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G = C33⋊12D8  order 432 = 24·33

3rd semidirect product of C33 and D8 acting via D8/C8=C2

metabelian, supersoluble, monomial

Aliases: C33⋊12D8, C32⋊8D24, (C3×C24)⋊9S3, C24⋊1(C3⋊S3), (C32×C24)⋊1C2, (C3×C6).67D12, C3⋊1(C32⋊5D8), C8⋊1(C33⋊C2), (C3×C12).198D6, C33⋊12D4⋊1C2, (C32×C6).62D4, C6.8(C12⋊S3), C2.4(C33⋊12D4), (C32×C12).76C22, C12.65(C2×C3⋊S3), C4.9(C2×C33⋊C2), SmallGroup(432,499)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C32×C12 — C33⋊12D8
Chief series
C1 — C3 — C32 — C33 — C32×C6 — C32×C12 — C33⋊12D4 — C33⋊12D8
Lower central
C33 — C32×C6 — C32×C12 — C33⋊12D8
Upper central
C1 — C2 — C4 — C8

Generators and relations for C33⋊12D8
 G = < a,b,c,d,e | a3=b3=c3=d8=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: 2872 in 308 conjugacy classes, 115 normal (9 characteristic)
C1, C2, C2, C3, C4, C22, S3, C6, C8, D4, C32, C12, D6, D8, C3⋊S3, C3×C6, C24, D12, C33, C3×C12, C2×C3⋊S3, D24, C33⋊C2, C32×C6, C3×C24, C12⋊S3, C32×C12, C2×C33⋊C2, C32⋊5D8, C32×C24, C33⋊12D4, C33⋊12D8
Quotients: C1, C2, C22, S3, D4, D6, D8, C3⋊S3, D12, C2×C3⋊S3, D24, C33⋊C2, C12⋊S3, C2×C33⋊C2, C32⋊5D8, C33⋊12D4, C33⋊12D8

Smallest permutation representation of C33⋊12D8
►On 216 points
Generators in S216
(1 85 117)(2 86 118)(3 87 119)(4 88 120)(5 81 113)(6 82 114)(7 83 115)(8 84 116)(9 184 29)(10 177 30)(11 178 31)(12 179 32)(13 180 25)(14 181 26)(15 182 27)(16 183 28)(17 131 65)(18 132 66)(19 133 67)(20 134 68)(21 135 69)(22 136 70)(23 129 71)(24 130 72)(33 125 55)(34 126 56)(35 127 49)(36 128 50)(37 121 51)(38 122 52)(39 123 53)(40 124 54)(41 106 159)(42 107 160)(43 108 153)(44 109 154)(45 110 155)(46 111 156)(47 112 157)(48 105 158)(57 93 208)(58 94 201)(59 95 202)(60 96 203)(61 89 204)(62 90 205)(63 91 206)(64 92 207)(73 187 144)(74 188 137)(75 189 138)(76 190 139)(77 191 140)(78 192 141)(79 185 142)(80 186 143)(97 166 152)(98 167 145)(99 168 146)(100 161 147)(101 162 148)(102 163 149)(103 164 150)(104 165 151)(169 197 216)(170 198 209)(171 199 210)(172 200 211)(173 193 212)(174 194 213)(175 195 214)(176 196 215)

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

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

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

111 conjugacy classes

class 1 2A2B2C3A···3M 4 6A···6M8A8B12A···12Z24A···24AZ
order12223···346···68812···1224···24
size111081082···222···2222···22···2

111 irreducible representations

dim111222222
type+++++++++
imageC1C2C2S3D4D6D8D12D24
kernelC33⋊12D8C32×C24C33⋊12D4C3×C24C32×C6C3×C12C33C3×C6C32
# reps1121311322652

Matrix representation of C33⋊12D8 ►in GL6(𝔽73)

010000
72720000
00727200
001000
00007272
000010
,
72720000
100000
000100
00727200
000010
000001
,
010000
72720000
001000
000100
000001
00007272
,
18680000
5230000
0055500
00685000
00001868
0000523
,
1470000
66590000
0071400
0076600
0000714
0000766

G:=sub<GL(6,GF(73))| [0,72,0,0,0,0,1,72,0,0,0,0,0,0,72,1,0,0,0,0,72,0,0,0,0,0,0,0,72,1,0,0,0,0,72,0],[72,1,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,72,0,0,0,0,1,72],[18,5,0,0,0,0,68,23,0,0,0,0,0,0,55,68,0,0,0,0,5,50,0,0,0,0,0,0,18,5,0,0,0,0,68,23],[14,66,0,0,0,0,7,59,0,0,0,0,0,0,7,7,0,0,0,0,14,66,0,0,0,0,0,0,7,7,0,0,0,0,14,66] >;
 

C33⋊12D8 in GAP, Magma, Sage, TeX 

C_3^3\rtimes_{12}D_8
 
% in TeX
 
G:=Group("C3^3:12D8");
 
// GroupNames label
 
G:=SmallGroup(432,499);
 
// by ID
 
G=gap.SmallGroup(432,499);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,85,92,254,58,1124,4037,14118]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^8=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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