metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C60⋊12D4, C20⋊2D12, D30⋊14D4, C6.50(D4×D5), (C2×D12)⋊11D5, C5⋊5(C12⋊D4), C12⋊4(C5⋊D4), C4⋊3(C5⋊D12), C3⋊1(C20⋊2D4), C4⋊Dic5⋊15S3, C10.51(S3×D4), (C10×D12)⋊11C2, C15⋊15(C4⋊D4), D6⋊Dic5⋊21C2, C10.63(C2×D12), (C2×C20).134D6, C30.159(C2×D4), C30.96(C4○D4), (C2×C12).135D10, (C2×Dic5).49D6, C6.15(D4⋊2D5), C2.26(C20⋊D6), (C2×C30).156C23, (C2×C60).205C22, (C22×S3).23D10, C2.19(D12⋊D5), C10.37(Q8⋊3S3), (C6×Dic5).94C22, (C2×Dic15).217C22, (C22×D15).110C22, (C2×C4×D15)⋊23C2, (C2×C5⋊D12)⋊8C2, C6.18(C2×C5⋊D4), (C3×C4⋊Dic5)⋊12C2, (C2×C4).215(S3×D5), C2.21(C2×C5⋊D12), C22.208(C2×S3×D5), (S3×C2×C10).39C22, (C2×C6).168(C22×D5), (C2×C10).168(C22×S3), SmallGroup(480,542)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C60⋊12D4
G = < a,b,c | a60=b4=c2=1, bab-1=a19, cac=a29, cbc=b-1 >
Subgroups: 1100 in 188 conjugacy classes, 54 normal (32 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×2], C4 [×3], C22, C22 [×10], C5, S3 [×4], C6 [×3], C2×C4, C2×C4 [×5], D4 [×6], C23 [×3], D5 [×2], C10 [×3], C10 [×2], Dic3, C12 [×2], C12 [×2], D6 [×10], C2×C6, C15, C22⋊C4 [×2], C4⋊C4, C22×C4, C2×D4 [×3], Dic5 [×3], C20 [×2], D10 [×4], C2×C10, C2×C10 [×6], C4×S3 [×2], D12 [×6], C2×Dic3, C2×C12, C2×C12 [×2], C22×S3 [×2], C22×S3, C5×S3 [×2], D15 [×2], C30 [×3], C4⋊D4, C4×D5 [×2], C2×Dic5 [×2], C2×Dic5, C5⋊D4 [×4], C2×C20, C5×D4 [×2], C22×D5, C22×C10 [×2], D6⋊C4 [×2], C3×C4⋊C4, S3×C2×C4, C2×D12, C2×D12 [×2], C3×Dic5 [×2], Dic15, C60 [×2], S3×C10 [×6], D30 [×2], D30 [×2], C2×C30, C4⋊Dic5, C23.D5 [×2], C2×C4×D5, C2×C5⋊D4 [×2], D4×C10, C12⋊D4, C5⋊D12 [×4], C6×Dic5 [×2], C5×D12 [×2], C4×D15 [×2], C2×Dic15, C2×C60, S3×C2×C10 [×2], C22×D15, C20⋊2D4, D6⋊Dic5 [×2], C3×C4⋊Dic5, C2×C5⋊D12 [×2], C10×D12, C2×C4×D15, C60⋊12D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×4], C23, D5, D6 [×3], C2×D4 [×2], C4○D4, D10 [×3], D12 [×2], C22×S3, C4⋊D4, C5⋊D4 [×2], C22×D5, C2×D12, S3×D4, Q8⋊3S3, S3×D5, D4×D5, D4⋊2D5, C2×C5⋊D4, C12⋊D4, C5⋊D12 [×2], C2×S3×D5, C20⋊2D4, D12⋊D5, C20⋊D6, C2×C5⋊D12, C60⋊12D4
►On 240 points
Generators in S240
(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)(181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)
(1 119 224 177)(2 78 225 136)(3 97 226 155)(4 116 227 174)(5 75 228 133)(6 94 229 152)(7 113 230 171)(8 72 231 130)(9 91 232 149)(10 110 233 168)(11 69 234 127)(12 88 235 146)(13 107 236 165)(14 66 237 124)(15 85 238 143)(16 104 239 162)(17 63 240 121)(18 82 181 140)(19 101 182 159)(20 120 183 178)(21 79 184 137)(22 98 185 156)(23 117 186 175)(24 76 187 134)(25 95 188 153)(26 114 189 172)(27 73 190 131)(28 92 191 150)(29 111 192 169)(30 70 193 128)(31 89 194 147)(32 108 195 166)(33 67 196 125)(34 86 197 144)(35 105 198 163)(36 64 199 122)(37 83 200 141)(38 102 201 160)(39 61 202 179)(40 80 203 138)(41 99 204 157)(42 118 205 176)(43 77 206 135)(44 96 207 154)(45 115 208 173)(46 74 209 132)(47 93 210 151)(48 112 211 170)(49 71 212 129)(50 90 213 148)(51 109 214 167)(52 68 215 126)(53 87 216 145)(54 106 217 164)(55 65 218 123)(56 84 219 142)(57 103 220 161)(58 62 221 180)(59 81 222 139)(60 100 223 158)
(2 30)(3 59)(4 28)(5 57)(6 26)(7 55)(8 24)(9 53)(10 22)(11 51)(12 20)(13 49)(14 18)(15 47)(17 45)(19 43)(21 41)(23 39)(25 37)(27 35)(29 33)(32 60)(34 58)(36 56)(38 54)(40 52)(42 50)(44 48)(61 175)(62 144)(63 173)(64 142)(65 171)(66 140)(67 169)(68 138)(69 167)(70 136)(71 165)(72 134)(73 163)(74 132)(75 161)(76 130)(77 159)(78 128)(79 157)(80 126)(81 155)(82 124)(83 153)(84 122)(85 151)(86 180)(87 149)(88 178)(89 147)(90 176)(91 145)(92 174)(93 143)(94 172)(95 141)(96 170)(97 139)(98 168)(99 137)(100 166)(101 135)(102 164)(103 133)(104 162)(105 131)(106 160)(107 129)(108 158)(109 127)(110 156)(111 125)(112 154)(113 123)(114 152)(115 121)(116 150)(117 179)(118 148)(119 177)(120 146)(181 237)(182 206)(183 235)(184 204)(185 233)(186 202)(187 231)(188 200)(189 229)(190 198)(191 227)(192 196)(193 225)(195 223)(197 221)(199 219)(201 217)(203 215)(205 213)(207 211)(208 240)(210 238)(212 236)(214 234)(216 232)(218 230)(220 228)(222 226)
G:=sub<Sym(240)| (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)(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240), (1,119,224,177)(2,78,225,136)(3,97,226,155)(4,116,227,174)(5,75,228,133)(6,94,229,152)(7,113,230,171)(8,72,231,130)(9,91,232,149)(10,110,233,168)(11,69,234,127)(12,88,235,146)(13,107,236,165)(14,66,237,124)(15,85,238,143)(16,104,239,162)(17,63,240,121)(18,82,181,140)(19,101,182,159)(20,120,183,178)(21,79,184,137)(22,98,185,156)(23,117,186,175)(24,76,187,134)(25,95,188,153)(26,114,189,172)(27,73,190,131)(28,92,191,150)(29,111,192,169)(30,70,193,128)(31,89,194,147)(32,108,195,166)(33,67,196,125)(34,86,197,144)(35,105,198,163)(36,64,199,122)(37,83,200,141)(38,102,201,160)(39,61,202,179)(40,80,203,138)(41,99,204,157)(42,118,205,176)(43,77,206,135)(44,96,207,154)(45,115,208,173)(46,74,209,132)(47,93,210,151)(48,112,211,170)(49,71,212,129)(50,90,213,148)(51,109,214,167)(52,68,215,126)(53,87,216,145)(54,106,217,164)(55,65,218,123)(56,84,219,142)(57,103,220,161)(58,62,221,180)(59,81,222,139)(60,100,223,158), (2,30)(3,59)(4,28)(5,57)(6,26)(7,55)(8,24)(9,53)(10,22)(11,51)(12,20)(13,49)(14,18)(15,47)(17,45)(19,43)(21,41)(23,39)(25,37)(27,35)(29,33)(32,60)(34,58)(36,56)(38,54)(40,52)(42,50)(44,48)(61,175)(62,144)(63,173)(64,142)(65,171)(66,140)(67,169)(68,138)(69,167)(70,136)(71,165)(72,134)(73,163)(74,132)(75,161)(76,130)(77,159)(78,128)(79,157)(80,126)(81,155)(82,124)(83,153)(84,122)(85,151)(86,180)(87,149)(88,178)(89,147)(90,176)(91,145)(92,174)(93,143)(94,172)(95,141)(96,170)(97,139)(98,168)(99,137)(100,166)(101,135)(102,164)(103,133)(104,162)(105,131)(106,160)(107,129)(108,158)(109,127)(110,156)(111,125)(112,154)(113,123)(114,152)(115,121)(116,150)(117,179)(118,148)(119,177)(120,146)(181,237)(182,206)(183,235)(184,204)(185,233)(186,202)(187,231)(188,200)(189,229)(190,198)(191,227)(192,196)(193,225)(195,223)(197,221)(199,219)(201,217)(203,215)(205,213)(207,211)(208,240)(210,238)(212,236)(214,234)(216,232)(218,230)(220,228)(222,226)>;
G:=Group( (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)(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240), (1,119,224,177)(2,78,225,136)(3,97,226,155)(4,116,227,174)(5,75,228,133)(6,94,229,152)(7,113,230,171)(8,72,231,130)(9,91,232,149)(10,110,233,168)(11,69,234,127)(12,88,235,146)(13,107,236,165)(14,66,237,124)(15,85,238,143)(16,104,239,162)(17,63,240,121)(18,82,181,140)(19,101,182,159)(20,120,183,178)(21,79,184,137)(22,98,185,156)(23,117,186,175)(24,76,187,134)(25,95,188,153)(26,114,189,172)(27,73,190,131)(28,92,191,150)(29,111,192,169)(30,70,193,128)(31,89,194,147)(32,108,195,166)(33,67,196,125)(34,86,197,144)(35,105,198,163)(36,64,199,122)(37,83,200,141)(38,102,201,160)(39,61,202,179)(40,80,203,138)(41,99,204,157)(42,118,205,176)(43,77,206,135)(44,96,207,154)(45,115,208,173)(46,74,209,132)(47,93,210,151)(48,112,211,170)(49,71,212,129)(50,90,213,148)(51,109,214,167)(52,68,215,126)(53,87,216,145)(54,106,217,164)(55,65,218,123)(56,84,219,142)(57,103,220,161)(58,62,221,180)(59,81,222,139)(60,100,223,158), (2,30)(3,59)(4,28)(5,57)(6,26)(7,55)(8,24)(9,53)(10,22)(11,51)(12,20)(13,49)(14,18)(15,47)(17,45)(19,43)(21,41)(23,39)(25,37)(27,35)(29,33)(32,60)(34,58)(36,56)(38,54)(40,52)(42,50)(44,48)(61,175)(62,144)(63,173)(64,142)(65,171)(66,140)(67,169)(68,138)(69,167)(70,136)(71,165)(72,134)(73,163)(74,132)(75,161)(76,130)(77,159)(78,128)(79,157)(80,126)(81,155)(82,124)(83,153)(84,122)(85,151)(86,180)(87,149)(88,178)(89,147)(90,176)(91,145)(92,174)(93,143)(94,172)(95,141)(96,170)(97,139)(98,168)(99,137)(100,166)(101,135)(102,164)(103,133)(104,162)(105,131)(106,160)(107,129)(108,158)(109,127)(110,156)(111,125)(112,154)(113,123)(114,152)(115,121)(116,150)(117,179)(118,148)(119,177)(120,146)(181,237)(182,206)(183,235)(184,204)(185,233)(186,202)(187,231)(188,200)(189,229)(190,198)(191,227)(192,196)(193,225)(195,223)(197,221)(199,219)(201,217)(203,215)(205,213)(207,211)(208,240)(210,238)(212,236)(214,234)(216,232)(218,230)(220,228)(222,226) );
G=PermutationGroup([(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),(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)], [(1,119,224,177),(2,78,225,136),(3,97,226,155),(4,116,227,174),(5,75,228,133),(6,94,229,152),(7,113,230,171),(8,72,231,130),(9,91,232,149),(10,110,233,168),(11,69,234,127),(12,88,235,146),(13,107,236,165),(14,66,237,124),(15,85,238,143),(16,104,239,162),(17,63,240,121),(18,82,181,140),(19,101,182,159),(20,120,183,178),(21,79,184,137),(22,98,185,156),(23,117,186,175),(24,76,187,134),(25,95,188,153),(26,114,189,172),(27,73,190,131),(28,92,191,150),(29,111,192,169),(30,70,193,128),(31,89,194,147),(32,108,195,166),(33,67,196,125),(34,86,197,144),(35,105,198,163),(36,64,199,122),(37,83,200,141),(38,102,201,160),(39,61,202,179),(40,80,203,138),(41,99,204,157),(42,118,205,176),(43,77,206,135),(44,96,207,154),(45,115,208,173),(46,74,209,132),(47,93,210,151),(48,112,211,170),(49,71,212,129),(50,90,213,148),(51,109,214,167),(52,68,215,126),(53,87,216,145),(54,106,217,164),(55,65,218,123),(56,84,219,142),(57,103,220,161),(58,62,221,180),(59,81,222,139),(60,100,223,158)], [(2,30),(3,59),(4,28),(5,57),(6,26),(7,55),(8,24),(9,53),(10,22),(11,51),(12,20),(13,49),(14,18),(15,47),(17,45),(19,43),(21,41),(23,39),(25,37),(27,35),(29,33),(32,60),(34,58),(36,56),(38,54),(40,52),(42,50),(44,48),(61,175),(62,144),(63,173),(64,142),(65,171),(66,140),(67,169),(68,138),(69,167),(70,136),(71,165),(72,134),(73,163),(74,132),(75,161),(76,130),(77,159),(78,128),(79,157),(80,126),(81,155),(82,124),(83,153),(84,122),(85,151),(86,180),(87,149),(88,178),(89,147),(90,176),(91,145),(92,174),(93,143),(94,172),(95,141),(96,170),(97,139),(98,168),(99,137),(100,166),(101,135),(102,164),(103,133),(104,162),(105,131),(106,160),(107,129),(108,158),(109,127),(110,156),(111,125),(112,154),(113,123),(114,152),(115,121),(116,150),(117,179),(118,148),(119,177),(120,146),(181,237),(182,206),(183,235),(184,204),(185,233),(186,202),(187,231),(188,200),(189,229),(190,198),(191,227),(192,196),(193,225),(195,223),(197,221),(199,219),(201,217),(203,215),(205,213),(207,211),(208,240),(210,238),(212,236),(214,234),(216,232),(218,230),(220,228),(222,226)])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6A | 6B | 6C | 10A | ··· | 10F | 10G | ··· | 10N | 12A | 12B | 12C | 12D | 12E | 12F | 15A | 15B | 20A | 20B | 20C | 20D | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 10 | ··· | 10 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 12 | 12 | 30 | 30 | 2 | 2 | 2 | 20 | 20 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 12 | ··· | 12 | 4 | 4 | 20 | 20 | 20 | 20 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | C4○D4 | D10 | D10 | D12 | C5⋊D4 | S3×D4 | Q8⋊3S3 | S3×D5 | D4×D5 | D4⋊2D5 | C5⋊D12 | C2×S3×D5 | D12⋊D5 | C20⋊D6 |
| kernel | C60⋊12D4 | D6⋊Dic5 | C3×C4⋊Dic5 | C2×C5⋊D12 | C10×D12 | C2×C4×D15 | C4⋊Dic5 | C60 | D30 | C2×D12 | C2×Dic5 | C2×C20 | C30 | C2×C12 | C22×S3 | C20 | C12 | C10 | C10 | C2×C4 | C6 | C6 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 4 | 4 | 8 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of C60⋊12D4 ►in GL6(𝔽61)
| 44 | 44 | 0 | 0 | 0 | 0 |
| 17 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 1 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 20 |
| 0 | 0 | 0 | 0 | 6 | 60 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 17 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 15 | 0 | 0 |
| 0 | 0 | 46 | 38 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 20 |
| 0 | 0 | 0 | 0 | 0 | 60 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 17 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(61))| [44,17,0,0,0,0,44,60,0,0,0,0,0,0,0,1,0,0,0,0,60,60,0,0,0,0,0,0,1,6,0,0,0,0,20,60],[1,17,0,0,0,0,0,60,0,0,0,0,0,0,23,46,0,0,0,0,15,38,0,0,0,0,0,0,1,0,0,0,0,0,20,60],[1,17,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C60⋊12D4 in GAP, Magma, Sage, TeX
C_{60}\rtimes_{12}D_4 % in TeX
G:=Group("C60:12D4"); // GroupNames label
G:=SmallGroup(480,542);
// by ID
G=gap.SmallGroup(480,542);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,422,219,100,1356,18822]);
// Polycyclic
G:=Group<a,b,c|a^60=b^4=c^2=1,b*a*b^-1=a^19,c*a*c=a^29,c*b*c=b^-1>;
// generators/relations