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G = C207(C4⋊C4)  order 320 = 26·5

1st semidirect product of C20 and C4⋊C4 acting via C4⋊C4/C2×C4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C207(C4⋊C4), C4⋊Dic516C4, (C2×C4).65D20, C10.45(C4×D4), C2.18(C4×D20), C10.6(C4⋊Q8), C10.17(C4×Q8), (C2×C20).52Q8, (C2×C20).469D4, (C2×C42).13D5, C43(C10.D4), C2.1(C207D4), C2.1(C202Q8), (C2×C4).40Dic10, C2.10(C4×Dic10), C22.33(C2×D20), C10.55(C4⋊D4), (C22×C4).394D10, C10.52(C22⋊Q8), C10.2(C42.C2), C2.1(C20.6Q8), C2.1(C20.48D4), C22.39(C4○D20), C22.16(C2×Dic10), C23.261(C22×D5), C10.10C42.9C2, (C22×C20).469C22, (C22×C10).303C23, C53(C23.65C23), (C22×Dic5).26C22, (C2×C4×C20).9C2, C10.47(C2×C4⋊C4), (C2×C4).108(C4×D5), (C2×C10).23(C2×Q8), C22.116(C2×C4×D5), (C2×C20).396(C2×C4), (C2×C10).423(C2×D4), (C2×C4⋊Dic5).14C2, C2.4(C2×C10.D4), C22.38(C2×C5⋊D4), (C2×C10).64(C4○D4), (C2×C4).237(C5⋊D4), (C2×Dic5).26(C2×C4), (C2×C10).194(C22×C4), (C2×C10.D4).11C2, SmallGroup(320,555)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C207(C4⋊C4)
C1C5C10C2×C10C22×C10C22×Dic5C2×C4⋊Dic5 — C207(C4⋊C4)
C5C2×C10 — C207(C4⋊C4)
C1C23C2×C42

Generators and relations for C207(C4⋊C4)
 G = < a,b,c | a20=b4=c4=1, bab-1=a-1, ac=ca, cbc-1=b-1 >

Subgroups: 510 in 170 conjugacy classes, 87 normal (43 characteristic)
C1, C2 [×7], C4 [×4], C4 [×10], C22 [×7], C5, C2×C4 [×10], C2×C4 [×18], C23, C10 [×7], C42 [×2], C4⋊C4 [×10], C22×C4 [×3], C22×C4 [×4], Dic5 [×6], C20 [×4], C20 [×4], C2×C10 [×7], C2.C42 [×2], C2×C42, C2×C4⋊C4 [×4], C2×Dic5 [×4], C2×Dic5 [×10], C2×C20 [×10], C2×C20 [×4], C22×C10, C23.65C23, C10.D4 [×4], C4⋊Dic5 [×4], C4⋊Dic5 [×2], C4×C20 [×2], C22×Dic5 [×4], C22×C20 [×3], C10.10C42 [×2], C2×C10.D4 [×2], C2×C4⋊Dic5 [×2], C2×C4×C20, C207(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], D10 [×3], C2×C4⋊C4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C42.C2, C4⋊Q8, Dic10 [×4], C4×D5 [×2], D20 [×2], C5⋊D4 [×2], C22×D5, C23.65C23, C10.D4 [×4], C2×Dic10 [×2], C2×C4×D5, C2×D20, C4○D20 [×2], C2×C5⋊D4, C4×Dic10, C202Q8, C20.6Q8, C4×D20, C2×C10.D4, C20.48D4, C207D4, C207(C4⋊C4)

Smallest permutation representation of C207(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 50 188 316)(2 49 189 315)(3 48 190 314)(4 47 191 313)(5 46 192 312)(6 45 193 311)(7 44 194 310)(8 43 195 309)(9 42 196 308)(10 41 197 307)(11 60 198 306)(12 59 199 305)(13 58 200 304)(14 57 181 303)(15 56 182 302)(16 55 183 301)(17 54 184 320)(18 53 185 319)(19 52 186 318)(20 51 187 317)(21 299 79 82)(22 298 80 81)(23 297 61 100)(24 296 62 99)(25 295 63 98)(26 294 64 97)(27 293 65 96)(28 292 66 95)(29 291 67 94)(30 290 68 93)(31 289 69 92)(32 288 70 91)(33 287 71 90)(34 286 72 89)(35 285 73 88)(36 284 74 87)(37 283 75 86)(38 282 76 85)(39 281 77 84)(40 300 78 83)(101 248 142 129)(102 247 143 128)(103 246 144 127)(104 245 145 126)(105 244 146 125)(106 243 147 124)(107 242 148 123)(108 241 149 122)(109 260 150 121)(110 259 151 140)(111 258 152 139)(112 257 153 138)(113 256 154 137)(114 255 155 136)(115 254 156 135)(116 253 157 134)(117 252 158 133)(118 251 159 132)(119 250 160 131)(120 249 141 130)(161 270 226 217)(162 269 227 216)(163 268 228 215)(164 267 229 214)(165 266 230 213)(166 265 231 212)(167 264 232 211)(168 263 233 210)(169 262 234 209)(170 261 235 208)(171 280 236 207)(172 279 237 206)(173 278 238 205)(174 277 239 204)(175 276 240 203)(176 275 221 202)(177 274 222 201)(178 273 223 220)(179 272 224 219)(180 271 225 218)
(1 105 212 78)(2 106 213 79)(3 107 214 80)(4 108 215 61)(5 109 216 62)(6 110 217 63)(7 111 218 64)(8 112 219 65)(9 113 220 66)(10 114 201 67)(11 115 202 68)(12 116 203 69)(13 117 204 70)(14 118 205 71)(15 119 206 72)(16 120 207 73)(17 101 208 74)(18 102 209 75)(19 103 210 76)(20 104 211 77)(21 189 147 266)(22 190 148 267)(23 191 149 268)(24 192 150 269)(25 193 151 270)(26 194 152 271)(27 195 153 272)(28 196 154 273)(29 197 155 274)(30 198 156 275)(31 199 157 276)(32 200 158 277)(33 181 159 278)(34 182 160 279)(35 183 141 280)(36 184 142 261)(37 185 143 262)(38 186 144 263)(39 187 145 264)(40 188 146 265)(41 136 177 291)(42 137 178 292)(43 138 179 293)(44 139 180 294)(45 140 161 295)(46 121 162 296)(47 122 163 297)(48 123 164 298)(49 124 165 299)(50 125 166 300)(51 126 167 281)(52 127 168 282)(53 128 169 283)(54 129 170 284)(55 130 171 285)(56 131 172 286)(57 132 173 287)(58 133 174 288)(59 134 175 289)(60 135 176 290)(81 314 242 229)(82 315 243 230)(83 316 244 231)(84 317 245 232)(85 318 246 233)(86 319 247 234)(87 320 248 235)(88 301 249 236)(89 302 250 237)(90 303 251 238)(91 304 252 239)(92 305 253 240)(93 306 254 221)(94 307 255 222)(95 308 256 223)(96 309 257 224)(97 310 258 225)(98 311 259 226)(99 312 260 227)(100 313 241 228)

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

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

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

92 conjugacy classes

class 1 2A···2G4A···4L4M···4T5A5B10A···10N20A···20AV
order12···24···44···45510···1020···20
size11···12···220···20222···22···2

92 irreducible representations

dim1111112222222222
type++++++-++-+
imageC1C2C2C2C2C4D4Q8D5C4○D4D10Dic10C4×D5D20C5⋊D4C4○D20
kernelC207(C4⋊C4)C10.10C42C2×C10.D4C2×C4⋊Dic5C2×C4×C20C4⋊Dic5C2×C20C2×C20C2×C42C2×C10C22×C4C2×C4C2×C4C2×C4C2×C4C22
# reps122218442461688816

Matrix representation of C207(C4⋊C4) in GL6(𝔽41)

34400000
100000
00344000
001000
00002711
00003032
,
27110000
27140000
00193200
00222200
00003817
0000383
,
3200000
0320000
0024100
00401700
0000119
00003230

G:=sub<GL(6,GF(41))| [34,1,0,0,0,0,40,0,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,27,30,0,0,0,0,11,32],[27,27,0,0,0,0,11,14,0,0,0,0,0,0,19,22,0,0,0,0,32,22,0,0,0,0,0,0,38,38,0,0,0,0,17,3],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,24,40,0,0,0,0,1,17,0,0,0,0,0,0,11,32,0,0,0,0,9,30] >;

C207(C4⋊C4) in GAP, Magma, Sage, TeX

C_{20}\rtimes_7(C_4\rtimes C_4)
% in TeX

G:=Group("C20:7(C4:C4)");
// GroupNames label

G:=SmallGroup(320,555);
// by ID

G=gap.SmallGroup(320,555);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,120,758,58,12550]);
// Polycyclic

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

׿
×
𝔽