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G = C20.SD16order 320 = 26·5

16th non-split extension by C20 of SD16 acting via SD16/C4=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C20.16SD16, C42.221D10, C52C88Q8, C4⋊Q8.5D5, C53(C83Q8), C4.35(Q8×D5), C4⋊C4.80D10, C4.3(Q8⋊D5), C20.36(C2×Q8), (C2×C20).152D4, C10.31(C4⋊Q8), C4.4(D4.D5), C202Q8.20C2, C10.60(C2×SD16), (C4×C20).126C22, (C2×C20).397C23, C20.Q8.16C2, C4⋊Dic5.157C22, C2.11(Dic5⋊Q8), (C5×C4⋊Q8).5C2, C2.11(C2×Q8⋊D5), (C4×C52C8).12C2, C2.14(C2×D4.D5), (C2×C10).528(C2×D4), (C2×C4).134(C5⋊D4), (C5×C4⋊C4).127C22, (C2×C4).494(C22×D5), C22.200(C2×C5⋊D4), (C2×C52C8).268C22, SmallGroup(320,706)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C20.SD16
C1C5C10C2×C10C2×C20C2×C52C8C4×C52C8 — C20.SD16
C5C10C2×C20 — C20.SD16
C1C22C42C4⋊Q8

Generators and relations for C20.SD16
 G = < a,b,c | a20=b8=1, c2=a10, bab-1=a9, cac-1=a11, cbc-1=b3 >

Subgroups: 318 in 98 conjugacy classes, 51 normal (23 characteristic)
C1, C2 [×3], C4 [×6], C4 [×4], C22, C5, C8 [×4], C2×C4 [×3], C2×C4 [×4], Q8 [×4], C10 [×3], C42, C4⋊C4 [×2], C4⋊C4 [×4], C2×C8 [×2], C2×Q8 [×2], Dic5 [×2], C20 [×6], C20 [×2], C2×C10, C4×C8, C4.Q8 [×4], C4⋊Q8, C4⋊Q8, C52C8 [×4], Dic10 [×2], C2×Dic5 [×2], C2×C20 [×3], C2×C20 [×2], C5×Q8 [×2], C83Q8, C2×C52C8 [×2], C4⋊Dic5 [×2], C4⋊Dic5, C4×C20, C5×C4⋊C4 [×2], C5×C4⋊C4, C2×Dic10, Q8×C10, C4×C52C8, C20.Q8 [×4], C202Q8, C5×C4⋊Q8, C20.SD16
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], Q8 [×4], C23, D5, SD16 [×4], C2×D4, C2×Q8 [×2], D10 [×3], C4⋊Q8, C2×SD16 [×2], C5⋊D4 [×2], C22×D5, C83Q8, D4.D5 [×2], Q8⋊D5 [×2], Q8×D5 [×2], C2×C5⋊D4, C2×D4.D5, C2×Q8⋊D5, Dic5⋊Q8, C20.SD16

Smallest permutation representation of C20.SD16
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 66 154 292 269 203 112 175)(2 75 155 281 270 212 113 164)(3 64 156 290 271 201 114 173)(4 73 157 299 272 210 115 162)(5 62 158 288 273 219 116 171)(6 71 159 297 274 208 117 180)(7 80 160 286 275 217 118 169)(8 69 141 295 276 206 119 178)(9 78 142 284 277 215 120 167)(10 67 143 293 278 204 101 176)(11 76 144 282 279 213 102 165)(12 65 145 291 280 202 103 174)(13 74 146 300 261 211 104 163)(14 63 147 289 262 220 105 172)(15 72 148 298 263 209 106 161)(16 61 149 287 264 218 107 170)(17 70 150 296 265 207 108 179)(18 79 151 285 266 216 109 168)(19 68 152 294 267 205 110 177)(20 77 153 283 268 214 111 166)(21 93 133 226 255 315 55 187)(22 82 134 235 256 304 56 196)(23 91 135 224 257 313 57 185)(24 100 136 233 258 302 58 194)(25 89 137 222 259 311 59 183)(26 98 138 231 260 320 60 192)(27 87 139 240 241 309 41 181)(28 96 140 229 242 318 42 190)(29 85 121 238 243 307 43 199)(30 94 122 227 244 316 44 188)(31 83 123 236 245 305 45 197)(32 92 124 225 246 314 46 186)(33 81 125 234 247 303 47 195)(34 90 126 223 248 312 48 184)(35 99 127 232 249 301 49 193)(36 88 128 221 250 310 50 182)(37 97 129 230 251 319 51 191)(38 86 130 239 252 308 52 200)(39 95 131 228 253 317 53 189)(40 84 132 237 254 306 54 198)
(1 29 11 39)(2 40 12 30)(3 31 13 21)(4 22 14 32)(5 33 15 23)(6 24 16 34)(7 35 17 25)(8 26 18 36)(9 37 19 27)(10 28 20 38)(41 142 51 152)(42 153 52 143)(43 144 53 154)(44 155 54 145)(45 146 55 156)(46 157 56 147)(47 148 57 158)(48 159 58 149)(49 150 59 160)(50 141 60 151)(61 223 71 233)(62 234 72 224)(63 225 73 235)(64 236 74 226)(65 227 75 237)(66 238 76 228)(67 229 77 239)(68 240 78 230)(69 231 79 221)(70 222 80 232)(81 298 91 288)(82 289 92 299)(83 300 93 290)(84 291 94 281)(85 282 95 292)(86 293 96 283)(87 284 97 294)(88 295 98 285)(89 286 99 296)(90 297 100 287)(101 140 111 130)(102 131 112 121)(103 122 113 132)(104 133 114 123)(105 124 115 134)(106 135 116 125)(107 126 117 136)(108 137 118 127)(109 128 119 138)(110 139 120 129)(161 313 171 303)(162 304 172 314)(163 315 173 305)(164 306 174 316)(165 317 175 307)(166 308 176 318)(167 319 177 309)(168 310 178 320)(169 301 179 311)(170 312 180 302)(181 215 191 205)(182 206 192 216)(183 217 193 207)(184 208 194 218)(185 219 195 209)(186 210 196 220)(187 201 197 211)(188 212 198 202)(189 203 199 213)(190 214 200 204)(241 277 251 267)(242 268 252 278)(243 279 253 269)(244 270 254 280)(245 261 255 271)(246 272 256 262)(247 263 257 273)(248 274 258 264)(249 265 259 275)(250 276 260 266)

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

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

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

50 conjugacy classes

class 1 2A2B2C4A···4F4G4H4I4J5A5B8A···8H10A···10F20A···20L20M···20T
order12224···44444558···810···1020···2020···20
size11112···28840402210···102···24···48···8

50 irreducible representations

dim111112222222444
type+++++-++++-+-
imageC1C2C2C2C2Q8D4D5SD16D10D10C5⋊D4D4.D5Q8⋊D5Q8×D5
kernelC20.SD16C4×C52C8C20.Q8C202Q8C5×C4⋊Q8C52C8C2×C20C4⋊Q8C20C42C4⋊C4C2×C4C4C4C4
# reps114114228248444

Matrix representation of C20.SD16 in GL6(𝔽41)

100000
010000
00344000
001000
0000040
000010
,
26260000
15260000
00191900
0092200
00002615
00002626
,
18280000
28230000
00174000
0012400
00002734
00003414

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,40,0],[26,15,0,0,0,0,26,26,0,0,0,0,0,0,19,9,0,0,0,0,19,22,0,0,0,0,0,0,26,26,0,0,0,0,15,26],[18,28,0,0,0,0,28,23,0,0,0,0,0,0,17,1,0,0,0,0,40,24,0,0,0,0,0,0,27,34,0,0,0,0,34,14] >;

C20.SD16 in GAP, Magma, Sage, TeX

C_{20}.{\rm SD}_{16}
% in TeX

G:=Group("C20.SD16");
// GroupNames label

G:=SmallGroup(320,706);
// by ID

G=gap.SmallGroup(320,706);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,64,1094,135,58,438,102,12550]);
// Polycyclic

G:=Group<a,b,c|a^20=b^8=1,c^2=a^10,b*a*b^-1=a^9,c*a*c^-1=a^11,c*b*c^-1=b^3>;
// generators/relations

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