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G = C33⋊24SD16  order 432 = 24·33

3rd semidirect product of C33 and SD16 acting via SD16/D4=C2

metabelian, supersoluble, monomial

Aliases: C33⋊24SD16, C33⋊7C8⋊5C2, C33⋊8Q8⋊4C2, (C3×C12).132D6, D4.(C33⋊C2), (D4×C33).3C2, (C32×C6).81D4, (D4×C32).16S3, C3⋊3(C32⋊9SD16), C32⋊15(D4.S3), C6.25(C32⋊7D4), C2.5(C33⋊15D4), (C32×C12).32C22, C12.18(C2×C3⋊S3), (C3×D4).5(C3⋊S3), C4.2(C2×C33⋊C2), (C3×C6).116(C3⋊D4), SmallGroup(432,508)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C32×C12 — C33⋊24SD16
Chief series
C1 — C3 — C32 — C33 — C32×C6 — C32×C12 — C33⋊8Q8 — C33⋊24SD16
Lower central
C33 — C32×C6 — C32×C12 — C33⋊24SD16
Upper central
C1 — C2 — C4 — D4

Generators and relations for C33⋊24SD16
 G = < a,b,c,d,e | a3=b3=c3=d8=e2=1, ab=ba, ac=ca, dad-1=a-1, ae=ea, bc=cb, dbd-1=b-1, be=eb, dcd-1=c-1, ce=ec, ede=d3 >

Subgroups: 1200 in 280 conjugacy classes, 115 normal (11 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C8, D4, Q8, C32, Dic3, C12, C2×C6, SD16, C3×C6, C3×C6, C3⋊C8, Dic6, C3×D4, C33, C3⋊Dic3, C3×C12, C62, D4.S3, C32×C6, C32×C6, C32⋊4C8, C32⋊4Q8, D4×C32, C33⋊5C4, C32×C12, C3×C62, C32⋊9SD16, C33⋊7C8, C33⋊8Q8, D4×C33, C33⋊24SD16
Quotients: C1, C2, C22, S3, D4, D6, SD16, C3⋊S3, C3⋊D4, C2×C3⋊S3, D4.S3, C33⋊C2, C32⋊7D4, C2×C33⋊C2, C32⋊9SD16, C33⋊15D4, C33⋊24SD16

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

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

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

(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)

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

72 conjugacy classes

class 1 2A2B3A···3M4A4B6A···6M6N···6AM8A8B12A···12M
order1223···3446···66···68812···12
size1142···221082···24···454544···4

72 irreducible representations

dim1111222224
type+++++++-
imageC1C2C2C2S3D4D6SD16C3⋊D4D4.S3
kernelC33⋊24SD16C33⋊7C8C33⋊8Q8D4×C33D4×C32C32×C6C3×C12C33C3×C6C32
# reps11111311322613

Matrix representation of C33⋊24SD16 ►in GL8(𝔽73)

10000000
01000000
006400000
006980000
000064000
000016800
00000010
00000001
,
7272000000
10000000
006400000
006980000
00008000
0000576400
00000010
00000001
,
01000000
7272000000
00800000
004640000
00008000
0000576400
00000010
00000001
,
132000000
6260000000
005890000
0056150000
0000117100
0000606200
000000055
000000412
,
10000000
01000000
00100000
0052720000
00001000
00000100
00000010
0000004872

G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,64,69,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,64,16,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[72,1,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,64,69,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,8,57,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[0,72,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,0,8,4,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,8,57,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[13,62,0,0,0,0,0,0,2,60,0,0,0,0,0,0,0,0,58,56,0,0,0,0,0,0,9,15,0,0,0,0,0,0,0,0,11,60,0,0,0,0,0,0,71,62,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,55,12],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,52,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,48,0,0,0,0,0,0,0,72] >;
 

C33⋊24SD16 in GAP, Magma, Sage, TeX 

C_3^3\rtimes_{24}{\rm SD}_{16}
 
% in TeX
 
G:=Group("C3^3:24SD16");
 
// GroupNames label
 
G:=SmallGroup(432,508);
 
// by ID
 
G=gap.SmallGroup(432,508);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,85,254,135,58,1124,4037,14118]);
 
// 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,d*a*d^-1=a^-1,a*e=e*a,b*c=c*b,d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=c^-1,c*e=e*c,e*d*e=d^3>;
 
// generators/relations
 

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