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G = C2×C33⋊12D4  order 432 = 24·33

Direct product of C2 and C33⋊12D4

direct product, metabelian, supersoluble, monomial

Aliases: C2×C33⋊12D4, C62.159D6, (C3×C6)⋊8D12, (C6×C12)⋊12S3, (C3×C12)⋊22D6, C33⋊31(C2×D4), (C32×C6)⋊12D4, C6⋊1(C12⋊S3), C32⋊15(C2×D12), (C32×C12)⋊13C22, (C32×C6).97C23, (C3×C62).68C22, (C3×C6×C12)⋊5C2, C12⋊7(C2×C3⋊S3), (C2×C12)⋊3(C3⋊S3), C3⋊2(C2×C12⋊S3), C4⋊2(C2×C33⋊C2), C6.41(C22×C3⋊S3), (C2×C4)⋊2(C33⋊C2), (C3×C6).186(C22×S3), (C22×C33⋊C2)⋊4C2, C2.4(C22×C33⋊C2), (C2×C33⋊C2)⋊12C22, C22.10(C2×C33⋊C2), (C2×C6).48(C2×C3⋊S3), SmallGroup(432,722)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C32×C6 — C2×C33⋊12D4
Chief series
C1 — C3 — C32 — C33 — C32×C6 — C2×C33⋊C2 — C22×C33⋊C2 — C2×C33⋊12D4
Lower central
C33 — C32×C6 — C2×C33⋊12D4
Upper central
C1 — C22 — C2×C4

Generators and relations for C2×C33⋊12D4
 G = < a,b,c,d,e,f | a2=b3=c3=d3=e4=f2=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, fbf=b-1, cd=dc, ce=ec, fcf=c-1, de=ed, fdf=d-1, fef=e-1 >

Subgroups: 5192 in 756 conjugacy classes, 235 normal (9 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, S3, C6, C2×C4, D4, C23, C32, C12, D6, C2×C6, C2×D4, C3⋊S3, C3×C6, D12, C2×C12, C22×S3, C33, C3×C12, C2×C3⋊S3, C62, C2×D12, C33⋊C2, C32×C6, C32×C6, C12⋊S3, C6×C12, C22×C3⋊S3, C32×C12, C2×C33⋊C2, C2×C33⋊C2, C3×C62, C2×C12⋊S3, C33⋊12D4, C3×C6×C12, C22×C33⋊C2, C2×C33⋊12D4
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C3⋊S3, D12, C22×S3, C2×C3⋊S3, C2×D12, C33⋊C2, C12⋊S3, C22×C3⋊S3, C2×C33⋊C2, C2×C12⋊S3, C33⋊12D4, C22×C33⋊C2, C2×C33⋊12D4

Smallest permutation representation of C2×C33⋊12D4
►On 216 points
Generators in S216
(1 148)(2 145)(3 146)(4 147)(5 175)(6 176)(7 173)(8 174)(9 179)(10 180)(11 177)(12 178)(13 183)(14 184)(15 181)(16 182)(17 187)(18 188)(19 185)(20 186)(21 191)(22 192)(23 189)(24 190)(25 166)(26 167)(27 168)(28 165)(29 170)(30 171)(31 172)(32 169)(33 118)(34 119)(35 120)(36 117)(37 122)(38 123)(39 124)(40 121)(41 126)(42 127)(43 128)(44 125)(45 130)(46 131)(47 132)(48 129)(49 134)(50 135)(51 136)(52 133)(53 109)(54 110)(55 111)(56 112)(57 115)(58 116)(59 113)(60 114)(61 196)(62 193)(63 194)(64 195)(65 200)(66 197)(67 198)(68 199)(69 204)(70 201)(71 202)(72 203)(73 208)(74 205)(75 206)(76 207)(77 212)(78 209)(79 210)(80 211)(81 137)(82 138)(83 139)(84 140)(85 144)(86 141)(87 142)(88 143)(89 151)(90 152)(91 149)(92 150)(93 155)(94 156)(95 153)(96 154)(97 159)(98 160)(99 157)(100 158)(101 163)(102 164)(103 161)(104 162)(105 213)(106 214)(107 215)(108 216)

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

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

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

(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)

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

114 conjugacy classes

class 1 2A2B2C2D2E2F2G3A···3M4A4B6A···6AM12A···12AZ
order122222223···3446···612···12
size1111545454542···2222···22···2

114 irreducible representations

dim111122222
type+++++++++
imageC1C2C2C2S3D4D6D6D12
kernelC2×C33⋊12D4C33⋊12D4C3×C6×C12C22×C33⋊C2C6×C12C32×C6C3×C12C62C3×C6
# reps1412132261352

Matrix representation of C2×C33⋊12D4 ►in GL6(𝔽13)

100000
010000
0012000
0001200
0000120
0000012
,
010000
12120000
00121200
001000
000010
000001
,
12120000
100000
00121200
001000
0000121
0000120
,
010000
12120000
000100
00121200
000010
000001
,
360000
7100000
0010700
006300
0000120
0000012
,
1200000
110000
0012000
001100
0000012
0000120

G:=sub<GL(6,GF(13))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[0,12,0,0,0,0,1,12,0,0,0,0,0,0,12,1,0,0,0,0,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[12,1,0,0,0,0,12,0,0,0,0,0,0,0,12,1,0,0,0,0,12,0,0,0,0,0,0,0,12,12,0,0,0,0,1,0],[0,12,0,0,0,0,1,12,0,0,0,0,0,0,0,12,0,0,0,0,1,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[3,7,0,0,0,0,6,10,0,0,0,0,0,0,10,6,0,0,0,0,7,3,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,1,0,0,0,0,0,1,0,0,0,0,0,0,12,1,0,0,0,0,0,1,0,0,0,0,0,0,0,12,0,0,0,0,12,0] >;
 

C2×C33⋊12D4 in GAP, Magma, Sage, TeX 

C_2\times C_3^3\rtimes_{12}D_4
 
% in TeX
 
G:=Group("C2xC3^3:12D4");
 
// GroupNames label
 
G:=SmallGroup(432,722);
 
// by ID
 
G=gap.SmallGroup(432,722);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,254,58,1124,4037,14118]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^3=c^3=d^3=e^4=f^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,f*b*f=b^-1,c*d=d*c,c*e=e*c,f*c*f=c^-1,d*e=e*d,f*d*f=d^-1,f*e*f=e^-1>;
 
// generators/relations
 

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