 167)(63 304 135 178)(64 315 136 169)(65 306 137 180)(66 317 138 171)(67 308 139 162)(68 319 140 173)(69 310 121 164)(70 301 122 175)(71 312 123 166)(72 303 124 177)(73 314 125 168)(74 305 126 179)(75 316 127 170)(76 307 128 161)(77 318 129 172)(78 309 130 163)(79 320 131 174)(80 311 132 165)
(1 31 119 67)(2 40 120 76)(3 29 101 65)(4 38 102 74)(5 27 103 63)(6 36 104 72)(7 25 105 61)(8 34 106 70)(9 23 107 79)(10 32 108 68)(11 21 109 77)(12 30 110 66)(13 39 111 75)(14 28 112 64)(15 37 113 73)(16 26 114 62)(17 35 115 71)(18 24 116 80)(19 33 117 69)(20 22 118 78)(41 304 239 86)(42 313 240 95)(43 302 221 84)(44 311 222 93)(45 320 223 82)(46 309 224 91)(47 318 225 100)(48 307 226 89)(49 316 227 98)(50 305 228 87)(51 314 229 96)(52 303 230 85)(53 312 231 94)(54 301 232 83)(55 310 233 92)(56 319 234 81)(57 308 235 90)(58 317 236 99)(59 306 237 88)(60 315 238 97)(121 159 268 182)(122 148 269 191)(123 157 270 200)(124 146 271 189)(125 155 272 198)(126 144 273 187)(127 153 274 196)(128 142 275 185)(129 151 276 194)(130 160 277 183)(131 149 278 192)(132 158 279 181)(133 147 280 190)(134 156 261 199)(135 145 262 188)(136 154 263 197)(137 143 264 186)(138 152 265 195)(139 141 266 184)(140 150 267 193)(161 293 257 201)(162 282 258 210)(163 291 259 219)(164 300 260 208)(165 289 241 217)(166 298 242 206)(167 287 243 215)(168 296 244 204)(169 285 245 213)(170 294 246 202)(171 283 247 211)(172 292 248 220)(173 281 249 209)(174 290 250 218)(175 299 251 207)(176 288 252 216)(177 297 253 205)(178 286 254 214)(179 295 255 203)(180 284 256 212)

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

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

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

68 conjugacy classes

class 1 2A···2G4A4B4C4D4E4F4G4H4I···4P4Q4R4S4T5A5B10A···10N20A···20X
order12···2444444444···444445510···1020···20
size11···12222444410···1020202020222···24···4

68 irreducible representations

dim11111122222222224444
type++++++-+-+-+-++--+
imageC1C2C2C2C2C4D4Q8D4Q8D5C4○D4Dic5D10Dic10D20D4×D5D42D5Q8×D5Q82D5
kernelC206(C4⋊C4)C10.10C42C2×C4×Dic5C2×C4⋊Dic5C10×C4⋊C4C5×C4⋊C4C2×Dic5C2×Dic5C2×C20C2×C20C2×C4⋊C4C2×C10C4⋊C4C22×C4C2×C4C2×C4C22C22C22C22
# reps12131822222486882222

Matrix representation of C206(C4⋊C4) in GL6(𝔽41)

26150000
15150000
000100
0040700
000071
0000400
,
40390000
010000
001000
000100
00003032
0000911
,
4000000
0400000
0017100
00382400
000090
00001932

G:=sub<GL(6,GF(41))| [26,15,0,0,0,0,15,15,0,0,0,0,0,0,0,40,0,0,0,0,1,7,0,0,0,0,0,0,7,40,0,0,0,0,1,0],[40,0,0,0,0,0,39,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,30,9,0,0,0,0,32,11],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,17,38,0,0,0,0,1,24,0,0,0,0,0,0,9,19,0,0,0,0,0,32] >;

C206(C4⋊C4) in GAP, Magma, Sage, TeX

C_{20}\rtimes_6(C_4\rtimes C_4)
% in TeX

G:=Group("C20:6(C4:C4)");
// GroupNames label

G:=SmallGroup(320,612);
// by ID

G=gap.SmallGroup(320,612);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,232,422,387,100,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=b^4=c^4=1,b*a*b^-1=a^11,c*a*c^-1=a^9,c*b*c^-1=b^-1>;
// generators/relations

׿
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