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G = C205(C4⋊C4)  order 320 = 26·5

2nd semidirect product of C20 and C4⋊C4 acting via C4⋊C4/C22=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C205(C4⋊C4), C2.4(C20⋊Q8), (C2×C20).18Q8, Dic54(C4⋊C4), C53(C429C4), (C4×Dic5)⋊11C4, (C2×C20).138D4, C10.20(C4⋊Q8), C22.22(Q8×D5), C2.2(C20⋊D4), C42(C10.D4), (C2×Dic5).22Q8, (C2×C4).29Dic10, C22.107(D4×D5), (C22×C4).38D10, C10.14(C41D4), (C2×Dic5).153D4, C2.3(Dic5⋊Q8), (C22×C20).28C22, C22.27(C2×Dic10), C23.290(C22×D5), (C22×C10).340C23, (C22×Dic5).211C22, C2.20(D5×C4⋊C4), C10.59(C2×C4⋊C4), (C2×C4⋊C4).13D5, (C10×C4⋊C4).12C2, (C2×C4×Dic5).6C2, (C2×C4).152(C4×D5), (C2×C10).76(C2×Q8), C22.133(C2×C4×D5), (C2×C20).256(C2×C4), (C2×C10).329(C2×D4), (C2×C4⋊Dic5).34C2, C22.63(C2×C5⋊D4), (C2×C4).127(C5⋊D4), C2.11(C2×C10.D4), (C2×C10).217(C22×C4), (C2×Dic5).149(C2×C4), (C2×C10.D4).14C2, SmallGroup(320,603)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C205(C4⋊C4)
C1C5C10C2×C10C22×C10C22×Dic5C2×C4×Dic5 — C205(C4⋊C4)
C5C2×C10 — C205(C4⋊C4)
C1C23C2×C4⋊C4

Generators and relations for C205(C4⋊C4)
 G = < a,b,c | a20=b4=c4=1, bab-1=a9, cac-1=a11, cbc-1=b-1 >

Subgroups: 558 in 186 conjugacy classes, 95 normal (23 characteristic)
C1, C2 [×3], C2 [×4], C4 [×4], C4 [×12], C22 [×3], C22 [×4], C5, C2×C4 [×6], C2×C4 [×24], C23, C10 [×3], C10 [×4], C42 [×4], C4⋊C4 [×12], C22×C4, C22×C4 [×2], C22×C4 [×4], Dic5 [×8], Dic5 [×2], C20 [×4], C20 [×2], C2×C10 [×3], C2×C10 [×4], C2×C42, C2×C4⋊C4, C2×C4⋊C4 [×5], C2×Dic5 [×12], C2×Dic5 [×6], C2×C20 [×6], C2×C20 [×6], C22×C10, C429C4, C4×Dic5 [×4], C10.D4 [×8], C4⋊Dic5 [×2], C5×C4⋊C4 [×2], C22×Dic5 [×4], C22×C20, C22×C20 [×2], C2×C4×Dic5, C2×C10.D4 [×4], C2×C4⋊Dic5, C10×C4⋊C4, C205(C4⋊C4)
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×6], Q8 [×6], C23, D5, C4⋊C4 [×12], C22×C4, C2×D4 [×3], C2×Q8 [×3], D10 [×3], C2×C4⋊C4 [×3], C41D4, C4⋊Q8 [×3], Dic10 [×2], C4×D5 [×2], C5⋊D4 [×2], C22×D5, C429C4, C10.D4 [×4], C2×Dic10, C2×C4×D5, D4×D5 [×2], Q8×D5 [×2], C2×C5⋊D4, C20⋊Q8 [×2], D5×C4⋊C4 [×2], C2×C10.D4, C20⋊D4, Dic5⋊Q8, C205(C4⋊C4)

Smallest permutation representation of C205(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)
(1 266 290 311)(2 275 291 320)(3 264 292 309)(4 273 293 318)(5 262 294 307)(6 271 295 316)(7 280 296 305)(8 269 297 314)(9 278 298 303)(10 267 299 312)(11 276 300 301)(12 265 281 310)(13 274 282 319)(14 263 283 308)(15 272 284 317)(16 261 285 306)(17 270 286 315)(18 279 287 304)(19 268 288 313)(20 277 289 302)(21 94 119 79)(22 83 120 68)(23 92 101 77)(24 81 102 66)(25 90 103 75)(26 99 104 64)(27 88 105 73)(28 97 106 62)(29 86 107 71)(30 95 108 80)(31 84 109 69)(32 93 110 78)(33 82 111 67)(34 91 112 76)(35 100 113 65)(36 89 114 74)(37 98 115 63)(38 87 116 72)(39 96 117 61)(40 85 118 70)(41 210 154 192)(42 219 155 181)(43 208 156 190)(44 217 157 199)(45 206 158 188)(46 215 159 197)(47 204 160 186)(48 213 141 195)(49 202 142 184)(50 211 143 193)(51 220 144 182)(52 209 145 191)(53 218 146 200)(54 207 147 189)(55 216 148 198)(56 205 149 187)(57 214 150 196)(58 203 151 185)(59 212 152 194)(60 201 153 183)(121 252 166 226)(122 241 167 235)(123 250 168 224)(124 259 169 233)(125 248 170 222)(126 257 171 231)(127 246 172 240)(128 255 173 229)(129 244 174 238)(130 253 175 227)(131 242 176 236)(132 251 177 225)(133 260 178 234)(134 249 179 223)(135 258 180 232)(136 247 161 221)(137 256 162 230)(138 245 163 239)(139 254 164 228)(140 243 165 237)
(1 206 31 123)(2 217 32 134)(3 208 33 125)(4 219 34 136)(5 210 35 127)(6 201 36 138)(7 212 37 129)(8 203 38 140)(9 214 39 131)(10 205 40 122)(11 216 21 133)(12 207 22 124)(13 218 23 135)(14 209 24 126)(15 220 25 137)(16 211 26 128)(17 202 27 139)(18 213 28 130)(19 204 29 121)(20 215 30 132)(41 100 240 262)(42 91 221 273)(43 82 222 264)(44 93 223 275)(45 84 224 266)(46 95 225 277)(47 86 226 268)(48 97 227 279)(49 88 228 270)(50 99 229 261)(51 90 230 272)(52 81 231 263)(53 92 232 274)(54 83 233 265)(55 94 234 276)(56 85 235 267)(57 96 236 278)(58 87 237 269)(59 98 238 280)(60 89 239 271)(61 242 303 150)(62 253 304 141)(63 244 305 152)(64 255 306 143)(65 246 307 154)(66 257 308 145)(67 248 309 156)(68 259 310 147)(69 250 311 158)(70 241 312 149)(71 252 313 160)(72 243 314 151)(73 254 315 142)(74 245 316 153)(75 256 317 144)(76 247 318 155)(77 258 319 146)(78 249 320 157)(79 260 301 148)(80 251 302 159)(101 180 282 200)(102 171 283 191)(103 162 284 182)(104 173 285 193)(105 164 286 184)(106 175 287 195)(107 166 288 186)(108 177 289 197)(109 168 290 188)(110 179 291 199)(111 170 292 190)(112 161 293 181)(113 172 294 192)(114 163 295 183)(115 174 296 194)(116 165 297 185)(117 176 298 196)(118 167 299 187)(119 178 300 198)(120 169 281 189)

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

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

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

68 conjugacy classes

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

68 irreducible representations

dim11111122222222244
type++++++-+-++-+-
imageC1C2C2C2C2C4D4Q8D4Q8D5D10Dic10C4×D5C5⋊D4D4×D5Q8×D5
kernelC205(C4⋊C4)C2×C4×Dic5C2×C10.D4C2×C4⋊Dic5C10×C4⋊C4C4×Dic5C2×Dic5C2×Dic5C2×C20C2×C20C2×C4⋊C4C22×C4C2×C4C2×C4C2×C4C22C22
# reps11411844222688844

Matrix representation of C205(C4⋊C4) in GL6(𝔽41)

3510000
4000000
0034100
0033100
00002038
00003821
,
100000
6400000
00161500
0022500
0000213
0000320
,
900000
090000
00112800
00223000
000001
0000400

G:=sub<GL(6,GF(41))| [35,40,0,0,0,0,1,0,0,0,0,0,0,0,34,33,0,0,0,0,1,1,0,0,0,0,0,0,20,38,0,0,0,0,38,21],[1,6,0,0,0,0,0,40,0,0,0,0,0,0,16,2,0,0,0,0,15,25,0,0,0,0,0,0,21,3,0,0,0,0,3,20],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,11,22,0,0,0,0,28,30,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;

C205(C4⋊C4) in GAP, Magma, Sage, TeX

C_{20}\rtimes_5(C_4\rtimes C_4)
% in TeX

G:=Group("C20:5(C4:C4)");
// GroupNames label

G:=SmallGroup(320,603);
// by ID

G=gap.SmallGroup(320,603);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,422,387,58,12550]);
// Polycyclic

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

׿
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