Copied to
clipboard

G = C40⋊3Q8  order 320 = 26·5

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

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C40⋊3Q8, C8⋊2Dic10, C5⋊2(C8⋊Q8), C5⋊2C8⋊1Q8, C20⋊Q8.7C2, C4.21(Q8×D5), C4⋊C4.33D10, (C2×C8).59D10, C4.Q8.3D5, C2.9(C20⋊Q8), C20.57(C2×Q8), C40⋊8C4.2C2, C10.14(C4⋊Q8), C40⋊5C4.17C2, (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×C5⋊2C8).53C22, (C2×C4).375(C22×D5), SmallGroup(320,483)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C20 — C40⋊3Q8
Chief series
C1 — C5 — C10 — C2×C10 — C2×C20 — C4×Dic5 — C40⋊8C4 — C40⋊3Q8
Lower central
C5 — C10 — C2×C20 — C40⋊3Q8
Upper central
C1 — C22 — C2×C4 — C4.Q8

Generators and relations for C40⋊3Q8
 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, C4, C4, C22, C5, C8, C8, C2×C4, C2×C4, Q8, C10, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C8⋊C4, C4.Q8, C4.Q8, C2.D8, C42.C2, C4⋊Q8, C5⋊2C8, C40, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C8⋊Q8, C2×C5⋊2C8, C4×Dic5, C10.D4, C4⋊Dic5, C4⋊Dic5, C5×C4⋊C4, C2×C40, C2×Dic10, C10.D8, C20.Q8, C40⋊8C4, C40⋊5C4, C5×C4.Q8, C20⋊Q8, C4.Dic10, C40⋊3Q8
Quotients: C1, C2, C22, D4, Q8, C23, D5, C2×D4, C2×Q8, D10, C4⋊Q8, C8⋊C22, C8.C22, Dic10, C22×D5, C8⋊Q8, C2×Dic10, D4×D5, Q8×D5, C20⋊Q8, D40⋊C2, SD16⋊D5, C40⋊3Q8

Smallest permutation representation of C40⋊3Q8
►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)

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

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

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
kernelC40⋊3Q8C10.D8C20.Q8C40⋊8C4C40⋊5C4C5×C4.Q8C20⋊Q8C4.Dic10C5⋊2C8C40C2×Dic5C4.Q8C4⋊C4C2×C8C8C10C10C4C22C2C2
# reps111111112222428112244

Matrix representation of C40⋊3Q8 ►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] >;
 

C40⋊3Q8 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
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁