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G = C403Q8order 320 = 26·5

3rd semidirect product of C40 and Q8 acting via Q8/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C403Q8, C82Dic10, C52(C8⋊Q8), C52C81Q8, C20⋊Q8.7C2, C4.21(Q8×D5), C4⋊C4.33D10, (C2×C8).59D10, C4.Q8.3D5, C2.9(C20⋊Q8), C20.57(C2×Q8), C408C4.2C2, C10.14(C4⋊Q8), C405C4.17C2, (C2×Dic5).46D4, C4.21(C2×Dic10), C10.D8.4C2, C22.211(D4×D5), C4.Dic10.5C2, C20.Q8.6C2, C2.20(D40⋊C2), C10.67(C8⋊C22), (C2×C20).272C23, (C2×C40).108C22, C2.21(SD16⋊D5), C10.39(C8.C22), C4⋊Dic5.104C22, (C4×Dic5).35C22, (C5×C4.Q8).3C2, (C2×C10).277(C2×D4), (C5×C4⋊C4).65C22, (C2×C52C8).53C22, (C2×C4).375(C22×D5), SmallGroup(320,483)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C403Q8
C1C5C10C2×C10C2×C20C4×Dic5C408C4 — C403Q8
C5C10C2×C20 — C403Q8
C1C22C2×C4C4.Q8

Generators and relations for C403Q8
 G = < a,b,c | a40=b4=1, c2=b2, bab-1=a11, cac-1=a29, cbc-1=b-1 >

Subgroups: 334 in 90 conjugacy classes, 43 normal (37 characteristic)
C1, C2 [×3], C4 [×2], C4 [×6], C22, C5, C8 [×2], C8 [×2], C2×C4, C2×C4 [×6], Q8 [×2], C10 [×3], C42, C4⋊C4 [×2], C4⋊C4 [×5], C2×C8, C2×C8, C2×Q8, Dic5 [×4], C20 [×2], C20 [×2], C2×C10, C8⋊C4, C4.Q8, C4.Q8, C2.D8 [×2], C42.C2, C4⋊Q8, C52C8 [×2], C40 [×2], Dic10 [×2], C2×Dic5 [×2], C2×Dic5 [×2], C2×C20, C2×C20 [×2], C8⋊Q8, C2×C52C8, C4×Dic5, C10.D4 [×2], C4⋊Dic5 [×2], C4⋊Dic5, C5×C4⋊C4 [×2], C2×C40, C2×Dic10, C10.D8, C20.Q8, C408C4, C405C4, C5×C4.Q8, C20⋊Q8, C4.Dic10, C403Q8
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], Q8 [×4], C23, D5, C2×D4, C2×Q8 [×2], D10 [×3], C4⋊Q8, C8⋊C22, C8.C22, Dic10 [×2], C22×D5, C8⋊Q8, C2×Dic10, D4×D5, Q8×D5, C20⋊Q8, D40⋊C2, SD16⋊D5, C403Q8

Smallest permutation representation of C403Q8
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)
(1 238 135 195)(2 209 136 166)(3 220 137 177)(4 231 138 188)(5 202 139 199)(6 213 140 170)(7 224 141 181)(8 235 142 192)(9 206 143 163)(10 217 144 174)(11 228 145 185)(12 239 146 196)(13 210 147 167)(14 221 148 178)(15 232 149 189)(16 203 150 200)(17 214 151 171)(18 225 152 182)(19 236 153 193)(20 207 154 164)(21 218 155 175)(22 229 156 186)(23 240 157 197)(24 211 158 168)(25 222 159 179)(26 233 160 190)(27 204 121 161)(28 215 122 172)(29 226 123 183)(30 237 124 194)(31 208 125 165)(32 219 126 176)(33 230 127 187)(34 201 128 198)(35 212 129 169)(36 223 130 180)(37 234 131 191)(38 205 132 162)(39 216 133 173)(40 227 134 184)(41 299 97 243)(42 310 98 254)(43 281 99 265)(44 292 100 276)(45 303 101 247)(46 314 102 258)(47 285 103 269)(48 296 104 280)(49 307 105 251)(50 318 106 262)(51 289 107 273)(52 300 108 244)(53 311 109 255)(54 282 110 266)(55 293 111 277)(56 304 112 248)(57 315 113 259)(58 286 114 270)(59 297 115 241)(60 308 116 252)(61 319 117 263)(62 290 118 274)(63 301 119 245)(64 312 120 256)(65 283 81 267)(66 294 82 278)(67 305 83 249)(68 316 84 260)(69 287 85 271)(70 298 86 242)(71 309 87 253)(72 320 88 264)(73 291 89 275)(74 302 90 246)(75 313 91 257)(76 284 92 268)(77 295 93 279)(78 306 94 250)(79 317 95 261)(80 288 96 272)
(1 69 135 85)(2 58 136 114)(3 47 137 103)(4 76 138 92)(5 65 139 81)(6 54 140 110)(7 43 141 99)(8 72 142 88)(9 61 143 117)(10 50 144 106)(11 79 145 95)(12 68 146 84)(13 57 147 113)(14 46 148 102)(15 75 149 91)(16 64 150 120)(17 53 151 109)(18 42 152 98)(19 71 153 87)(20 60 154 116)(21 49 155 105)(22 78 156 94)(23 67 157 83)(24 56 158 112)(25 45 159 101)(26 74 160 90)(27 63 121 119)(28 52 122 108)(29 41 123 97)(30 70 124 86)(31 59 125 115)(32 48 126 104)(33 77 127 93)(34 66 128 82)(35 55 129 111)(36 44 130 100)(37 73 131 89)(38 62 132 118)(39 51 133 107)(40 80 134 96)(161 301 204 245)(162 290 205 274)(163 319 206 263)(164 308 207 252)(165 297 208 241)(166 286 209 270)(167 315 210 259)(168 304 211 248)(169 293 212 277)(170 282 213 266)(171 311 214 255)(172 300 215 244)(173 289 216 273)(174 318 217 262)(175 307 218 251)(176 296 219 280)(177 285 220 269)(178 314 221 258)(179 303 222 247)(180 292 223 276)(181 281 224 265)(182 310 225 254)(183 299 226 243)(184 288 227 272)(185 317 228 261)(186 306 229 250)(187 295 230 279)(188 284 231 268)(189 313 232 257)(190 302 233 246)(191 291 234 275)(192 320 235 264)(193 309 236 253)(194 298 237 242)(195 287 238 271)(196 316 239 260)(197 305 240 249)(198 294 201 278)(199 283 202 267)(200 312 203 256)

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

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

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

44 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H5A5B8A8B8C8D10A···10F20A20B20C20D20E···20L40A···40H
order12224444444455888810···102020202020···2040···40
size1111228820204040224420202···244448···84···4

44 irreducible representations

dim111111112222222444444
type++++++++--++++-+--++-
imageC1C2C2C2C2C2C2C2Q8Q8D4D5D10D10Dic10C8⋊C22C8.C22Q8×D5D4×D5D40⋊C2SD16⋊D5
kernelC403Q8C10.D8C20.Q8C408C4C405C4C5×C4.Q8C20⋊Q8C4.Dic10C52C8C40C2×Dic5C4.Q8C4⋊C4C2×C8C8C10C10C4C22C2C2
# reps111111112222428112244

Matrix representation of C403Q8 in GL10(𝔽41)

1000000000
0100000000
004025000000
00141000000
001322350000
00252236380000
0000002121328
0000001751619
0000002151212
000000021243
,
4500000000
133700000000
002939000000
001012000000
002637010000
002418100000
0000000010
000000114039
0000001000
00000000040
,
331500000000
23800000000
003271100000
0092916150000
0073736340000
00282517140000
0000002173740
00000038243834
000000371428
000000380323

G:=sub<GL(10,GF(41))| [1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,40,14,13,25,0,0,0,0,0,0,25,1,22,22,0,0,0,0,0,0,0,0,3,36,0,0,0,0,0,0,0,0,5,38,0,0,0,0,0,0,0,0,0,0,21,17,21,0,0,0,0,0,0,0,21,5,5,21,0,0,0,0,0,0,3,16,12,24,0,0,0,0,0,0,28,19,12,3],[4,13,0,0,0,0,0,0,0,0,5,37,0,0,0,0,0,0,0,0,0,0,29,10,26,24,0,0,0,0,0,0,39,12,37,18,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,40,0,0,0,0,0,0,0,0,0,39,0,40],[33,23,0,0,0,0,0,0,0,0,15,8,0,0,0,0,0,0,0,0,0,0,3,9,7,28,0,0,0,0,0,0,27,29,37,25,0,0,0,0,0,0,11,16,36,17,0,0,0,0,0,0,0,15,34,14,0,0,0,0,0,0,0,0,0,0,21,38,3,38,0,0,0,0,0,0,7,24,7,0,0,0,0,0,0,0,37,38,14,3,0,0,0,0,0,0,40,34,28,23] >;

C403Q8 in GAP, Magma, Sage, TeX

C_{40}\rtimes_3Q_8
% in TeX

G:=Group("C40:3Q8");
// GroupNames label

G:=SmallGroup(320,483);
// by ID

G=gap.SmallGroup(320,483);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,477,120,254,555,58,438,102,12550]);
// Polycyclic

G:=Group<a,b,c|a^40=b^4=1,c^2=b^2,b*a*b^-1=a^11,c*a*c^-1=a^29,c*b*c^-1=b^-1>;
// generators/relations

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