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G = C4011Q8order 320 = 26·5

4th semidirect product of C40 and Q8 acting via Q8/C4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C4011Q8, C89Dic10, C42.251D10, C20.37M4(2), C54(C84Q8), (C4×C8).16D5, (C4×C40).22C2, C10.15(C4×Q8), C20.80(C2×Q8), C203C8.4C2, C408C4.6C2, (C2×C8).280D10, C4.6(C8⋊D5), C4⋊Dic5.18C4, C2.8(C4×Dic10), C10.26(C8○D4), (C4×Dic10).2C2, C4.45(C2×Dic10), C20.8Q8.1C2, C4.123(C4○D20), C20.239(C4○D4), (C2×C40).339C22, (C2×C20).801C23, (C4×C20).322C22, (C2×Dic10).18C4, C10.D4.11C4, C10.35(C2×M4(2)), C2.6(D20.3C4), (C4×Dic5).198C22, C2.6(C2×C8⋊D5), C22.94(C2×C4×D5), (C2×C4).102(C4×D5), (C2×C20).392(C2×C4), (C2×Dic5).12(C2×C4), (C2×C4).743(C22×D5), (C2×C10).157(C22×C4), (C2×C52C8).190C22, SmallGroup(320,306)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C4011Q8
C1C5C10C20C2×C20C4×Dic5C4×Dic10 — C4011Q8
C5C2×C10 — C4011Q8
C1C2×C4C4×C8

Generators and relations for C4011Q8
 G = < a,b,c | a40=b4=1, c2=b2, ab=ba, cac-1=a29, cbc-1=b-1 >

Subgroups: 254 in 94 conjugacy classes, 55 normal (33 characteristic)
C1, C2 [×3], C4 [×2], C4 [×2], C4 [×5], C22, C5, C8 [×2], C8 [×3], C2×C4 [×3], C2×C4 [×4], Q8 [×2], C10 [×3], C42, C42 [×2], C4⋊C4 [×3], C2×C8 [×2], C2×C8 [×2], C2×Q8, Dic5 [×4], C20 [×2], C20 [×2], C20, C2×C10, C4×C8, C8⋊C4 [×2], C4⋊C8 [×3], C4×Q8, C52C8 [×2], C40 [×2], C40, Dic10 [×2], C2×Dic5 [×4], C2×C20 [×3], C84Q8, C2×C52C8 [×2], C4×Dic5 [×2], C10.D4 [×2], C4⋊Dic5, C4×C20, C2×C40 [×2], C2×Dic10, C203C8, C20.8Q8 [×2], C408C4 [×2], C4×C40, C4×Dic10, C4011Q8
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], Q8 [×2], C23, D5, M4(2) [×2], C22×C4, C2×Q8, C4○D4, D10 [×3], C4×Q8, C2×M4(2), C8○D4, Dic10 [×2], C4×D5 [×2], C22×D5, C84Q8, C8⋊D5 [×2], C2×Dic10, C2×C4×D5, C4○D20, C4×Dic10, C2×C8⋊D5, D20.3C4, C4011Q8

Smallest permutation representation of C4011Q8
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 74 85 307)(2 75 86 308)(3 76 87 309)(4 77 88 310)(5 78 89 311)(6 79 90 312)(7 80 91 313)(8 41 92 314)(9 42 93 315)(10 43 94 316)(11 44 95 317)(12 45 96 318)(13 46 97 319)(14 47 98 320)(15 48 99 281)(16 49 100 282)(17 50 101 283)(18 51 102 284)(19 52 103 285)(20 53 104 286)(21 54 105 287)(22 55 106 288)(23 56 107 289)(24 57 108 290)(25 58 109 291)(26 59 110 292)(27 60 111 293)(28 61 112 294)(29 62 113 295)(30 63 114 296)(31 64 115 297)(32 65 116 298)(33 66 117 299)(34 67 118 300)(35 68 119 301)(36 69 120 302)(37 70 81 303)(38 71 82 304)(39 72 83 305)(40 73 84 306)(121 177 205 247)(122 178 206 248)(123 179 207 249)(124 180 208 250)(125 181 209 251)(126 182 210 252)(127 183 211 253)(128 184 212 254)(129 185 213 255)(130 186 214 256)(131 187 215 257)(132 188 216 258)(133 189 217 259)(134 190 218 260)(135 191 219 261)(136 192 220 262)(137 193 221 263)(138 194 222 264)(139 195 223 265)(140 196 224 266)(141 197 225 267)(142 198 226 268)(143 199 227 269)(144 200 228 270)(145 161 229 271)(146 162 230 272)(147 163 231 273)(148 164 232 274)(149 165 233 275)(150 166 234 276)(151 167 235 277)(152 168 236 278)(153 169 237 279)(154 170 238 280)(155 171 239 241)(156 172 240 242)(157 173 201 243)(158 174 202 244)(159 175 203 245)(160 176 204 246)
(1 204 85 160)(2 233 86 149)(3 222 87 138)(4 211 88 127)(5 240 89 156)(6 229 90 145)(7 218 91 134)(8 207 92 123)(9 236 93 152)(10 225 94 141)(11 214 95 130)(12 203 96 159)(13 232 97 148)(14 221 98 137)(15 210 99 126)(16 239 100 155)(17 228 101 144)(18 217 102 133)(19 206 103 122)(20 235 104 151)(21 224 105 140)(22 213 106 129)(23 202 107 158)(24 231 108 147)(25 220 109 136)(26 209 110 125)(27 238 111 154)(28 227 112 143)(29 216 113 132)(30 205 114 121)(31 234 115 150)(32 223 116 139)(33 212 117 128)(34 201 118 157)(35 230 119 146)(36 219 120 135)(37 208 81 124)(38 237 82 153)(39 226 83 142)(40 215 84 131)(41 179 314 249)(42 168 315 278)(43 197 316 267)(44 186 317 256)(45 175 318 245)(46 164 319 274)(47 193 320 263)(48 182 281 252)(49 171 282 241)(50 200 283 270)(51 189 284 259)(52 178 285 248)(53 167 286 277)(54 196 287 266)(55 185 288 255)(56 174 289 244)(57 163 290 273)(58 192 291 262)(59 181 292 251)(60 170 293 280)(61 199 294 269)(62 188 295 258)(63 177 296 247)(64 166 297 276)(65 195 298 265)(66 184 299 254)(67 173 300 243)(68 162 301 272)(69 191 302 261)(70 180 303 250)(71 169 304 279)(72 198 305 268)(73 187 306 257)(74 176 307 246)(75 165 308 275)(76 194 309 264)(77 183 310 253)(78 172 311 242)(79 161 312 271)(80 190 313 260)

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

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

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

92 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K4L5A5B8A···8H8I8J8K8L10A···10F20A···20X40A···40AF
order1222444444444444558···8888810···1020···2040···40
size11111111222220202020222···2202020202···22···22···2

92 irreducible representations

dim111111111222222222222
type++++++-+++-
imageC1C2C2C2C2C2C4C4C4Q8D5M4(2)C4○D4D10D10C8○D4Dic10C4×D5C8⋊D5C4○D20D20.3C4
kernelC4011Q8C203C8C20.8Q8C408C4C4×C40C4×Dic10C10.D4C4⋊Dic5C2×Dic10C40C4×C8C20C20C42C2×C8C10C8C2×C4C4C4C2
# reps11221142222422448816816

Matrix representation of C4011Q8 in GL4(𝔽41) generated by

35600
354000
0067
00347
,
22800
133900
0010
0001
,
14400
22700
0058
003836
G:=sub<GL(4,GF(41))| [35,35,0,0,6,40,0,0,0,0,6,34,0,0,7,7],[2,13,0,0,28,39,0,0,0,0,1,0,0,0,0,1],[14,2,0,0,4,27,0,0,0,0,5,38,0,0,8,36] >;

C4011Q8 in GAP, Magma, Sage, TeX

C_{40}\rtimes_{11}Q_8
% in TeX

G:=Group("C40:11Q8");
// GroupNames label

G:=SmallGroup(320,306);
// by ID

G=gap.SmallGroup(320,306);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,253,120,758,58,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^40=b^4=1,c^2=b^2,a*b=b*a,c*a*c^-1=a^29,c*b*c^-1=b^-1>;
// generators/relations

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