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G = C33⋊15D8  order 432 = 24·33

3rd semidirect product of C33 and D8 acting via D8/D4=C2

metabelian, supersoluble, monomial

Aliases: C33⋊15D8, C33⋊7C8⋊4C2, D4⋊(C33⋊C2), (D4×C32)⋊8S3, (D4×C33)⋊3C2, (C3×C12).131D6, C33⋊12D4⋊4C2, C3⋊3(C32⋊7D8), (C32×C6).80D4, C32⋊13(D4⋊S3), C2.4(C33⋊15D4), C6.24(C32⋊7D4), (C32×C12).31C22, (C3×D4)⋊1(C3⋊S3), C12.17(C2×C3⋊S3), C4.1(C2×C33⋊C2), (C3×C6).115(C3⋊D4), SmallGroup(432,507)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C32×C12 — C33⋊15D8
Chief series
C1 — C3 — C32 — C33 — C32×C6 — C32×C12 — C33⋊12D4 — C33⋊15D8
Lower central
C33 — C32×C6 — C32×C12 — C33⋊15D8
Upper central
C1 — C2 — C4 — D4

Generators and relations for C33⋊15D8
 G = < a,b,c,d,e | a3=b3=c3=d8=e2=1, ab=ba, ac=ca, dad-1=eae=a-1, bc=cb, dbd-1=ebe=b-1, dcd-1=ece=c-1, ede=d-1 >

Subgroups: 1936 in 308 conjugacy classes, 115 normal (11 characteristic)
C1, C2, C2, C3, C4, C22, S3, C6, C6, C8, D4, D4, C32, C12, D6, C2×C6, D8, C3⋊S3, C3×C6, C3×C6, C3⋊C8, D12, C3×D4, C33, C3×C12, C2×C3⋊S3, C62, D4⋊S3, C33⋊C2, C32×C6, C32×C6, C32⋊4C8, C12⋊S3, D4×C32, C32×C12, C2×C33⋊C2, C3×C62, C32⋊7D8, C33⋊7C8, C33⋊12D4, D4×C33, C33⋊15D8
Quotients: C1, C2, C22, S3, D4, D6, D8, C3⋊S3, C3⋊D4, C2×C3⋊S3, D4⋊S3, C33⋊C2, C32⋊7D4, C2×C33⋊C2, C32⋊7D8, C33⋊15D4, C33⋊15D8

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

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

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

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

72 conjugacy classes

class 1 2A2B2C3A···3M 4 6A···6M6N···6AM8A8B12A···12M
order12223···346···66···68812···12
size1141082···222···24···454544···4

72 irreducible representations

dim1111222224
type+++++++++
imageC1C2C2C2S3D4D6D8C3⋊D4D4⋊S3
kernelC33⋊15D8C33⋊7C8C33⋊12D4D4×C33D4×C32C32×C6C3×C12C33C3×C6C32
# reps11111311322613

Matrix representation of C33⋊15D8 ►in GL8(𝔽73)

817000000
064000000
00100000
00010000
00001000
00000100
00000010
00000001
,
10000000
01000000
0071100000
00710000
00008000
0000106400
00000010
00000001
,
10000000
01000000
00100000
00010000
00008000
0000106400
00000010
00000001
,
7271000000
11000000
0045110000
0035280000
0000114700
0000726200
0000005716
0000005757
,
10000000
7272000000
0045110000
0035280000
0000114700
0000726200
0000005716
0000001616

G:=sub<GL(8,GF(73))| [8,0,0,0,0,0,0,0,17,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,71,7,0,0,0,0,0,0,10,1,0,0,0,0,0,0,0,0,8,10,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,8,10,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[72,1,0,0,0,0,0,0,71,1,0,0,0,0,0,0,0,0,45,35,0,0,0,0,0,0,11,28,0,0,0,0,0,0,0,0,11,72,0,0,0,0,0,0,47,62,0,0,0,0,0,0,0,0,57,57,0,0,0,0,0,0,16,57],[1,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,45,35,0,0,0,0,0,0,11,28,0,0,0,0,0,0,0,0,11,72,0,0,0,0,0,0,47,62,0,0,0,0,0,0,0,0,57,16,0,0,0,0,0,0,16,16] >;
 

C33⋊15D8 in GAP, Magma, Sage, TeX 

C_3^3\rtimes_{15}D_8
 
% in TeX
 
G:=Group("C3^3:15D8");
 
// GroupNames label
 
G:=SmallGroup(432,507);
 
// by ID
 
G=gap.SmallGroup(432,507);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,85,254,135,58,1124,4037,14118]);
 
// 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=e*a*e=a^-1,b*c=c*b,d*b*d^-1=e*b*e=b^-1,d*c*d^-1=e*c*e=c^-1,e*d*e=d^-1>;
 
// generators/relations
 

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