direct product, metabelian, supersoluble, monomial
Aliases: C2×C36⋊S3, C6⋊1D36, C36⋊7D6, C18⋊1D12, C12⋊7D18, C62.136D6, (C2×C36)⋊3S3, (C6×C36)⋊7C2, C9⋊2(C2×D12), C3⋊2(C2×D36), (C2×C12)⋊3D9, (C3×C18)⋊6D4, (C6×C12).32S3, (C3×C6).60D12, (C2×C6).43D18, (C2×C18).43D6, (C3×C36)⋊10C22, (C3×C12).195D6, C6.41(C22×D9), C32.5(C2×D12), C6.6(C12⋊S3), (C6×C18).49C22, (C3×C18).50C23, C18.41(C22×S3), C4⋊2(C2×C9⋊S3), (C3×C9)⋊12(C2×D4), (C2×C4)⋊2(C9⋊S3), C3.(C2×C12⋊S3), C12.63(C2×C3⋊S3), (C2×C9⋊S3)⋊8C22, (C22×C9⋊S3)⋊4C2, C2.4(C22×C9⋊S3), (C2×C12).9(C3⋊S3), C22.10(C2×C9⋊S3), C6.30(C22×C3⋊S3), (C3×C6).164(C22×S3), (C2×C6).36(C2×C3⋊S3), SmallGroup(432,382)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C36⋊S3
G = < a,b,c,d | a2=b36=c3=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 2132 in 270 conjugacy classes, 91 normal (17 characteristic)
C1, C2, C2, C2, C3, C3, C4, C22, C22, S3, C6, C6, C2×C4, D4, C23, C9, C32, C12, D6, C2×C6, C2×C6, C2×D4, D9, C18, C3⋊S3, C3×C6, C3×C6, D12, C2×C12, C2×C12, C22×S3, C3×C9, C36, D18, C2×C18, C3×C12, C2×C3⋊S3, C62, C2×D12, C9⋊S3, C3×C18, C3×C18, D36, C2×C36, C22×D9, C12⋊S3, C6×C12, C22×C3⋊S3, C3×C36, C2×C9⋊S3, C2×C9⋊S3, C6×C18, C2×D36, C2×C12⋊S3, C36⋊S3, C6×C36, C22×C9⋊S3, C2×C36⋊S3
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, D9, C3⋊S3, D12, C22×S3, D18, C2×C3⋊S3, C2×D12, C9⋊S3, D36, C22×D9, C12⋊S3, C22×C3⋊S3, C2×C9⋊S3, C2×D36, C2×C12⋊S3, C36⋊S3, C22×C9⋊S3, C2×C36⋊S3
►On 216 points
Generators in S216
(1 113)(2 114)(3 115)(4 116)(5 117)(6 118)(7 119)(8 120)(9 121)(10 122)(11 123)(12 124)(13 125)(14 126)(15 127)(16 128)(17 129)(18 130)(19 131)(20 132)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 141)(30 142)(31 143)(32 144)(33 109)(34 110)(35 111)(36 112)(37 203)(38 204)(39 205)(40 206)(41 207)(42 208)(43 209)(44 210)(45 211)(46 212)(47 213)(48 214)(49 215)(50 216)(51 181)(52 182)(53 183)(54 184)(55 185)(56 186)(57 187)(58 188)(59 189)(60 190)(61 191)(62 192)(63 193)(64 194)(65 195)(66 196)(67 197)(68 198)(69 199)(70 200)(71 201)(72 202)(73 155)(74 156)(75 157)(76 158)(77 159)(78 160)(79 161)(80 162)(81 163)(82 164)(83 165)(84 166)(85 167)(86 168)(87 169)(88 170)(89 171)(90 172)(91 173)(92 174)(93 175)(94 176)(95 177)(96 178)(97 179)(98 180)(99 145)(100 146)(101 147)(102 148)(103 149)(104 150)(105 151)(106 152)(107 153)(108 154)
(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)
(1 152 185)(2 153 186)(3 154 187)(4 155 188)(5 156 189)(6 157 190)(7 158 191)(8 159 192)(9 160 193)(10 161 194)(11 162 195)(12 163 196)(13 164 197)(14 165 198)(15 166 199)(16 167 200)(17 168 201)(18 169 202)(19 170 203)(20 171 204)(21 172 205)(22 173 206)(23 174 207)(24 175 208)(25 176 209)(26 177 210)(27 178 211)(28 179 212)(29 180 213)(30 145 214)(31 146 215)(32 147 216)(33 148 181)(34 149 182)(35 150 183)(36 151 184)(37 131 88)(38 132 89)(39 133 90)(40 134 91)(41 135 92)(42 136 93)(43 137 94)(44 138 95)(45 139 96)(46 140 97)(47 141 98)(48 142 99)(49 143 100)(50 144 101)(51 109 102)(52 110 103)(53 111 104)(54 112 105)(55 113 106)(56 114 107)(57 115 108)(58 116 73)(59 117 74)(60 118 75)(61 119 76)(62 120 77)(63 121 78)(64 122 79)(65 123 80)(66 124 81)(67 125 82)(68 126 83)(69 127 84)(70 128 85)(71 129 86)(72 130 87)
(1 140)(2 139)(3 138)(4 137)(5 136)(6 135)(7 134)(8 133)(9 132)(10 131)(11 130)(12 129)(13 128)(14 127)(15 126)(16 125)(17 124)(18 123)(19 122)(20 121)(21 120)(22 119)(23 118)(24 117)(25 116)(26 115)(27 114)(28 113)(29 112)(30 111)(31 110)(32 109)(33 144)(34 143)(35 142)(36 141)(37 161)(38 160)(39 159)(40 158)(41 157)(42 156)(43 155)(44 154)(45 153)(46 152)(47 151)(48 150)(49 149)(50 148)(51 147)(52 146)(53 145)(54 180)(55 179)(56 178)(57 177)(58 176)(59 175)(60 174)(61 173)(62 172)(63 171)(64 170)(65 169)(66 168)(67 167)(68 166)(69 165)(70 164)(71 163)(72 162)(73 209)(74 208)(75 207)(76 206)(77 205)(78 204)(79 203)(80 202)(81 201)(82 200)(83 199)(84 198)(85 197)(86 196)(87 195)(88 194)(89 193)(90 192)(91 191)(92 190)(93 189)(94 188)(95 187)(96 186)(97 185)(98 184)(99 183)(100 182)(101 181)(102 216)(103 215)(104 214)(105 213)(106 212)(107 211)(108 210)
G:=sub<Sym(216)| (1,113)(2,114)(3,115)(4,116)(5,117)(6,118)(7,119)(8,120)(9,121)(10,122)(11,123)(12,124)(13,125)(14,126)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,141)(30,142)(31,143)(32,144)(33,109)(34,110)(35,111)(36,112)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,213)(48,214)(49,215)(50,216)(51,181)(52,182)(53,183)(54,184)(55,185)(56,186)(57,187)(58,188)(59,189)(60,190)(61,191)(62,192)(63,193)(64,194)(65,195)(66,196)(67,197)(68,198)(69,199)(70,200)(71,201)(72,202)(73,155)(74,156)(75,157)(76,158)(77,159)(78,160)(79,161)(80,162)(81,163)(82,164)(83,165)(84,166)(85,167)(86,168)(87,169)(88,170)(89,171)(90,172)(91,173)(92,174)(93,175)(94,176)(95,177)(96,178)(97,179)(98,180)(99,145)(100,146)(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154), (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), (1,152,185)(2,153,186)(3,154,187)(4,155,188)(5,156,189)(6,157,190)(7,158,191)(8,159,192)(9,160,193)(10,161,194)(11,162,195)(12,163,196)(13,164,197)(14,165,198)(15,166,199)(16,167,200)(17,168,201)(18,169,202)(19,170,203)(20,171,204)(21,172,205)(22,173,206)(23,174,207)(24,175,208)(25,176,209)(26,177,210)(27,178,211)(28,179,212)(29,180,213)(30,145,214)(31,146,215)(32,147,216)(33,148,181)(34,149,182)(35,150,183)(36,151,184)(37,131,88)(38,132,89)(39,133,90)(40,134,91)(41,135,92)(42,136,93)(43,137,94)(44,138,95)(45,139,96)(46,140,97)(47,141,98)(48,142,99)(49,143,100)(50,144,101)(51,109,102)(52,110,103)(53,111,104)(54,112,105)(55,113,106)(56,114,107)(57,115,108)(58,116,73)(59,117,74)(60,118,75)(61,119,76)(62,120,77)(63,121,78)(64,122,79)(65,123,80)(66,124,81)(67,125,82)(68,126,83)(69,127,84)(70,128,85)(71,129,86)(72,130,87), (1,140)(2,139)(3,138)(4,137)(5,136)(6,135)(7,134)(8,133)(9,132)(10,131)(11,130)(12,129)(13,128)(14,127)(15,126)(16,125)(17,124)(18,123)(19,122)(20,121)(21,120)(22,119)(23,118)(24,117)(25,116)(26,115)(27,114)(28,113)(29,112)(30,111)(31,110)(32,109)(33,144)(34,143)(35,142)(36,141)(37,161)(38,160)(39,159)(40,158)(41,157)(42,156)(43,155)(44,154)(45,153)(46,152)(47,151)(48,150)(49,149)(50,148)(51,147)(52,146)(53,145)(54,180)(55,179)(56,178)(57,177)(58,176)(59,175)(60,174)(61,173)(62,172)(63,171)(64,170)(65,169)(66,168)(67,167)(68,166)(69,165)(70,164)(71,163)(72,162)(73,209)(74,208)(75,207)(76,206)(77,205)(78,204)(79,203)(80,202)(81,201)(82,200)(83,199)(84,198)(85,197)(86,196)(87,195)(88,194)(89,193)(90,192)(91,191)(92,190)(93,189)(94,188)(95,187)(96,186)(97,185)(98,184)(99,183)(100,182)(101,181)(102,216)(103,215)(104,214)(105,213)(106,212)(107,211)(108,210)>;
G:=Group( (1,113)(2,114)(3,115)(4,116)(5,117)(6,118)(7,119)(8,120)(9,121)(10,122)(11,123)(12,124)(13,125)(14,126)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,141)(30,142)(31,143)(32,144)(33,109)(34,110)(35,111)(36,112)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,213)(48,214)(49,215)(50,216)(51,181)(52,182)(53,183)(54,184)(55,185)(56,186)(57,187)(58,188)(59,189)(60,190)(61,191)(62,192)(63,193)(64,194)(65,195)(66,196)(67,197)(68,198)(69,199)(70,200)(71,201)(72,202)(73,155)(74,156)(75,157)(76,158)(77,159)(78,160)(79,161)(80,162)(81,163)(82,164)(83,165)(84,166)(85,167)(86,168)(87,169)(88,170)(89,171)(90,172)(91,173)(92,174)(93,175)(94,176)(95,177)(96,178)(97,179)(98,180)(99,145)(100,146)(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154), (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), (1,152,185)(2,153,186)(3,154,187)(4,155,188)(5,156,189)(6,157,190)(7,158,191)(8,159,192)(9,160,193)(10,161,194)(11,162,195)(12,163,196)(13,164,197)(14,165,198)(15,166,199)(16,167,200)(17,168,201)(18,169,202)(19,170,203)(20,171,204)(21,172,205)(22,173,206)(23,174,207)(24,175,208)(25,176,209)(26,177,210)(27,178,211)(28,179,212)(29,180,213)(30,145,214)(31,146,215)(32,147,216)(33,148,181)(34,149,182)(35,150,183)(36,151,184)(37,131,88)(38,132,89)(39,133,90)(40,134,91)(41,135,92)(42,136,93)(43,137,94)(44,138,95)(45,139,96)(46,140,97)(47,141,98)(48,142,99)(49,143,100)(50,144,101)(51,109,102)(52,110,103)(53,111,104)(54,112,105)(55,113,106)(56,114,107)(57,115,108)(58,116,73)(59,117,74)(60,118,75)(61,119,76)(62,120,77)(63,121,78)(64,122,79)(65,123,80)(66,124,81)(67,125,82)(68,126,83)(69,127,84)(70,128,85)(71,129,86)(72,130,87), (1,140)(2,139)(3,138)(4,137)(5,136)(6,135)(7,134)(8,133)(9,132)(10,131)(11,130)(12,129)(13,128)(14,127)(15,126)(16,125)(17,124)(18,123)(19,122)(20,121)(21,120)(22,119)(23,118)(24,117)(25,116)(26,115)(27,114)(28,113)(29,112)(30,111)(31,110)(32,109)(33,144)(34,143)(35,142)(36,141)(37,161)(38,160)(39,159)(40,158)(41,157)(42,156)(43,155)(44,154)(45,153)(46,152)(47,151)(48,150)(49,149)(50,148)(51,147)(52,146)(53,145)(54,180)(55,179)(56,178)(57,177)(58,176)(59,175)(60,174)(61,173)(62,172)(63,171)(64,170)(65,169)(66,168)(67,167)(68,166)(69,165)(70,164)(71,163)(72,162)(73,209)(74,208)(75,207)(76,206)(77,205)(78,204)(79,203)(80,202)(81,201)(82,200)(83,199)(84,198)(85,197)(86,196)(87,195)(88,194)(89,193)(90,192)(91,191)(92,190)(93,189)(94,188)(95,187)(96,186)(97,185)(98,184)(99,183)(100,182)(101,181)(102,216)(103,215)(104,214)(105,213)(106,212)(107,211)(108,210) );
G=PermutationGroup([[(1,113),(2,114),(3,115),(4,116),(5,117),(6,118),(7,119),(8,120),(9,121),(10,122),(11,123),(12,124),(13,125),(14,126),(15,127),(16,128),(17,129),(18,130),(19,131),(20,132),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,141),(30,142),(31,143),(32,144),(33,109),(34,110),(35,111),(36,112),(37,203),(38,204),(39,205),(40,206),(41,207),(42,208),(43,209),(44,210),(45,211),(46,212),(47,213),(48,214),(49,215),(50,216),(51,181),(52,182),(53,183),(54,184),(55,185),(56,186),(57,187),(58,188),(59,189),(60,190),(61,191),(62,192),(63,193),(64,194),(65,195),(66,196),(67,197),(68,198),(69,199),(70,200),(71,201),(72,202),(73,155),(74,156),(75,157),(76,158),(77,159),(78,160),(79,161),(80,162),(81,163),(82,164),(83,165),(84,166),(85,167),(86,168),(87,169),(88,170),(89,171),(90,172),(91,173),(92,174),(93,175),(94,176),(95,177),(96,178),(97,179),(98,180),(99,145),(100,146),(101,147),(102,148),(103,149),(104,150),(105,151),(106,152),(107,153),(108,154)], [(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)], [(1,152,185),(2,153,186),(3,154,187),(4,155,188),(5,156,189),(6,157,190),(7,158,191),(8,159,192),(9,160,193),(10,161,194),(11,162,195),(12,163,196),(13,164,197),(14,165,198),(15,166,199),(16,167,200),(17,168,201),(18,169,202),(19,170,203),(20,171,204),(21,172,205),(22,173,206),(23,174,207),(24,175,208),(25,176,209),(26,177,210),(27,178,211),(28,179,212),(29,180,213),(30,145,214),(31,146,215),(32,147,216),(33,148,181),(34,149,182),(35,150,183),(36,151,184),(37,131,88),(38,132,89),(39,133,90),(40,134,91),(41,135,92),(42,136,93),(43,137,94),(44,138,95),(45,139,96),(46,140,97),(47,141,98),(48,142,99),(49,143,100),(50,144,101),(51,109,102),(52,110,103),(53,111,104),(54,112,105),(55,113,106),(56,114,107),(57,115,108),(58,116,73),(59,117,74),(60,118,75),(61,119,76),(62,120,77),(63,121,78),(64,122,79),(65,123,80),(66,124,81),(67,125,82),(68,126,83),(69,127,84),(70,128,85),(71,129,86),(72,130,87)], [(1,140),(2,139),(3,138),(4,137),(5,136),(6,135),(7,134),(8,133),(9,132),(10,131),(11,130),(12,129),(13,128),(14,127),(15,126),(16,125),(17,124),(18,123),(19,122),(20,121),(21,120),(22,119),(23,118),(24,117),(25,116),(26,115),(27,114),(28,113),(29,112),(30,111),(31,110),(32,109),(33,144),(34,143),(35,142),(36,141),(37,161),(38,160),(39,159),(40,158),(41,157),(42,156),(43,155),(44,154),(45,153),(46,152),(47,151),(48,150),(49,149),(50,148),(51,147),(52,146),(53,145),(54,180),(55,179),(56,178),(57,177),(58,176),(59,175),(60,174),(61,173),(62,172),(63,171),(64,170),(65,169),(66,168),(67,167),(68,166),(69,165),(70,164),(71,163),(72,162),(73,209),(74,208),(75,207),(76,206),(77,205),(78,204),(79,203),(80,202),(81,201),(82,200),(83,199),(84,198),(85,197),(86,196),(87,195),(88,194),(89,193),(90,192),(91,191),(92,190),(93,189),(94,188),(95,187),(96,186),(97,185),(98,184),(99,183),(100,182),(101,181),(102,216),(103,215),(104,214),(105,213),(106,212),(107,211),(108,210)]])
114 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 3C | 3D | 4A | 4B | 6A | ··· | 6L | 9A | ··· | 9I | 12A | ··· | 12P | 18A | ··· | 18AA | 36A | ··· | 36AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 6 | ··· | 6 | 9 | ··· | 9 | 12 | ··· | 12 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | 1 | 1 | 54 | 54 | 54 | 54 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
114 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + |
| image | C1 | C2 | C2 | C2 | S3 | S3 | D4 | D6 | D6 | D6 | D6 | D9 | D12 | D12 | D18 | D18 | D36 |
| kernel | C2×C36⋊S3 | C36⋊S3 | C6×C36 | C22×C9⋊S3 | C2×C36 | C6×C12 | C3×C18 | C36 | C2×C18 | C3×C12 | C62 | C2×C12 | C18 | C3×C6 | C12 | C2×C6 | C6 |
| # reps | 1 | 4 | 1 | 2 | 3 | 1 | 2 | 6 | 3 | 2 | 1 | 9 | 12 | 4 | 18 | 9 | 36 |
Matrix representation of C2×C36⋊S3 ►in GL4(𝔽37) generated by
| 36 | 0 | 0 | 0 |
| 0 | 36 | 0 | 0 |
| 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 36 |
| 4 | 29 | 0 | 0 |
| 8 | 12 | 0 | 0 |
| 0 | 0 | 36 | 36 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 36 | 36 | 0 | 0 |
| 0 | 0 | 36 | 36 |
| 0 | 0 | 1 | 0 |
| 4 | 29 | 0 | 0 |
| 25 | 33 | 0 | 0 |
| 0 | 0 | 36 | 0 |
| 0 | 0 | 1 | 1 |
G:=sub<GL(4,GF(37))| [36,0,0,0,0,36,0,0,0,0,36,0,0,0,0,36],[4,8,0,0,29,12,0,0,0,0,36,1,0,0,36,0],[0,36,0,0,1,36,0,0,0,0,36,1,0,0,36,0],[4,25,0,0,29,33,0,0,0,0,36,1,0,0,0,1] >;
C2×C36⋊S3 in GAP, Magma, Sage, TeX
C_2\times C_{36}\rtimes S_3 % in TeX
G:=Group("C2xC36:S3"); // GroupNames label
G:=SmallGroup(432,382);
// by ID
G=gap.SmallGroup(432,382);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,254,58,6164,662,4037,14118]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^36=c^3=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations