metabelian, supersoluble, monomial
Aliases: C33⋊18M4(2), C62.26Dic3, (C6×C12).37S3, C4.(C33⋊5C4), C33⋊7C8⋊12C2, (C3×C12).230D6, (C3×C62).11C4, (C32×C12).7C4, C12.3(C3⋊Dic3), (C3×C12).17Dic3, C22.(C33⋊5C4), C3⋊2(C12.58D6), (C32×C12).98C22, C32⋊11(C4.Dic3), (C3×C6×C12).6C2, C12.77(C2×C3⋊S3), C6.13(C2×C3⋊Dic3), C2.3(C2×C33⋊5C4), (C2×C12).14(C3⋊S3), (C32×C6).73(C2×C4), C4.15(C2×C33⋊C2), (C3×C6).72(C2×Dic3), (C2×C6).12(C3⋊Dic3), (C2×C4).2(C33⋊C2), SmallGroup(432,502)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊18M4(2)
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=d5 >
Subgroups: 776 in 280 conjugacy classes, 171 normal (13 characteristic)
C1, C2, C2, C3, C4, C22, C6, C6, C8, C2×C4, C32, C12, C2×C6, M4(2), C3×C6, C3×C6, C3⋊C8, C2×C12, C33, C3×C12, C62, C4.Dic3, C32×C6, C32×C6, C32⋊4C8, C6×C12, C32×C12, C3×C62, C12.58D6, C33⋊7C8, C3×C6×C12, C33⋊18M4(2)
Quotients: C1, C2, C4, C22, S3, C2×C4, Dic3, D6, M4(2), C3⋊S3, C2×Dic3, C3⋊Dic3, C2×C3⋊S3, C4.Dic3, C33⋊C2, C2×C3⋊Dic3, C33⋊5C4, C2×C33⋊C2, C12.58D6, C2×C33⋊5C4, C33⋊18M4(2)
►On 216 points
Generators in S216
(1 85 117)(2 118 86)(3 87 119)(4 120 88)(5 81 113)(6 114 82)(7 83 115)(8 116 84)(9 184 29)(10 30 177)(11 178 31)(12 32 179)(13 180 25)(14 26 181)(15 182 27)(16 28 183)(17 131 65)(18 66 132)(19 133 67)(20 68 134)(21 135 69)(22 70 136)(23 129 71)(24 72 130)(33 55 125)(34 126 56)(35 49 127)(36 128 50)(37 51 121)(38 122 52)(39 53 123)(40 124 54)(41 106 159)(42 160 107)(43 108 153)(44 154 109)(45 110 155)(46 156 111)(47 112 157)(48 158 105)(57 208 93)(58 94 201)(59 202 95)(60 96 203)(61 204 89)(62 90 205)(63 206 91)(64 92 207)(73 187 144)(74 137 188)(75 189 138)(76 139 190)(77 191 140)(78 141 192)(79 185 142)(80 143 186)(97 166 152)(98 145 167)(99 168 146)(100 147 161)(101 162 148)(102 149 163)(103 164 150)(104 151 165)(169 216 197)(170 198 209)(171 210 199)(172 200 211)(173 212 193)(174 194 213)(175 214 195)(176 196 215)
(1 194 182)(2 183 195)(3 196 184)(4 177 197)(5 198 178)(6 179 199)(7 200 180)(8 181 193)(9 119 176)(10 169 120)(11 113 170)(12 171 114)(13 115 172)(14 173 116)(15 117 174)(16 175 118)(17 124 94)(18 95 125)(19 126 96)(20 89 127)(21 128 90)(22 91 121)(23 122 92)(24 93 123)(25 83 211)(26 212 84)(27 85 213)(28 214 86)(29 87 215)(30 216 88)(31 81 209)(32 210 82)(33 66 59)(34 60 67)(35 68 61)(36 62 69)(37 70 63)(38 64 71)(39 72 57)(40 58 65)(41 146 77)(42 78 147)(43 148 79)(44 80 149)(45 150 73)(46 74 151)(47 152 75)(48 76 145)(49 134 204)(50 205 135)(51 136 206)(52 207 129)(53 130 208)(54 201 131)(55 132 202)(56 203 133)(97 189 112)(98 105 190)(99 191 106)(100 107 192)(101 185 108)(102 109 186)(103 187 110)(104 111 188)(137 165 156)(138 157 166)(139 167 158)(140 159 168)(141 161 160)(142 153 162)(143 163 154)(144 155 164)
(1 112 36)(2 37 105)(3 106 38)(4 39 107)(5 108 40)(6 33 109)(7 110 34)(8 35 111)(9 77 129)(10 130 78)(11 79 131)(12 132 80)(13 73 133)(14 134 74)(15 75 135)(16 136 76)(17 31 142)(18 143 32)(19 25 144)(20 137 26)(21 27 138)(22 139 28)(23 29 140)(24 141 30)(41 52 119)(42 120 53)(43 54 113)(44 114 55)(45 56 115)(46 116 49)(47 50 117)(48 118 51)(57 100 197)(58 198 101)(59 102 199)(60 200 103)(61 104 193)(62 194 97)(63 98 195)(64 196 99)(65 178 185)(66 186 179)(67 180 187)(68 188 181)(69 182 189)(70 190 183)(71 184 191)(72 192 177)(81 153 124)(82 125 154)(83 155 126)(84 127 156)(85 157 128)(86 121 158)(87 159 122)(88 123 160)(89 165 212)(90 213 166)(91 167 214)(92 215 168)(93 161 216)(94 209 162)(95 163 210)(96 211 164)(145 175 206)(146 207 176)(147 169 208)(148 201 170)(149 171 202)(150 203 172)(151 173 204)(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)
(2 6)(4 8)(10 14)(12 16)(18 22)(20 24)(26 30)(28 32)(33 37)(35 39)(42 46)(44 48)(49 53)(51 55)(57 61)(59 63)(66 70)(68 72)(74 78)(76 80)(82 86)(84 88)(89 93)(91 95)(98 102)(100 104)(105 109)(107 111)(114 118)(116 120)(121 125)(123 127)(130 134)(132 136)(137 141)(139 143)(145 149)(147 151)(154 158)(156 160)(161 165)(163 167)(169 173)(171 175)(177 181)(179 183)(186 190)(188 192)(193 197)(195 199)(202 206)(204 208)(210 214)(212 216)
G:=sub<Sym(216)| (1,85,117)(2,118,86)(3,87,119)(4,120,88)(5,81,113)(6,114,82)(7,83,115)(8,116,84)(9,184,29)(10,30,177)(11,178,31)(12,32,179)(13,180,25)(14,26,181)(15,182,27)(16,28,183)(17,131,65)(18,66,132)(19,133,67)(20,68,134)(21,135,69)(22,70,136)(23,129,71)(24,72,130)(33,55,125)(34,126,56)(35,49,127)(36,128,50)(37,51,121)(38,122,52)(39,53,123)(40,124,54)(41,106,159)(42,160,107)(43,108,153)(44,154,109)(45,110,155)(46,156,111)(47,112,157)(48,158,105)(57,208,93)(58,94,201)(59,202,95)(60,96,203)(61,204,89)(62,90,205)(63,206,91)(64,92,207)(73,187,144)(74,137,188)(75,189,138)(76,139,190)(77,191,140)(78,141,192)(79,185,142)(80,143,186)(97,166,152)(98,145,167)(99,168,146)(100,147,161)(101,162,148)(102,149,163)(103,164,150)(104,151,165)(169,216,197)(170,198,209)(171,210,199)(172,200,211)(173,212,193)(174,194,213)(175,214,195)(176,196,215), (1,194,182)(2,183,195)(3,196,184)(4,177,197)(5,198,178)(6,179,199)(7,200,180)(8,181,193)(9,119,176)(10,169,120)(11,113,170)(12,171,114)(13,115,172)(14,173,116)(15,117,174)(16,175,118)(17,124,94)(18,95,125)(19,126,96)(20,89,127)(21,128,90)(22,91,121)(23,122,92)(24,93,123)(25,83,211)(26,212,84)(27,85,213)(28,214,86)(29,87,215)(30,216,88)(31,81,209)(32,210,82)(33,66,59)(34,60,67)(35,68,61)(36,62,69)(37,70,63)(38,64,71)(39,72,57)(40,58,65)(41,146,77)(42,78,147)(43,148,79)(44,80,149)(45,150,73)(46,74,151)(47,152,75)(48,76,145)(49,134,204)(50,205,135)(51,136,206)(52,207,129)(53,130,208)(54,201,131)(55,132,202)(56,203,133)(97,189,112)(98,105,190)(99,191,106)(100,107,192)(101,185,108)(102,109,186)(103,187,110)(104,111,188)(137,165,156)(138,157,166)(139,167,158)(140,159,168)(141,161,160)(142,153,162)(143,163,154)(144,155,164), (1,112,36)(2,37,105)(3,106,38)(4,39,107)(5,108,40)(6,33,109)(7,110,34)(8,35,111)(9,77,129)(10,130,78)(11,79,131)(12,132,80)(13,73,133)(14,134,74)(15,75,135)(16,136,76)(17,31,142)(18,143,32)(19,25,144)(20,137,26)(21,27,138)(22,139,28)(23,29,140)(24,141,30)(41,52,119)(42,120,53)(43,54,113)(44,114,55)(45,56,115)(46,116,49)(47,50,117)(48,118,51)(57,100,197)(58,198,101)(59,102,199)(60,200,103)(61,104,193)(62,194,97)(63,98,195)(64,196,99)(65,178,185)(66,186,179)(67,180,187)(68,188,181)(69,182,189)(70,190,183)(71,184,191)(72,192,177)(81,153,124)(82,125,154)(83,155,126)(84,127,156)(85,157,128)(86,121,158)(87,159,122)(88,123,160)(89,165,212)(90,213,166)(91,167,214)(92,215,168)(93,161,216)(94,209,162)(95,163,210)(96,211,164)(145,175,206)(146,207,176)(147,169,208)(148,201,170)(149,171,202)(150,203,172)(151,173,204)(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), (2,6)(4,8)(10,14)(12,16)(18,22)(20,24)(26,30)(28,32)(33,37)(35,39)(42,46)(44,48)(49,53)(51,55)(57,61)(59,63)(66,70)(68,72)(74,78)(76,80)(82,86)(84,88)(89,93)(91,95)(98,102)(100,104)(105,109)(107,111)(114,118)(116,120)(121,125)(123,127)(130,134)(132,136)(137,141)(139,143)(145,149)(147,151)(154,158)(156,160)(161,165)(163,167)(169,173)(171,175)(177,181)(179,183)(186,190)(188,192)(193,197)(195,199)(202,206)(204,208)(210,214)(212,216)>;
G:=Group( (1,85,117)(2,118,86)(3,87,119)(4,120,88)(5,81,113)(6,114,82)(7,83,115)(8,116,84)(9,184,29)(10,30,177)(11,178,31)(12,32,179)(13,180,25)(14,26,181)(15,182,27)(16,28,183)(17,131,65)(18,66,132)(19,133,67)(20,68,134)(21,135,69)(22,70,136)(23,129,71)(24,72,130)(33,55,125)(34,126,56)(35,49,127)(36,128,50)(37,51,121)(38,122,52)(39,53,123)(40,124,54)(41,106,159)(42,160,107)(43,108,153)(44,154,109)(45,110,155)(46,156,111)(47,112,157)(48,158,105)(57,208,93)(58,94,201)(59,202,95)(60,96,203)(61,204,89)(62,90,205)(63,206,91)(64,92,207)(73,187,144)(74,137,188)(75,189,138)(76,139,190)(77,191,140)(78,141,192)(79,185,142)(80,143,186)(97,166,152)(98,145,167)(99,168,146)(100,147,161)(101,162,148)(102,149,163)(103,164,150)(104,151,165)(169,216,197)(170,198,209)(171,210,199)(172,200,211)(173,212,193)(174,194,213)(175,214,195)(176,196,215), (1,194,182)(2,183,195)(3,196,184)(4,177,197)(5,198,178)(6,179,199)(7,200,180)(8,181,193)(9,119,176)(10,169,120)(11,113,170)(12,171,114)(13,115,172)(14,173,116)(15,117,174)(16,175,118)(17,124,94)(18,95,125)(19,126,96)(20,89,127)(21,128,90)(22,91,121)(23,122,92)(24,93,123)(25,83,211)(26,212,84)(27,85,213)(28,214,86)(29,87,215)(30,216,88)(31,81,209)(32,210,82)(33,66,59)(34,60,67)(35,68,61)(36,62,69)(37,70,63)(38,64,71)(39,72,57)(40,58,65)(41,146,77)(42,78,147)(43,148,79)(44,80,149)(45,150,73)(46,74,151)(47,152,75)(48,76,145)(49,134,204)(50,205,135)(51,136,206)(52,207,129)(53,130,208)(54,201,131)(55,132,202)(56,203,133)(97,189,112)(98,105,190)(99,191,106)(100,107,192)(101,185,108)(102,109,186)(103,187,110)(104,111,188)(137,165,156)(138,157,166)(139,167,158)(140,159,168)(141,161,160)(142,153,162)(143,163,154)(144,155,164), (1,112,36)(2,37,105)(3,106,38)(4,39,107)(5,108,40)(6,33,109)(7,110,34)(8,35,111)(9,77,129)(10,130,78)(11,79,131)(12,132,80)(13,73,133)(14,134,74)(15,75,135)(16,136,76)(17,31,142)(18,143,32)(19,25,144)(20,137,26)(21,27,138)(22,139,28)(23,29,140)(24,141,30)(41,52,119)(42,120,53)(43,54,113)(44,114,55)(45,56,115)(46,116,49)(47,50,117)(48,118,51)(57,100,197)(58,198,101)(59,102,199)(60,200,103)(61,104,193)(62,194,97)(63,98,195)(64,196,99)(65,178,185)(66,186,179)(67,180,187)(68,188,181)(69,182,189)(70,190,183)(71,184,191)(72,192,177)(81,153,124)(82,125,154)(83,155,126)(84,127,156)(85,157,128)(86,121,158)(87,159,122)(88,123,160)(89,165,212)(90,213,166)(91,167,214)(92,215,168)(93,161,216)(94,209,162)(95,163,210)(96,211,164)(145,175,206)(146,207,176)(147,169,208)(148,201,170)(149,171,202)(150,203,172)(151,173,204)(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), (2,6)(4,8)(10,14)(12,16)(18,22)(20,24)(26,30)(28,32)(33,37)(35,39)(42,46)(44,48)(49,53)(51,55)(57,61)(59,63)(66,70)(68,72)(74,78)(76,80)(82,86)(84,88)(89,93)(91,95)(98,102)(100,104)(105,109)(107,111)(114,118)(116,120)(121,125)(123,127)(130,134)(132,136)(137,141)(139,143)(145,149)(147,151)(154,158)(156,160)(161,165)(163,167)(169,173)(171,175)(177,181)(179,183)(186,190)(188,192)(193,197)(195,199)(202,206)(204,208)(210,214)(212,216) );
G=PermutationGroup([[(1,85,117),(2,118,86),(3,87,119),(4,120,88),(5,81,113),(6,114,82),(7,83,115),(8,116,84),(9,184,29),(10,30,177),(11,178,31),(12,32,179),(13,180,25),(14,26,181),(15,182,27),(16,28,183),(17,131,65),(18,66,132),(19,133,67),(20,68,134),(21,135,69),(22,70,136),(23,129,71),(24,72,130),(33,55,125),(34,126,56),(35,49,127),(36,128,50),(37,51,121),(38,122,52),(39,53,123),(40,124,54),(41,106,159),(42,160,107),(43,108,153),(44,154,109),(45,110,155),(46,156,111),(47,112,157),(48,158,105),(57,208,93),(58,94,201),(59,202,95),(60,96,203),(61,204,89),(62,90,205),(63,206,91),(64,92,207),(73,187,144),(74,137,188),(75,189,138),(76,139,190),(77,191,140),(78,141,192),(79,185,142),(80,143,186),(97,166,152),(98,145,167),(99,168,146),(100,147,161),(101,162,148),(102,149,163),(103,164,150),(104,151,165),(169,216,197),(170,198,209),(171,210,199),(172,200,211),(173,212,193),(174,194,213),(175,214,195),(176,196,215)], [(1,194,182),(2,183,195),(3,196,184),(4,177,197),(5,198,178),(6,179,199),(7,200,180),(8,181,193),(9,119,176),(10,169,120),(11,113,170),(12,171,114),(13,115,172),(14,173,116),(15,117,174),(16,175,118),(17,124,94),(18,95,125),(19,126,96),(20,89,127),(21,128,90),(22,91,121),(23,122,92),(24,93,123),(25,83,211),(26,212,84),(27,85,213),(28,214,86),(29,87,215),(30,216,88),(31,81,209),(32,210,82),(33,66,59),(34,60,67),(35,68,61),(36,62,69),(37,70,63),(38,64,71),(39,72,57),(40,58,65),(41,146,77),(42,78,147),(43,148,79),(44,80,149),(45,150,73),(46,74,151),(47,152,75),(48,76,145),(49,134,204),(50,205,135),(51,136,206),(52,207,129),(53,130,208),(54,201,131),(55,132,202),(56,203,133),(97,189,112),(98,105,190),(99,191,106),(100,107,192),(101,185,108),(102,109,186),(103,187,110),(104,111,188),(137,165,156),(138,157,166),(139,167,158),(140,159,168),(141,161,160),(142,153,162),(143,163,154),(144,155,164)], [(1,112,36),(2,37,105),(3,106,38),(4,39,107),(5,108,40),(6,33,109),(7,110,34),(8,35,111),(9,77,129),(10,130,78),(11,79,131),(12,132,80),(13,73,133),(14,134,74),(15,75,135),(16,136,76),(17,31,142),(18,143,32),(19,25,144),(20,137,26),(21,27,138),(22,139,28),(23,29,140),(24,141,30),(41,52,119),(42,120,53),(43,54,113),(44,114,55),(45,56,115),(46,116,49),(47,50,117),(48,118,51),(57,100,197),(58,198,101),(59,102,199),(60,200,103),(61,104,193),(62,194,97),(63,98,195),(64,196,99),(65,178,185),(66,186,179),(67,180,187),(68,188,181),(69,182,189),(70,190,183),(71,184,191),(72,192,177),(81,153,124),(82,125,154),(83,155,126),(84,127,156),(85,157,128),(86,121,158),(87,159,122),(88,123,160),(89,165,212),(90,213,166),(91,167,214),(92,215,168),(93,161,216),(94,209,162),(95,163,210),(96,211,164),(145,175,206),(146,207,176),(147,169,208),(148,201,170),(149,171,202),(150,203,172),(151,173,204),(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)], [(2,6),(4,8),(10,14),(12,16),(18,22),(20,24),(26,30),(28,32),(33,37),(35,39),(42,46),(44,48),(49,53),(51,55),(57,61),(59,63),(66,70),(68,72),(74,78),(76,80),(82,86),(84,88),(89,93),(91,95),(98,102),(100,104),(105,109),(107,111),(114,118),(116,120),(121,125),(123,127),(130,134),(132,136),(137,141),(139,143),(145,149),(147,151),(154,158),(156,160),(161,165),(163,167),(169,173),(171,175),(177,181),(179,183),(186,190),(188,192),(193,197),(195,199),(202,206),(204,208),(210,214),(212,216)]])
114 conjugacy classes
| class | 1 | 2A | 2B | 3A | ··· | 3M | 4A | 4B | 4C | 6A | ··· | 6AM | 8A | 8B | 8C | 8D | 12A | ··· | 12AZ |
| order | 1 | 2 | 2 | 3 | ··· | 3 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | 8 | 8 | 8 | 12 | ··· | 12 |
| size | 1 | 1 | 2 | 2 | ··· | 2 | 1 | 1 | 2 | 2 | ··· | 2 | 54 | 54 | 54 | 54 | 2 | ··· | 2 |
114 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C4 | C4 | S3 | Dic3 | D6 | Dic3 | M4(2) | C4.Dic3 |
| kernel | C33⋊18M4(2) | C33⋊7C8 | C3×C6×C12 | C32×C12 | C3×C62 | C6×C12 | C3×C12 | C3×C12 | C62 | C33 | C32 |
| # reps | 1 | 2 | 1 | 2 | 2 | 13 | 13 | 13 | 13 | 2 | 52 |
Matrix representation of C33⋊18M4(2) ►in GL6(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 |
| 0 | 0 | 54 | 8 | 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 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 0 |
| 0 | 0 | 0 | 0 | 16 | 64 |
| 64 | 0 | 0 | 0 | 0 | 0 |
| 10 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 |
| 0 | 0 | 54 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 0 |
| 0 | 0 | 0 | 0 | 16 | 64 |
| 32 | 69 | 0 | 0 | 0 | 0 |
| 19 | 41 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 26 | 0 | 0 |
| 0 | 0 | 28 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 70 |
| 0 | 0 | 0 | 0 | 45 | 53 |
| 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 | 0 |
| 0 | 0 | 0 | 0 | 62 | 72 |
G:=sub<GL(6,GF(73))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,64,54,0,0,0,0,0,8,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,16,0,0,0,0,0,64],[64,10,0,0,0,0,0,8,0,0,0,0,0,0,64,54,0,0,0,0,0,8,0,0,0,0,0,0,8,16,0,0,0,0,0,64],[32,19,0,0,0,0,69,41,0,0,0,0,0,0,1,28,0,0,0,0,26,72,0,0,0,0,0,0,20,45,0,0,0,0,70,53],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,62,0,0,0,0,0,72] >;
C33⋊18M4(2) in GAP, Magma, Sage, TeX
C_3^3\rtimes_{18}M_4(2) % in TeX
G:=Group("C3^3:18M4(2)"); // GroupNames label
G:=SmallGroup(432,502);
// by ID
G=gap.SmallGroup(432,502);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,141,58,1124,4037,14118]);
// 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^5>;
// generators/relations