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G = C20⋊Q16order 320 = 26·5

2nd semidirect product of C20 and Q16 acting via Q16/C4=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C202Q16, C42.83D10, Dic10.24D4, C4⋊Q8.9D5, C4.57(D4×D5), C42(C5⋊Q16), C54(C42Q16), C20.39(C2×D4), (C2×C20).159D4, (C2×Q8).47D10, C10.42(C2×Q16), C203C8.21C2, C20.85(C4○D4), C4.6(D42D5), C2.15(C202D4), (C2×C20).408C23, (C4×C20).137C22, (C4×Dic10).17C2, Q8⋊Dic5.13C2, (Q8×C10).65C22, C10.106(C4⋊D4), C10.99(C8.C22), C4⋊Dic5.349C22, C2.20(C20.C23), (C2×Dic10).283C22, (C5×C4⋊Q8).9C2, (C2×C5⋊Q16).6C2, C2.13(C2×C5⋊Q16), (C2×C10).539(C2×D4), (C2×C4).190(C5⋊D4), (C2×C4).505(C22×D5), C22.211(C2×C5⋊D4), (C2×C52C8).140C22, SmallGroup(320,717)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C20⋊Q16
C1C5C10C20C2×C20C2×Dic10C4×Dic10 — C20⋊Q16
C5C10C2×C20 — C20⋊Q16
C1C22C42C4⋊Q8

Generators and relations for C20⋊Q16
 G = < a,b,c | a20=b8=1, c2=b4, bab-1=a-1, cac-1=a11, cbc-1=b-1 >

Subgroups: 342 in 108 conjugacy classes, 45 normal (29 characteristic)
C1, C2 [×3], C4 [×2], C4 [×2], C4 [×6], C22, C5, C8 [×2], C2×C4 [×3], C2×C4 [×4], Q8 [×7], C10 [×3], C42, C42, C4⋊C4 [×4], C2×C8 [×2], Q16 [×4], C2×Q8 [×2], C2×Q8, Dic5 [×3], C20 [×2], C20 [×2], C20 [×3], C2×C10, Q8⋊C4 [×2], C4⋊C8, C4×Q8, C4⋊Q8, C2×Q16 [×2], C52C8 [×2], Dic10 [×2], Dic10, C2×Dic5 [×2], C2×C20 [×3], C2×C20 [×2], C5×Q8 [×4], C42Q16, C2×C52C8 [×2], C4×Dic5, C10.D4, C4⋊Dic5, C5⋊Q16 [×4], C4×C20, C5×C4⋊C4 [×2], C2×Dic10, Q8×C10 [×2], C203C8, Q8⋊Dic5 [×2], C4×Dic10, C2×C5⋊Q16 [×2], C5×C4⋊Q8, C20⋊Q16
Quotients: C1, C2 [×7], C22 [×7], D4 [×4], C23, D5, Q16 [×2], C2×D4 [×2], C4○D4, D10 [×3], C4⋊D4, C2×Q16, C8.C22, C5⋊D4 [×2], C22×D5, C42Q16, C5⋊Q16 [×2], D4×D5, D42D5, C2×C5⋊D4, C202D4, C20.C23, C2×C5⋊Q16, C20⋊Q16

Smallest permutation representation of C20⋊Q16
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)
(1 204 64 148 83 165 317 25)(2 203 65 147 84 164 318 24)(3 202 66 146 85 163 319 23)(4 201 67 145 86 162 320 22)(5 220 68 144 87 161 301 21)(6 219 69 143 88 180 302 40)(7 218 70 142 89 179 303 39)(8 217 71 141 90 178 304 38)(9 216 72 160 91 177 305 37)(10 215 73 159 92 176 306 36)(11 214 74 158 93 175 307 35)(12 213 75 157 94 174 308 34)(13 212 76 156 95 173 309 33)(14 211 77 155 96 172 310 32)(15 210 78 154 97 171 311 31)(16 209 79 153 98 170 312 30)(17 208 80 152 99 169 313 29)(18 207 61 151 100 168 314 28)(19 206 62 150 81 167 315 27)(20 205 63 149 82 166 316 26)(41 280 133 291 255 103 199 232)(42 279 134 290 256 102 200 231)(43 278 135 289 257 101 181 230)(44 277 136 288 258 120 182 229)(45 276 137 287 259 119 183 228)(46 275 138 286 260 118 184 227)(47 274 139 285 241 117 185 226)(48 273 140 284 242 116 186 225)(49 272 121 283 243 115 187 224)(50 271 122 282 244 114 188 223)(51 270 123 281 245 113 189 222)(52 269 124 300 246 112 190 221)(53 268 125 299 247 111 191 240)(54 267 126 298 248 110 192 239)(55 266 127 297 249 109 193 238)(56 265 128 296 250 108 194 237)(57 264 129 295 251 107 195 236)(58 263 130 294 252 106 196 235)(59 262 131 293 253 105 197 234)(60 261 132 292 254 104 198 233)
(1 245 83 51)(2 256 84 42)(3 247 85 53)(4 258 86 44)(5 249 87 55)(6 260 88 46)(7 251 89 57)(8 242 90 48)(9 253 91 59)(10 244 92 50)(11 255 93 41)(12 246 94 52)(13 257 95 43)(14 248 96 54)(15 259 97 45)(16 250 98 56)(17 241 99 47)(18 252 100 58)(19 243 81 49)(20 254 82 60)(21 109 144 266)(22 120 145 277)(23 111 146 268)(24 102 147 279)(25 113 148 270)(26 104 149 261)(27 115 150 272)(28 106 151 263)(29 117 152 274)(30 108 153 265)(31 119 154 276)(32 110 155 267)(33 101 156 278)(34 112 157 269)(35 103 158 280)(36 114 159 271)(37 105 160 262)(38 116 141 273)(39 107 142 264)(40 118 143 275)(61 130 314 196)(62 121 315 187)(63 132 316 198)(64 123 317 189)(65 134 318 200)(66 125 319 191)(67 136 320 182)(68 127 301 193)(69 138 302 184)(70 129 303 195)(71 140 304 186)(72 131 305 197)(73 122 306 188)(74 133 307 199)(75 124 308 190)(76 135 309 181)(77 126 310 192)(78 137 311 183)(79 128 312 194)(80 139 313 185)(161 238 220 297)(162 229 201 288)(163 240 202 299)(164 231 203 290)(165 222 204 281)(166 233 205 292)(167 224 206 283)(168 235 207 294)(169 226 208 285)(170 237 209 296)(171 228 210 287)(172 239 211 298)(173 230 212 289)(174 221 213 300)(175 232 214 291)(176 223 215 282)(177 234 216 293)(178 225 217 284)(179 236 218 295)(180 227 219 286)

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

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

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

47 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K5A5B8A8B8C8D10A···10F20A···20L20M···20T
order12224444444444455888810···1020···2020···20
size111122224882020202022202020202···24···48···8

47 irreducible representations

dim1111112222222244444
type+++++++++-++--+-
imageC1C2C2C2C2C2D4D4D5Q16C4○D4D10D10C5⋊D4C8.C22C5⋊Q16D4×D5D42D5C20.C23
kernelC20⋊Q16C203C8Q8⋊Dic5C4×Dic10C2×C5⋊Q16C5×C4⋊Q8Dic10C2×C20C4⋊Q8C20C20C42C2×Q8C2×C4C10C4C4C4C2
# reps1121212224224814224

Matrix representation of C20⋊Q16 in GL6(𝔽41)

6400000
100000
00403700
0021100
000010
000001
,
2150000
27390000
001400
0004000
0000017
00001217
,
2360000
35180000
001400
0004000
0000829
0000233

G:=sub<GL(6,GF(41))| [6,1,0,0,0,0,40,0,0,0,0,0,0,0,40,21,0,0,0,0,37,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[2,27,0,0,0,0,15,39,0,0,0,0,0,0,1,0,0,0,0,0,4,40,0,0,0,0,0,0,0,12,0,0,0,0,17,17],[23,35,0,0,0,0,6,18,0,0,0,0,0,0,1,0,0,0,0,0,4,40,0,0,0,0,0,0,8,2,0,0,0,0,29,33] >;

C20⋊Q16 in GAP, Magma, Sage, TeX

C_{20}\rtimes Q_{16}
% in TeX

G:=Group("C20:Q16");
// GroupNames label

G:=SmallGroup(320,717);
// by ID

G=gap.SmallGroup(320,717);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,120,254,219,184,1123,297,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=b^8=1,c^2=b^4,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations

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