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G = C33⋊9D9  order 486 = 2·35

3rd semidirect product of C33 and D9 acting via D9/C9=C2

metabelian, supersoluble, monomial, A-group

Aliases: C33⋊9D9, C34.15S3, (C33×C9)⋊7C2, C9⋊(C33⋊C2), C32⋊6(C9⋊S3), (C32×C9)⋊31S3, C3⋊(C32⋊4D9), C3.(C34⋊C2), C33.52(C3⋊S3), C32.13(C33⋊C2), (C3×C9)⋊11(C3⋊S3), SmallGroup(486,247)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C33×C9 — C33⋊9D9
Chief series
C1 — C3 — C32 — C33 — C34 — C33×C9 — C33⋊9D9
Lower central
C33×C9 — C33⋊9D9
Upper central
C1

Generators and relations for C33⋊9D9
 G = < a,b,c,d,e | a3=b3=c3=d9=e2=1, ab=ba, ac=ca, ad=da, eae=a-1, bc=cb, bd=db, ebe=b-1, cd=dc, ece=c-1, ede=d-1 >

Subgroups: 9652 in 792 conjugacy classes, 397 normal (5 characteristic)
C1, C2, C3, C3, S3, C9, C32, D9, C3⋊S3, C3×C9, C33, C9⋊S3, C33⋊C2, C32×C9, C34, C32⋊4D9, C34⋊C2, C33×C9, C33⋊9D9
Quotients: C1, C2, S3, D9, C3⋊S3, C9⋊S3, C33⋊C2, C32⋊4D9, C34⋊C2, C33⋊9D9

Smallest permutation representation of C33⋊9D9
►On 243 points
Generators in S243
(1 103 94)(2 104 95)(3 105 96)(4 106 97)(5 107 98)(6 108 99)(7 100 91)(8 101 92)(9 102 93)(10 110 19)(11 111 20)(12 112 21)(13 113 22)(14 114 23)(15 115 24)(16 116 25)(17 117 26)(18 109 27)(28 188 179)(29 189 180)(30 181 172)(31 182 173)(32 183 174)(33 184 175)(34 185 176)(35 186 177)(36 187 178)(37 56 47)(38 57 48)(39 58 49)(40 59 50)(41 60 51)(42 61 52)(43 62 53)(44 63 54)(45 55 46)(64 87 73)(65 88 74)(66 89 75)(67 90 76)(68 82 77)(69 83 78)(70 84 79)(71 85 80)(72 86 81)(118 136 127)(119 137 128)(120 138 129)(121 139 130)(122 140 131)(123 141 132)(124 142 133)(125 143 134)(126 144 135)(145 165 154)(146 166 155)(147 167 156)(148 168 157)(149 169 158)(150 170 159)(151 171 160)(152 163 161)(153 164 162)(190 211 202)(191 212 203)(192 213 204)(193 214 205)(194 215 206)(195 216 207)(196 208 199)(197 209 200)(198 210 201)(217 235 226)(218 236 227)(219 237 228)(220 238 229)(221 239 230)(222 240 231)(223 241 232)(224 242 233)(225 243 234)

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

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

(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)

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

123 conjugacy classes

class 1  2 3A···3AN9A···9CC
order123···39···9
size12432···22···2

123 irreducible representations

dim11222
type+++++
imageC1C2S3S3D9
kernelC33⋊9D9C33×C9C32×C9C34C33
# reps1139181

Matrix representation of C33⋊9D9 ►in GL8(𝔽19)

1818000000
10000000
00010000
0018180000
00000100
0000181800
00000001
0000001818
,
10000000
01000000
00100000
00010000
0000181800
00001000
00000001
0000001818
,
1818000000
10000000
0018180000
00100000
00000100
0000181800
00000001
0000001818
,
214000000
57000000
0012170000
002140000
0000121700
000021400
0000001217
000000214
,
214000000
1217000000
00570000
002140000
0000141200
000017500
0000001412
000000175

G:=sub<GL(8,GF(19))| [18,1,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,18,1,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[18,1,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,18,1,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[2,5,0,0,0,0,0,0,14,7,0,0,0,0,0,0,0,0,12,2,0,0,0,0,0,0,17,14,0,0,0,0,0,0,0,0,12,2,0,0,0,0,0,0,17,14,0,0,0,0,0,0,0,0,12,2,0,0,0,0,0,0,17,14],[2,12,0,0,0,0,0,0,14,17,0,0,0,0,0,0,0,0,5,2,0,0,0,0,0,0,7,14,0,0,0,0,0,0,0,0,14,17,0,0,0,0,0,0,12,5,0,0,0,0,0,0,0,0,14,17,0,0,0,0,0,0,12,5] >;
 

C33⋊9D9 in GAP, Magma, Sage, TeX 

C_3^3\rtimes_9D_9
 
% in TeX
 
G:=Group("C3^3:9D9");
 
// GroupNames label
 
G:=SmallGroup(486,247);
 
// by ID
 
G=gap.SmallGroup(486,247);
 
# by ID
 
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,1993,1951,218,867,3244,11669]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^9=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e=a^-1,b*c=c*b,b*d=d*b,e*b*e=b^-1,c*d=d*c,e*c*e=c^-1,e*d*e=d^-1>;
 
// generators/relations
 

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