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G = C40⋊Q8order 320 = 26·5

6th semidirect product of C40 and Q8 acting via Q8/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C406Q8, C86Dic10, C42.12D10, Dic5.4M4(2), C55(C84Q8), C8⋊C4.5D5, C10.16(C4×Q8), C20.81(C2×Q8), C203C8.5C2, (C2×C8).154D10, C4⋊Dic5.20C4, C408C4.12C2, C2.9(C4×Dic10), C2.8(D5×M4(2)), C10.44(C8○D4), (C4×C20).12C22, (C4×Dic10).4C2, (C8×Dic5).27C2, C4.46(C2×Dic10), C4.128(C4○D20), C20.244(C4○D4), (C2×C40).224C22, (C2×C20).809C23, (C2×Dic10).19C4, C10.D4.14C4, C10.48(C2×M4(2)), C20.8Q8.15C2, C2.6(D20.2C4), (C4×Dic5).200C22, (C2×C4).28(C4×D5), (C5×C8⋊C4).4C2, C22.97(C2×C4×D5), (C2×C20).209(C2×C4), (C2×Dic5).15(C2×C4), (C2×C4).751(C22×D5), (C2×C10).165(C22×C4), (C2×C52C8).301C22, SmallGroup(320,328)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C40⋊Q8
C1C5C10C20C2×C20C4×Dic5C4×Dic10 — C40⋊Q8
C5C2×C10 — C40⋊Q8
C1C2×C4C8⋊C4

Generators and relations for C40⋊Q8
 G = < a,b,c | a40=b4=1, c2=b2, bab-1=a21, cac-1=a9, cbc-1=b-1 >

Subgroups: 254 in 94 conjugacy classes, 53 normal (47 characteristic)
C1, C2 [×3], C4 [×2], C4 [×7], 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 [×2], Dic5 [×3], C20 [×2], C20 [×2], C2×C10, C4×C8, C8⋊C4, C8⋊C4, 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, C8×Dic5, C20.8Q8 [×2], C408C4, C5×C8⋊C4, C4×Dic10, C40⋊Q8
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, C2×Dic10, C2×C4×D5, C4○D20, C4×Dic10, D5×M4(2), D20.2C4, C40⋊Q8

Smallest permutation representation of C40⋊Q8
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 81 270 202)(2 102 271 223)(3 83 272 204)(4 104 273 225)(5 85 274 206)(6 106 275 227)(7 87 276 208)(8 108 277 229)(9 89 278 210)(10 110 279 231)(11 91 280 212)(12 112 241 233)(13 93 242 214)(14 114 243 235)(15 95 244 216)(16 116 245 237)(17 97 246 218)(18 118 247 239)(19 99 248 220)(20 120 249 201)(21 101 250 222)(22 82 251 203)(23 103 252 224)(24 84 253 205)(25 105 254 226)(26 86 255 207)(27 107 256 228)(28 88 257 209)(29 109 258 230)(30 90 259 211)(31 111 260 232)(32 92 261 213)(33 113 262 234)(34 94 263 215)(35 115 264 236)(36 96 265 217)(37 117 266 238)(38 98 267 219)(39 119 268 240)(40 100 269 221)(41 166 137 282)(42 187 138 303)(43 168 139 284)(44 189 140 305)(45 170 141 286)(46 191 142 307)(47 172 143 288)(48 193 144 309)(49 174 145 290)(50 195 146 311)(51 176 147 292)(52 197 148 313)(53 178 149 294)(54 199 150 315)(55 180 151 296)(56 161 152 317)(57 182 153 298)(58 163 154 319)(59 184 155 300)(60 165 156 281)(61 186 157 302)(62 167 158 283)(63 188 159 304)(64 169 160 285)(65 190 121 306)(66 171 122 287)(67 192 123 308)(68 173 124 289)(69 194 125 310)(70 175 126 291)(71 196 127 312)(72 177 128 293)(73 198 129 314)(74 179 130 295)(75 200 131 316)(76 181 132 297)(77 162 133 318)(78 183 134 299)(79 164 135 320)(80 185 136 301)
(1 164 270 320)(2 173 271 289)(3 182 272 298)(4 191 273 307)(5 200 274 316)(6 169 275 285)(7 178 276 294)(8 187 277 303)(9 196 278 312)(10 165 279 281)(11 174 280 290)(12 183 241 299)(13 192 242 308)(14 161 243 317)(15 170 244 286)(16 179 245 295)(17 188 246 304)(18 197 247 313)(19 166 248 282)(20 175 249 291)(21 184 250 300)(22 193 251 309)(23 162 252 318)(24 171 253 287)(25 180 254 296)(26 189 255 305)(27 198 256 314)(28 167 257 283)(29 176 258 292)(30 185 259 301)(31 194 260 310)(32 163 261 319)(33 172 262 288)(34 181 263 297)(35 190 264 306)(36 199 265 315)(37 168 266 284)(38 177 267 293)(39 186 268 302)(40 195 269 311)(41 220 137 99)(42 229 138 108)(43 238 139 117)(44 207 140 86)(45 216 141 95)(46 225 142 104)(47 234 143 113)(48 203 144 82)(49 212 145 91)(50 221 146 100)(51 230 147 109)(52 239 148 118)(53 208 149 87)(54 217 150 96)(55 226 151 105)(56 235 152 114)(57 204 153 83)(58 213 154 92)(59 222 155 101)(60 231 156 110)(61 240 157 119)(62 209 158 88)(63 218 159 97)(64 227 160 106)(65 236 121 115)(66 205 122 84)(67 214 123 93)(68 223 124 102)(69 232 125 111)(70 201 126 120)(71 210 127 89)(72 219 128 98)(73 228 129 107)(74 237 130 116)(75 206 131 85)(76 215 132 94)(77 224 133 103)(78 233 134 112)(79 202 135 81)(80 211 136 90)

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

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

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

68 conjugacy classes

class 1 2A2B2C4A4B4C4D4E4F4G4H4I4J4K4L5A5B8A8B8C8D8E8F8G8H8I8J8K8L10A···10F20A···20H20I···20P40A···40P
order12224444444444445588888888888810···1020···2020···2040···40
size1111111144101010102020222222441010101020202···22···24···44···4

68 irreducible representations

dim1111111111222222222244
type+++++++-+++-
imageC1C2C2C2C2C2C2C4C4C4Q8D5M4(2)C4○D4D10D10C8○D4Dic10C4×D5C4○D20D5×M4(2)D20.2C4
kernelC40⋊Q8C203C8C8×Dic5C20.8Q8C408C4C5×C8⋊C4C4×Dic10C10.D4C4⋊Dic5C2×Dic10C40C8⋊C4Dic5C20C42C2×C8C10C8C2×C4C4C2C2
# reps1112111422224224488844

Matrix representation of C40⋊Q8 in GL6(𝔽41)

32210000
2590000
009000
000900
00002219
00002232
,
100000
36400000
0083700
0063300
0000400
0000040
,
100000
010000
00232200
0021800
00002620
00003815

G:=sub<GL(6,GF(41))| [32,25,0,0,0,0,21,9,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,22,22,0,0,0,0,19,32],[1,36,0,0,0,0,0,40,0,0,0,0,0,0,8,6,0,0,0,0,37,33,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,23,2,0,0,0,0,22,18,0,0,0,0,0,0,26,38,0,0,0,0,20,15] >;

C40⋊Q8 in GAP, Magma, Sage, TeX

C_{40}\rtimes Q_8
% in TeX

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

G:=SmallGroup(320,328);
// by ID

G=gap.SmallGroup(320,328);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,253,120,387,58,136,12550]);
// Polycyclic

G:=Group<a,b,c|a^40=b^4=1,c^2=b^2,b*a*b^-1=a^21,c*a*c^-1=a^9,c*b*c^-1=b^-1>;
// generators/relations

׿
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