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G = C33⋊21SD16  order 432 = 24·33

3rd semidirect product of C33 and SD16 acting via SD16/C8=C2

metabelian, supersoluble, monomial

Aliases: C33⋊21SD16, C24⋊2(C3⋊S3), (C3×C24)⋊11S3, (C32×C24)⋊4C2, (C3×C6).66D12, C3⋊1(C24⋊2S3), C33⋊8Q8⋊1C2, C8⋊2(C33⋊C2), (C3×C12).197D6, (C32×C6).61D4, C6.7(C12⋊S3), C33⋊12D4.1C2, C32⋊11(C24⋊C2), C2.3(C33⋊12D4), (C32×C12).75C22, C12.64(C2×C3⋊S3), C4.8(C2×C33⋊C2), SmallGroup(432,498)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C32×C12 — C33⋊21SD16
Chief series
C1 — C3 — C32 — C33 — C32×C6 — C32×C12 — C33⋊12D4 — C33⋊21SD16
Lower central
C33 — C32×C6 — C32×C12 — C33⋊21SD16
Upper central
C1 — C2 — C4 — C8

Generators and relations for C33⋊21SD16
 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=d3 >

Subgroups: 2136 in 280 conjugacy classes, 115 normal (11 characteristic)
C1, C2, C2, C3, C4, C4, C22, S3, C6, C8, D4, Q8, C32, Dic3, C12, D6, SD16, C3⋊S3, C3×C6, C24, Dic6, D12, C33, C3⋊Dic3, C3×C12, C2×C3⋊S3, C24⋊C2, C33⋊C2, C32×C6, C3×C24, C32⋊4Q8, C12⋊S3, C33⋊5C4, C32×C12, C2×C33⋊C2, C24⋊2S3, C32×C24, C33⋊8Q8, C33⋊12D4, C33⋊21SD16
Quotients: C1, C2, C22, S3, D4, D6, SD16, C3⋊S3, D12, C2×C3⋊S3, C24⋊C2, C33⋊C2, C12⋊S3, C2×C33⋊C2, C24⋊2S3, C33⋊12D4, C33⋊21SD16

Smallest permutation representation of C33⋊21SD16
►On 216 points
Generators in S216
(1 162 68)(2 163 69)(3 164 70)(4 165 71)(5 166 72)(6 167 65)(7 168 66)(8 161 67)(9 20 107)(10 21 108)(11 22 109)(12 23 110)(13 24 111)(14 17 112)(15 18 105)(16 19 106)(25 59 181)(26 60 182)(27 61 183)(28 62 184)(29 63 177)(30 64 178)(31 57 179)(32 58 180)(33 127 53)(34 128 54)(35 121 55)(36 122 56)(37 123 49)(38 124 50)(39 125 51)(40 126 52)(41 133 146)(42 134 147)(43 135 148)(44 136 149)(45 129 150)(46 130 151)(47 131 152)(48 132 145)(73 210 143)(74 211 144)(75 212 137)(76 213 138)(77 214 139)(78 215 140)(79 216 141)(80 209 142)(81 113 155)(82 114 156)(83 115 157)(84 116 158)(85 117 159)(86 118 160)(87 119 153)(88 120 154)(89 208 172)(90 201 173)(91 202 174)(92 203 175)(93 204 176)(94 205 169)(95 206 170)(96 207 171)(97 189 193)(98 190 194)(99 191 195)(100 192 196)(101 185 197)(102 186 198)(103 187 199)(104 188 200)

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

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

(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)

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

111 conjugacy classes

class 1 2A2B3A···3M4A4B6A···6M8A8B12A···12Z24A···24AZ
order1223···3446···68812···1224···24
size111082···221082···2222···22···2

111 irreducible representations

dim1111222222
type++++++++
imageC1C2C2C2S3D4D6SD16D12C24⋊C2
kernelC33⋊21SD16C32×C24C33⋊8Q8C33⋊12D4C3×C24C32×C6C3×C12C33C3×C6C32
# reps11111311322652

Matrix representation of C33⋊21SD16 ►in GL6(𝔽73)

1700000
1710000
0072100
0072000
000013
00007271
,
7130000
7210000
001000
000100
000010
000001
,
100000
010000
0072100
0072000
000010
000001
,
7200000
0720000
0072000
0007200
00004733
00006214
,
7200000
7210000
0072000
0072100
000010
00007272

G:=sub<GL(6,GF(73))| [1,1,0,0,0,0,70,71,0,0,0,0,0,0,72,72,0,0,0,0,1,0,0,0,0,0,0,0,1,72,0,0,0,0,3,71],[71,72,0,0,0,0,3,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,47,62,0,0,0,0,33,14],[72,72,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,1,0,0,0,0,0,0,1,72,0,0,0,0,0,72] >;
 

C33⋊21SD16 in GAP, Magma, Sage, TeX 

C_3^3\rtimes_{21}{\rm SD}_{16}
 
% in TeX
 
G:=Group("C3^3:21SD16");
 
// GroupNames label
 
G:=SmallGroup(432,498);
 
// by ID
 
G=gap.SmallGroup(432,498);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,85,36,254,58,1124,4037,14118]);
 
// 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^3>;
 
// generators/relations
 

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