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G = Dic93Q8order 288 = 25·32

The semidirect product of Dic9 and Q8 acting through Inn(Dic9)

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic93Q8, Dic185C4, C92(C4×Q8), C4⋊C4.7D9, C4.4(C4×D9), C2.1(Q8×D9), C12.7(C4×S3), C6.32(S3×Q8), C36.10(C2×C4), (C2×C4).29D18, C18.10(C2×Q8), (C2×C12).179D6, Dic9⋊C4.5C2, C18.8(C22×C4), (C4×Dic9).8C2, Dic9.2(C2×C4), C18.24(C4○D4), C2.3(D42D9), C3.(Dic6⋊C4), (C2×C18).28C23, (C2×C36).55C22, (C2×Dic18).7C2, C6.79(D42S3), C22.15(C22×D9), (C2×Dic9).28C22, C6.47(S3×C2×C4), C2.10(C2×C4×D9), (C9×C4⋊C4).4C2, (C3×C4⋊C4).5S3, (C2×C6).185(C22×S3), SmallGroup(288,97)

Series: Derived Chief Lower central Upper central

C1C18 — Dic93Q8
C1C3C9C18C2×C18C2×Dic9C4×Dic9 — Dic93Q8
C9C18 — Dic93Q8
C1C22C4⋊C4

Generators and relations for Dic93Q8
 G = < a,b,c,d | a18=c4=1, b2=a9, d2=c2, bab-1=cac-1=a-1, ad=da, bc=cb, bd=db, dcd-1=c-1 >

Subgroups: 344 in 105 conjugacy classes, 54 normal (26 characteristic)
C1, C2 [×3], C3, C4 [×2], C4 [×9], C22, C6 [×3], C2×C4, C2×C4 [×2], C2×C4 [×4], Q8 [×4], C9, Dic3 [×7], C12 [×2], C12 [×2], C2×C6, C42 [×3], C4⋊C4, C4⋊C4 [×2], C2×Q8, C18 [×3], Dic6 [×4], C2×Dic3 [×4], C2×C12, C2×C12 [×2], C4×Q8, Dic9 [×6], Dic9, C36 [×2], C36 [×2], C2×C18, C4×Dic3 [×3], Dic3⋊C4 [×2], C3×C4⋊C4, C2×Dic6, Dic18 [×4], C2×Dic9 [×2], C2×Dic9 [×2], C2×C36, C2×C36 [×2], Dic6⋊C4, C4×Dic9, C4×Dic9 [×2], Dic9⋊C4 [×2], C9×C4⋊C4, C2×Dic18, Dic93Q8
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], Q8 [×2], C23, D6 [×3], C22×C4, C2×Q8, C4○D4, D9, C4×S3 [×2], C22×S3, C4×Q8, D18 [×3], S3×C2×C4, D42S3, S3×Q8, C4×D9 [×2], C22×D9, Dic6⋊C4, C2×C4×D9, D42D9, Q8×D9, Dic93Q8

Smallest permutation representation of Dic93Q8
Regular action on 288 points
Generators in S288
(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)
(1 146 10 155)(2 145 11 154)(3 162 12 153)(4 161 13 152)(5 160 14 151)(6 159 15 150)(7 158 16 149)(8 157 17 148)(9 156 18 147)(19 172 28 163)(20 171 29 180)(21 170 30 179)(22 169 31 178)(23 168 32 177)(24 167 33 176)(25 166 34 175)(26 165 35 174)(27 164 36 173)(37 182 46 191)(38 181 47 190)(39 198 48 189)(40 197 49 188)(41 196 50 187)(42 195 51 186)(43 194 52 185)(44 193 53 184)(45 192 54 183)(55 199 64 208)(56 216 65 207)(57 215 66 206)(58 214 67 205)(59 213 68 204)(60 212 69 203)(61 211 70 202)(62 210 71 201)(63 209 72 200)(73 233 82 224)(74 232 83 223)(75 231 84 222)(76 230 85 221)(77 229 86 220)(78 228 87 219)(79 227 88 218)(80 226 89 217)(81 225 90 234)(91 244 100 235)(92 243 101 252)(93 242 102 251)(94 241 103 250)(95 240 104 249)(96 239 105 248)(97 238 106 247)(98 237 107 246)(99 236 108 245)(109 263 118 254)(110 262 119 253)(111 261 120 270)(112 260 121 269)(113 259 122 268)(114 258 123 267)(115 257 124 266)(116 256 125 265)(117 255 126 264)(127 285 136 276)(128 284 137 275)(129 283 138 274)(130 282 139 273)(131 281 140 272)(132 280 141 271)(133 279 142 288)(134 278 143 287)(135 277 144 286)
(1 199 19 189)(2 216 20 188)(3 215 21 187)(4 214 22 186)(5 213 23 185)(6 212 24 184)(7 211 25 183)(8 210 26 182)(9 209 27 181)(10 208 28 198)(11 207 29 197)(12 206 30 196)(13 205 31 195)(14 204 32 194)(15 203 33 193)(16 202 34 192)(17 201 35 191)(18 200 36 190)(37 148 62 174)(38 147 63 173)(39 146 64 172)(40 145 65 171)(41 162 66 170)(42 161 67 169)(43 160 68 168)(44 159 69 167)(45 158 70 166)(46 157 71 165)(47 156 72 164)(48 155 55 163)(49 154 56 180)(50 153 57 179)(51 152 58 178)(52 151 59 177)(53 150 60 176)(54 149 61 175)(73 260 92 283)(74 259 93 282)(75 258 94 281)(76 257 95 280)(77 256 96 279)(78 255 97 278)(79 254 98 277)(80 253 99 276)(81 270 100 275)(82 269 101 274)(83 268 102 273)(84 267 103 272)(85 266 104 271)(86 265 105 288)(87 264 106 287)(88 263 107 286)(89 262 108 285)(90 261 91 284)(109 237 144 227)(110 236 127 226)(111 235 128 225)(112 252 129 224)(113 251 130 223)(114 250 131 222)(115 249 132 221)(116 248 133 220)(117 247 134 219)(118 246 135 218)(119 245 136 217)(120 244 137 234)(121 243 138 233)(122 242 139 232)(123 241 140 231)(124 240 141 230)(125 239 142 229)(126 238 143 228)
(1 99 19 80)(2 100 20 81)(3 101 21 82)(4 102 22 83)(5 103 23 84)(6 104 24 85)(7 105 25 86)(8 106 26 87)(9 107 27 88)(10 108 28 89)(11 91 29 90)(12 92 30 73)(13 93 31 74)(14 94 32 75)(15 95 33 76)(16 96 34 77)(17 97 35 78)(18 98 36 79)(37 143 62 126)(38 144 63 109)(39 127 64 110)(40 128 65 111)(41 129 66 112)(42 130 67 113)(43 131 68 114)(44 132 69 115)(45 133 70 116)(46 134 71 117)(47 135 72 118)(48 136 55 119)(49 137 56 120)(50 138 57 121)(51 139 58 122)(52 140 59 123)(53 141 60 124)(54 142 61 125)(145 235 171 225)(146 236 172 226)(147 237 173 227)(148 238 174 228)(149 239 175 229)(150 240 176 230)(151 241 177 231)(152 242 178 232)(153 243 179 233)(154 244 180 234)(155 245 163 217)(156 246 164 218)(157 247 165 219)(158 248 166 220)(159 249 167 221)(160 250 168 222)(161 251 169 223)(162 252 170 224)(181 286 209 263)(182 287 210 264)(183 288 211 265)(184 271 212 266)(185 272 213 267)(186 273 214 268)(187 274 215 269)(188 275 216 270)(189 276 199 253)(190 277 200 254)(191 278 201 255)(192 279 202 256)(193 280 203 257)(194 281 204 258)(195 282 205 259)(196 283 206 260)(197 284 207 261)(198 285 208 262)

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

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

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

60 conjugacy classes

class 1 2A2B2C 3 4A···4F4G4H4I4J4K···4P6A6B6C9A9B9C12A···12F18A···18I36A···36R
order122234···444444···466699912···1218···1836···36
size111122···2999918···182222224···42···24···4

60 irreducible representations

dim111111222222224444
type++++++-+++----
imageC1C2C2C2C2C4S3Q8D6C4○D4D9C4×S3D18C4×D9D42S3S3×Q8D42D9Q8×D9
kernelDic93Q8C4×Dic9Dic9⋊C4C9×C4⋊C4C2×Dic18Dic18C3×C4⋊C4Dic9C2×C12C18C4⋊C4C12C2×C4C4C6C6C2C2
# reps1321181232349121133

Matrix representation of Dic93Q8 in GL4(𝔽37) generated by

61700
202600
0010
0001
,
36800
9100
0010
0001
,
311100
17600
0001
00360
,
36000
03600
00834
003429
G:=sub<GL(4,GF(37))| [6,20,0,0,17,26,0,0,0,0,1,0,0,0,0,1],[36,9,0,0,8,1,0,0,0,0,1,0,0,0,0,1],[31,17,0,0,11,6,0,0,0,0,0,36,0,0,1,0],[36,0,0,0,0,36,0,0,0,0,8,34,0,0,34,29] >;

Dic93Q8 in GAP, Magma, Sage, TeX

{\rm Dic}_9\rtimes_3Q_8
% in TeX

G:=Group("Dic9:3Q8");
// GroupNames label

G:=SmallGroup(288,97);
// by ID

G=gap.SmallGroup(288,97);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,112,64,135,142,6725,292,9414]);
// Polycyclic

G:=Group<a,b,c,d|a^18=c^4=1,b^2=a^9,d^2=c^2,b*a*b^-1=c*a*c^-1=a^-1,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽