direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D26⋊C4, C23.31D26, C22.16D52, (C2×C4)⋊8D26, D26⋊7(C2×C4), C2.3(C2×D52), (C22×C52)⋊1C2, (C2×C26).36D4, C26.40(C2×D4), (C22×C4)⋊1D13, C26⋊2(C22⋊C4), (C2×C52)⋊10C22, (C22×D13)⋊4C4, (C2×C26).45C23, C26.31(C22×C4), (C23×D13).2C2, C22.17(C4×D13), (C22×Dic13)⋊3C2, (C2×Dic13)⋊6C22, C22.20(C13⋊D4), (C22×C26).37C22, C22.23(C22×D13), (C22×D13).26C22, C13⋊3(C2×C22⋊C4), C2.19(C2×C4×D13), C2.2(C2×C13⋊D4), (C2×C26).38(C2×C4), SmallGroup(416,148)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D26⋊C4
G = < a,b,c,d | a2=b26=c2=d4=1, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd-1=b13c >
Subgroups: 992 in 132 conjugacy classes, 57 normal (17 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C2×C4, C23, C23, C13, C22⋊C4, C22×C4, C22×C4, C24, D13, C26, C26, C2×C22⋊C4, Dic13, C52, D26, D26, C2×C26, C2×C26, C2×Dic13, C2×Dic13, C2×C52, C2×C52, C22×D13, C22×D13, C22×C26, D26⋊C4, C22×Dic13, C22×C52, C23×D13, C2×D26⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, C22⋊C4, C22×C4, C2×D4, D13, C2×C22⋊C4, D26, C4×D13, D52, C13⋊D4, C22×D13, D26⋊C4, C2×C4×D13, C2×D52, C2×C13⋊D4, C2×D26⋊C4
►On 208 points
Generators in S208
(1 133)(2 134)(3 135)(4 136)(5 137)(6 138)(7 139)(8 140)(9 141)(10 142)(11 143)(12 144)(13 145)(14 146)(15 147)(16 148)(17 149)(18 150)(19 151)(20 152)(21 153)(22 154)(23 155)(24 156)(25 131)(26 132)(27 119)(28 120)(29 121)(30 122)(31 123)(32 124)(33 125)(34 126)(35 127)(36 128)(37 129)(38 130)(39 105)(40 106)(41 107)(42 108)(43 109)(44 110)(45 111)(46 112)(47 113)(48 114)(49 115)(50 116)(51 117)(52 118)(53 201)(54 202)(55 203)(56 204)(57 205)(58 206)(59 207)(60 208)(61 183)(62 184)(63 185)(64 186)(65 187)(66 188)(67 189)(68 190)(69 191)(70 192)(71 193)(72 194)(73 195)(74 196)(75 197)(76 198)(77 199)(78 200)(79 169)(80 170)(81 171)(82 172)(83 173)(84 174)(85 175)(86 176)(87 177)(88 178)(89 179)(90 180)(91 181)(92 182)(93 157)(94 158)(95 159)(96 160)(97 161)(98 162)(99 163)(100 164)(101 165)(102 166)(103 167)(104 168)
(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)
(1 130)(2 129)(3 128)(4 127)(5 126)(6 125)(7 124)(8 123)(9 122)(10 121)(11 120)(12 119)(13 118)(14 117)(15 116)(16 115)(17 114)(18 113)(19 112)(20 111)(21 110)(22 109)(23 108)(24 107)(25 106)(26 105)(27 144)(28 143)(29 142)(30 141)(31 140)(32 139)(33 138)(34 137)(35 136)(36 135)(37 134)(38 133)(39 132)(40 131)(41 156)(42 155)(43 154)(44 153)(45 152)(46 151)(47 150)(48 149)(49 148)(50 147)(51 146)(52 145)(53 181)(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)(73 161)(74 160)(75 159)(76 158)(77 157)(78 182)(79 187)(80 186)(81 185)(82 184)(83 183)(84 208)(85 207)(86 206)(87 205)(88 204)(89 203)(90 202)(91 201)(92 200)(93 199)(94 198)(95 197)(96 196)(97 195)(98 194)(99 193)(100 192)(101 191)(102 190)(103 189)(104 188)
(1 99 52 72)(2 100 27 73)(3 101 28 74)(4 102 29 75)(5 103 30 76)(6 104 31 77)(7 79 32 78)(8 80 33 53)(9 81 34 54)(10 82 35 55)(11 83 36 56)(12 84 37 57)(13 85 38 58)(14 86 39 59)(15 87 40 60)(16 88 41 61)(17 89 42 62)(18 90 43 63)(19 91 44 64)(20 92 45 65)(21 93 46 66)(22 94 47 67)(23 95 48 68)(24 96 49 69)(25 97 50 70)(26 98 51 71)(105 207 146 176)(106 208 147 177)(107 183 148 178)(108 184 149 179)(109 185 150 180)(110 186 151 181)(111 187 152 182)(112 188 153 157)(113 189 154 158)(114 190 155 159)(115 191 156 160)(116 192 131 161)(117 193 132 162)(118 194 133 163)(119 195 134 164)(120 196 135 165)(121 197 136 166)(122 198 137 167)(123 199 138 168)(124 200 139 169)(125 201 140 170)(126 202 141 171)(127 203 142 172)(128 204 143 173)(129 205 144 174)(130 206 145 175)
G:=sub<Sym(208)| (1,133)(2,134)(3,135)(4,136)(5,137)(6,138)(7,139)(8,140)(9,141)(10,142)(11,143)(12,144)(13,145)(14,146)(15,147)(16,148)(17,149)(18,150)(19,151)(20,152)(21,153)(22,154)(23,155)(24,156)(25,131)(26,132)(27,119)(28,120)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,105)(40,106)(41,107)(42,108)(43,109)(44,110)(45,111)(46,112)(47,113)(48,114)(49,115)(50,116)(51,117)(52,118)(53,201)(54,202)(55,203)(56,204)(57,205)(58,206)(59,207)(60,208)(61,183)(62,184)(63,185)(64,186)(65,187)(66,188)(67,189)(68,190)(69,191)(70,192)(71,193)(72,194)(73,195)(74,196)(75,197)(76,198)(77,199)(78,200)(79,169)(80,170)(81,171)(82,172)(83,173)(84,174)(85,175)(86,176)(87,177)(88,178)(89,179)(90,180)(91,181)(92,182)(93,157)(94,158)(95,159)(96,160)(97,161)(98,162)(99,163)(100,164)(101,165)(102,166)(103,167)(104,168), (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), (1,130)(2,129)(3,128)(4,127)(5,126)(6,125)(7,124)(8,123)(9,122)(10,121)(11,120)(12,119)(13,118)(14,117)(15,116)(16,115)(17,114)(18,113)(19,112)(20,111)(21,110)(22,109)(23,108)(24,107)(25,106)(26,105)(27,144)(28,143)(29,142)(30,141)(31,140)(32,139)(33,138)(34,137)(35,136)(36,135)(37,134)(38,133)(39,132)(40,131)(41,156)(42,155)(43,154)(44,153)(45,152)(46,151)(47,150)(48,149)(49,148)(50,147)(51,146)(52,145)(53,181)(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)(73,161)(74,160)(75,159)(76,158)(77,157)(78,182)(79,187)(80,186)(81,185)(82,184)(83,183)(84,208)(85,207)(86,206)(87,205)(88,204)(89,203)(90,202)(91,201)(92,200)(93,199)(94,198)(95,197)(96,196)(97,195)(98,194)(99,193)(100,192)(101,191)(102,190)(103,189)(104,188), (1,99,52,72)(2,100,27,73)(3,101,28,74)(4,102,29,75)(5,103,30,76)(6,104,31,77)(7,79,32,78)(8,80,33,53)(9,81,34,54)(10,82,35,55)(11,83,36,56)(12,84,37,57)(13,85,38,58)(14,86,39,59)(15,87,40,60)(16,88,41,61)(17,89,42,62)(18,90,43,63)(19,91,44,64)(20,92,45,65)(21,93,46,66)(22,94,47,67)(23,95,48,68)(24,96,49,69)(25,97,50,70)(26,98,51,71)(105,207,146,176)(106,208,147,177)(107,183,148,178)(108,184,149,179)(109,185,150,180)(110,186,151,181)(111,187,152,182)(112,188,153,157)(113,189,154,158)(114,190,155,159)(115,191,156,160)(116,192,131,161)(117,193,132,162)(118,194,133,163)(119,195,134,164)(120,196,135,165)(121,197,136,166)(122,198,137,167)(123,199,138,168)(124,200,139,169)(125,201,140,170)(126,202,141,171)(127,203,142,172)(128,204,143,173)(129,205,144,174)(130,206,145,175)>;
G:=Group( (1,133)(2,134)(3,135)(4,136)(5,137)(6,138)(7,139)(8,140)(9,141)(10,142)(11,143)(12,144)(13,145)(14,146)(15,147)(16,148)(17,149)(18,150)(19,151)(20,152)(21,153)(22,154)(23,155)(24,156)(25,131)(26,132)(27,119)(28,120)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,105)(40,106)(41,107)(42,108)(43,109)(44,110)(45,111)(46,112)(47,113)(48,114)(49,115)(50,116)(51,117)(52,118)(53,201)(54,202)(55,203)(56,204)(57,205)(58,206)(59,207)(60,208)(61,183)(62,184)(63,185)(64,186)(65,187)(66,188)(67,189)(68,190)(69,191)(70,192)(71,193)(72,194)(73,195)(74,196)(75,197)(76,198)(77,199)(78,200)(79,169)(80,170)(81,171)(82,172)(83,173)(84,174)(85,175)(86,176)(87,177)(88,178)(89,179)(90,180)(91,181)(92,182)(93,157)(94,158)(95,159)(96,160)(97,161)(98,162)(99,163)(100,164)(101,165)(102,166)(103,167)(104,168), (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), (1,130)(2,129)(3,128)(4,127)(5,126)(6,125)(7,124)(8,123)(9,122)(10,121)(11,120)(12,119)(13,118)(14,117)(15,116)(16,115)(17,114)(18,113)(19,112)(20,111)(21,110)(22,109)(23,108)(24,107)(25,106)(26,105)(27,144)(28,143)(29,142)(30,141)(31,140)(32,139)(33,138)(34,137)(35,136)(36,135)(37,134)(38,133)(39,132)(40,131)(41,156)(42,155)(43,154)(44,153)(45,152)(46,151)(47,150)(48,149)(49,148)(50,147)(51,146)(52,145)(53,181)(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)(73,161)(74,160)(75,159)(76,158)(77,157)(78,182)(79,187)(80,186)(81,185)(82,184)(83,183)(84,208)(85,207)(86,206)(87,205)(88,204)(89,203)(90,202)(91,201)(92,200)(93,199)(94,198)(95,197)(96,196)(97,195)(98,194)(99,193)(100,192)(101,191)(102,190)(103,189)(104,188), (1,99,52,72)(2,100,27,73)(3,101,28,74)(4,102,29,75)(5,103,30,76)(6,104,31,77)(7,79,32,78)(8,80,33,53)(9,81,34,54)(10,82,35,55)(11,83,36,56)(12,84,37,57)(13,85,38,58)(14,86,39,59)(15,87,40,60)(16,88,41,61)(17,89,42,62)(18,90,43,63)(19,91,44,64)(20,92,45,65)(21,93,46,66)(22,94,47,67)(23,95,48,68)(24,96,49,69)(25,97,50,70)(26,98,51,71)(105,207,146,176)(106,208,147,177)(107,183,148,178)(108,184,149,179)(109,185,150,180)(110,186,151,181)(111,187,152,182)(112,188,153,157)(113,189,154,158)(114,190,155,159)(115,191,156,160)(116,192,131,161)(117,193,132,162)(118,194,133,163)(119,195,134,164)(120,196,135,165)(121,197,136,166)(122,198,137,167)(123,199,138,168)(124,200,139,169)(125,201,140,170)(126,202,141,171)(127,203,142,172)(128,204,143,173)(129,205,144,174)(130,206,145,175) );
G=PermutationGroup([[(1,133),(2,134),(3,135),(4,136),(5,137),(6,138),(7,139),(8,140),(9,141),(10,142),(11,143),(12,144),(13,145),(14,146),(15,147),(16,148),(17,149),(18,150),(19,151),(20,152),(21,153),(22,154),(23,155),(24,156),(25,131),(26,132),(27,119),(28,120),(29,121),(30,122),(31,123),(32,124),(33,125),(34,126),(35,127),(36,128),(37,129),(38,130),(39,105),(40,106),(41,107),(42,108),(43,109),(44,110),(45,111),(46,112),(47,113),(48,114),(49,115),(50,116),(51,117),(52,118),(53,201),(54,202),(55,203),(56,204),(57,205),(58,206),(59,207),(60,208),(61,183),(62,184),(63,185),(64,186),(65,187),(66,188),(67,189),(68,190),(69,191),(70,192),(71,193),(72,194),(73,195),(74,196),(75,197),(76,198),(77,199),(78,200),(79,169),(80,170),(81,171),(82,172),(83,173),(84,174),(85,175),(86,176),(87,177),(88,178),(89,179),(90,180),(91,181),(92,182),(93,157),(94,158),(95,159),(96,160),(97,161),(98,162),(99,163),(100,164),(101,165),(102,166),(103,167),(104,168)], [(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)], [(1,130),(2,129),(3,128),(4,127),(5,126),(6,125),(7,124),(8,123),(9,122),(10,121),(11,120),(12,119),(13,118),(14,117),(15,116),(16,115),(17,114),(18,113),(19,112),(20,111),(21,110),(22,109),(23,108),(24,107),(25,106),(26,105),(27,144),(28,143),(29,142),(30,141),(31,140),(32,139),(33,138),(34,137),(35,136),(36,135),(37,134),(38,133),(39,132),(40,131),(41,156),(42,155),(43,154),(44,153),(45,152),(46,151),(47,150),(48,149),(49,148),(50,147),(51,146),(52,145),(53,181),(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),(73,161),(74,160),(75,159),(76,158),(77,157),(78,182),(79,187),(80,186),(81,185),(82,184),(83,183),(84,208),(85,207),(86,206),(87,205),(88,204),(89,203),(90,202),(91,201),(92,200),(93,199),(94,198),(95,197),(96,196),(97,195),(98,194),(99,193),(100,192),(101,191),(102,190),(103,189),(104,188)], [(1,99,52,72),(2,100,27,73),(3,101,28,74),(4,102,29,75),(5,103,30,76),(6,104,31,77),(7,79,32,78),(8,80,33,53),(9,81,34,54),(10,82,35,55),(11,83,36,56),(12,84,37,57),(13,85,38,58),(14,86,39,59),(15,87,40,60),(16,88,41,61),(17,89,42,62),(18,90,43,63),(19,91,44,64),(20,92,45,65),(21,93,46,66),(22,94,47,67),(23,95,48,68),(24,96,49,69),(25,97,50,70),(26,98,51,71),(105,207,146,176),(106,208,147,177),(107,183,148,178),(108,184,149,179),(109,185,150,180),(110,186,151,181),(111,187,152,182),(112,188,153,157),(113,189,154,158),(114,190,155,159),(115,191,156,160),(116,192,131,161),(117,193,132,162),(118,194,133,163),(119,195,134,164),(120,196,135,165),(121,197,136,166),(122,198,137,167),(123,199,138,168),(124,200,139,169),(125,201,140,170),(126,202,141,171),(127,203,142,172),(128,204,143,173),(129,205,144,174),(130,206,145,175)]])
116 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 13A | ··· | 13F | 26A | ··· | 26AP | 52A | ··· | 52AV |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | ··· | 1 | 26 | 26 | 26 | 26 | 2 | 2 | 2 | 2 | 26 | 26 | 26 | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
116 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D13 | D26 | D26 | C4×D13 | D52 | C13⋊D4 |
| kernel | C2×D26⋊C4 | D26⋊C4 | C22×Dic13 | C22×C52 | C23×D13 | C22×D13 | C2×C26 | C22×C4 | C2×C4 | C23 | C22 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 4 | 6 | 12 | 6 | 24 | 24 | 24 |
Matrix representation of C2×D26⋊C4 ►in GL5(𝔽53)
| 52 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 0 | 52 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 39 | 33 | 0 | 0 |
| 0 | 34 | 22 | 0 | 0 |
| 0 | 0 | 0 | 11 | 51 |
| 0 | 0 | 0 | 45 | 16 |
| 52 | 0 | 0 | 0 | 0 |
| 0 | 16 | 44 | 0 | 0 |
| 0 | 46 | 37 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 24 | 52 |
| 30 | 0 | 0 | 0 | 0 |
| 0 | 30 | 0 | 0 | 0 |
| 0 | 0 | 30 | 0 | 0 |
| 0 | 0 | 0 | 25 | 20 |
| 0 | 0 | 0 | 27 | 28 |
G:=sub<GL(5,GF(53))| [52,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,52,0,0,0,0,0,52],[1,0,0,0,0,0,39,34,0,0,0,33,22,0,0,0,0,0,11,45,0,0,0,51,16],[52,0,0,0,0,0,16,46,0,0,0,44,37,0,0,0,0,0,1,24,0,0,0,0,52],[30,0,0,0,0,0,30,0,0,0,0,0,30,0,0,0,0,0,25,27,0,0,0,20,28] >;
C2×D26⋊C4 in GAP, Magma, Sage, TeX
C_2\times D_{26}\rtimes C_4 % in TeX
G:=Group("C2xD26:C4"); // GroupNames label
G:=SmallGroup(416,148);
// by ID
G=gap.SmallGroup(416,148);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,362,50,13829]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^26=c^2=d^4=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,d*c*d^-1=b^13*c>;
// generators/relations