Copied to
clipboard

G = C3318M4(2)  order 432 = 24·33

3rd semidirect product of C33 and M4(2) acting via M4(2)/C2×C4=C2

metabelian, supersoluble, monomial

Aliases: C3318M4(2), C62.26Dic3, (C6×C12).37S3, C4.(C335C4), C337C812C2, (C3×C12).230D6, (C3×C62).11C4, (C32×C12).7C4, C12.3(C3⋊Dic3), (C3×C12).17Dic3, C22.(C335C4), C32(C12.58D6), (C32×C12).98C22, C3211(C4.Dic3), (C3×C6×C12).6C2, C12.77(C2×C3⋊S3), C6.13(C2×C3⋊Dic3), C2.3(C2×C335C4), (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

C1C32×C6 — C3318M4(2)
C1C3C32C33C32×C6C32×C12C337C8 — C3318M4(2)
C33C32×C6 — C3318M4(2)
C1C4C2×C4

Generators and relations for C3318M4(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 [×13], C4 [×2], C22, C6 [×13], C6 [×13], C8 [×2], C2×C4, C32 [×13], C12 [×26], C2×C6 [×13], M4(2), C3×C6 [×13], C3×C6 [×13], C3⋊C8 [×26], C2×C12 [×13], C33, C3×C12 [×26], C62 [×13], C4.Dic3 [×13], C32×C6, C32×C6, C324C8 [×26], C6×C12 [×13], C32×C12 [×2], C3×C62, C12.58D6 [×13], C337C8 [×2], C3×C6×C12, C3318M4(2)
Quotients: C1, C2 [×3], C4 [×2], C22, S3 [×13], C2×C4, Dic3 [×26], D6 [×13], M4(2), C3⋊S3 [×13], C2×Dic3 [×13], C3⋊Dic3 [×26], C2×C3⋊S3 [×13], C4.Dic3 [×13], C33⋊C2, C2×C3⋊Dic3 [×13], C335C4 [×2], C2×C33⋊C2, C12.58D6 [×13], C2×C335C4, C3318M4(2)

Smallest permutation representation of C3318M4(2)
On 216 points
Generators in S216
(1 50 9)(2 10 51)(3 52 11)(4 12 53)(5 54 13)(6 14 55)(7 56 15)(8 16 49)(17 176 136)(18 129 169)(19 170 130)(20 131 171)(21 172 132)(22 133 173)(23 174 134)(24 135 175)(25 71 184)(26 177 72)(27 65 178)(28 179 66)(29 67 180)(30 181 68)(31 69 182)(32 183 70)(33 88 155)(34 156 81)(35 82 157)(36 158 83)(37 84 159)(38 160 85)(39 86 153)(40 154 87)(41 123 109)(42 110 124)(43 125 111)(44 112 126)(45 127 105)(46 106 128)(47 121 107)(48 108 122)(57 196 215)(58 216 197)(59 198 209)(60 210 199)(61 200 211)(62 212 193)(63 194 213)(64 214 195)(73 149 188)(74 189 150)(75 151 190)(76 191 152)(77 145 192)(78 185 146)(79 147 186)(80 187 148)(89 139 204)(90 205 140)(91 141 206)(92 207 142)(93 143 208)(94 201 144)(95 137 202)(96 203 138)(97 166 117)(98 118 167)(99 168 119)(100 120 161)(101 162 113)(102 114 163)(103 164 115)(104 116 165)
(1 194 74)(2 75 195)(3 196 76)(4 77 197)(5 198 78)(6 79 199)(7 200 80)(8 73 193)(9 63 150)(10 151 64)(11 57 152)(12 145 58)(13 59 146)(14 147 60)(15 61 148)(16 149 62)(17 153 95)(18 96 154)(19 155 89)(20 90 156)(21 157 91)(22 92 158)(23 159 93)(24 94 160)(25 99 110)(26 111 100)(27 101 112)(28 105 102)(29 103 106)(30 107 104)(31 97 108)(32 109 98)(33 139 170)(34 171 140)(35 141 172)(36 173 142)(37 143 174)(38 175 144)(39 137 176)(40 169 138)(41 118 183)(42 184 119)(43 120 177)(44 178 113)(45 114 179)(46 180 115)(47 116 181)(48 182 117)(49 188 212)(50 213 189)(51 190 214)(52 215 191)(53 192 216)(54 209 185)(55 186 210)(56 211 187)(65 162 126)(66 127 163)(67 164 128)(68 121 165)(69 166 122)(70 123 167)(71 168 124)(72 125 161)(81 131 205)(82 206 132)(83 133 207)(84 208 134)(85 135 201)(86 202 136)(87 129 203)(88 204 130)
(1 31 171)(2 172 32)(3 25 173)(4 174 26)(5 27 175)(6 176 28)(7 29 169)(8 170 30)(9 182 131)(10 132 183)(11 184 133)(12 134 177)(13 178 135)(14 136 179)(15 180 129)(16 130 181)(17 66 55)(18 56 67)(19 68 49)(20 50 69)(21 70 51)(22 52 71)(23 72 53)(24 54 65)(33 107 73)(34 74 108)(35 109 75)(36 76 110)(37 111 77)(38 78 112)(39 105 79)(40 80 106)(41 151 82)(42 83 152)(43 145 84)(44 85 146)(45 147 86)(46 87 148)(47 149 88)(48 81 150)(57 119 207)(58 208 120)(59 113 201)(60 202 114)(61 115 203)(62 204 116)(63 117 205)(64 206 118)(89 165 212)(90 213 166)(91 167 214)(92 215 168)(93 161 216)(94 209 162)(95 163 210)(96 211 164)(97 140 194)(98 195 141)(99 142 196)(100 197 143)(101 144 198)(102 199 137)(103 138 200)(104 193 139)(121 188 155)(122 156 189)(123 190 157)(124 158 191)(125 192 159)(126 160 185)(127 186 153)(128 154 187)
(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)(17 21)(19 23)(26 30)(28 32)(33 37)(35 39)(41 45)(43 47)(49 53)(51 55)(58 62)(60 64)(66 70)(68 72)(73 77)(75 79)(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)(153 157)(155 159)(161 165)(163 167)(170 174)(172 176)(177 181)(179 183)(186 190)(188 192)(193 197)(195 199)(202 206)(204 208)(210 214)(212 216)

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

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

G=PermutationGroup([(1,50,9),(2,10,51),(3,52,11),(4,12,53),(5,54,13),(6,14,55),(7,56,15),(8,16,49),(17,176,136),(18,129,169),(19,170,130),(20,131,171),(21,172,132),(22,133,173),(23,174,134),(24,135,175),(25,71,184),(26,177,72),(27,65,178),(28,179,66),(29,67,180),(30,181,68),(31,69,182),(32,183,70),(33,88,155),(34,156,81),(35,82,157),(36,158,83),(37,84,159),(38,160,85),(39,86,153),(40,154,87),(41,123,109),(42,110,124),(43,125,111),(44,112,126),(45,127,105),(46,106,128),(47,121,107),(48,108,122),(57,196,215),(58,216,197),(59,198,209),(60,210,199),(61,200,211),(62,212,193),(63,194,213),(64,214,195),(73,149,188),(74,189,150),(75,151,190),(76,191,152),(77,145,192),(78,185,146),(79,147,186),(80,187,148),(89,139,204),(90,205,140),(91,141,206),(92,207,142),(93,143,208),(94,201,144),(95,137,202),(96,203,138),(97,166,117),(98,118,167),(99,168,119),(100,120,161),(101,162,113),(102,114,163),(103,164,115),(104,116,165)], [(1,194,74),(2,75,195),(3,196,76),(4,77,197),(5,198,78),(6,79,199),(7,200,80),(8,73,193),(9,63,150),(10,151,64),(11,57,152),(12,145,58),(13,59,146),(14,147,60),(15,61,148),(16,149,62),(17,153,95),(18,96,154),(19,155,89),(20,90,156),(21,157,91),(22,92,158),(23,159,93),(24,94,160),(25,99,110),(26,111,100),(27,101,112),(28,105,102),(29,103,106),(30,107,104),(31,97,108),(32,109,98),(33,139,170),(34,171,140),(35,141,172),(36,173,142),(37,143,174),(38,175,144),(39,137,176),(40,169,138),(41,118,183),(42,184,119),(43,120,177),(44,178,113),(45,114,179),(46,180,115),(47,116,181),(48,182,117),(49,188,212),(50,213,189),(51,190,214),(52,215,191),(53,192,216),(54,209,185),(55,186,210),(56,211,187),(65,162,126),(66,127,163),(67,164,128),(68,121,165),(69,166,122),(70,123,167),(71,168,124),(72,125,161),(81,131,205),(82,206,132),(83,133,207),(84,208,134),(85,135,201),(86,202,136),(87,129,203),(88,204,130)], [(1,31,171),(2,172,32),(3,25,173),(4,174,26),(5,27,175),(6,176,28),(7,29,169),(8,170,30),(9,182,131),(10,132,183),(11,184,133),(12,134,177),(13,178,135),(14,136,179),(15,180,129),(16,130,181),(17,66,55),(18,56,67),(19,68,49),(20,50,69),(21,70,51),(22,52,71),(23,72,53),(24,54,65),(33,107,73),(34,74,108),(35,109,75),(36,76,110),(37,111,77),(38,78,112),(39,105,79),(40,80,106),(41,151,82),(42,83,152),(43,145,84),(44,85,146),(45,147,86),(46,87,148),(47,149,88),(48,81,150),(57,119,207),(58,208,120),(59,113,201),(60,202,114),(61,115,203),(62,204,116),(63,117,205),(64,206,118),(89,165,212),(90,213,166),(91,167,214),(92,215,168),(93,161,216),(94,209,162),(95,163,210),(96,211,164),(97,140,194),(98,195,141),(99,142,196),(100,197,143),(101,144,198),(102,199,137),(103,138,200),(104,193,139),(121,188,155),(122,156,189),(123,190,157),(124,158,191),(125,192,159),(126,160,185),(127,186,153),(128,154,187)], [(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),(17,21),(19,23),(26,30),(28,32),(33,37),(35,39),(41,45),(43,47),(49,53),(51,55),(58,62),(60,64),(66,70),(68,72),(73,77),(75,79),(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),(153,157),(155,159),(161,165),(163,167),(170,174),(172,176),(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 2A2B3A···3M4A4B4C6A···6AM8A8B8C8D12A···12AZ
order1223···34446···6888812···12
size1122···21122···2545454542···2

114 irreducible representations

dim11111222222
type++++-+-
imageC1C2C2C4C4S3Dic3D6Dic3M4(2)C4.Dic3
kernelC3318M4(2)C337C8C3×C6×C12C32×C12C3×C62C6×C12C3×C12C3×C12C62C33C32
# reps1212213131313252

Matrix representation of C3318M4(2) in GL6(𝔽73)

100000
010000
0064000
0054800
000010
000001
,
100000
010000
001000
000100
000080
00001664
,
6400000
1080000
0064000
0054800
000080
00001664
,
32690000
19410000
0012600
00287200
00002070
00004553
,
100000
010000
001000
000100
000010
00006272

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] >;

C3318M4(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

׿
×
𝔽