metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C60⋊11D4, C12⋊2D20, D30⋊13D4, C6.49(D4×D5), (C2×D20)⋊11S3, (C6×D20)⋊11C2, C5⋊1(D6⋊3D4), C4⋊3(C3⋊D20), C3⋊5(C4⋊2D20), C20⋊4(C3⋊D4), C4⋊Dic3⋊15D5, C10.50(S3×D4), C6.63(C2×D20), C15⋊14(C4⋊D4), (C2×C20).133D6, C30.158(C2×D4), C30.95(C4○D4), (C2×C12).134D10, (C22×D5).25D6, D10⋊Dic3⋊21C2, C2.25(C20⋊D6), (C2×C30).155C23, (C2×C60).204C22, C6.37(Q8⋊2D5), (C2×Dic3).49D10, C2.19(D20⋊S3), C10.16(D4⋊2S3), (C10×Dic3).94C22, (C2×Dic15).216C22, (C22×D15).109C22, (C2×C4×D15)⋊22C2, (C2×C3⋊D20)⋊8C2, (C5×C4⋊Dic3)⋊12C2, (C2×C4).214(S3×D5), C2.21(C2×C3⋊D20), C10.18(C2×C3⋊D4), (D5×C2×C6).39C22, C22.207(C2×S3×D5), (C2×C6).167(C22×D5), (C2×C10).167(C22×S3), SmallGroup(480,541)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C60⋊11D4
G = < a,b,c | a60=b4=c2=1, bab-1=a11, cac=a29, cbc=b-1 >
Subgroups: 1180 in 188 conjugacy classes, 54 normal (32 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×2], C4 [×3], C22, C22 [×10], C5, S3 [×2], C6 [×3], C6 [×2], C2×C4, C2×C4 [×5], D4 [×6], C23 [×3], D5 [×4], C10 [×3], Dic3 [×3], C12 [×2], D6 [×4], C2×C6, C2×C6 [×6], C15, C22⋊C4 [×2], C4⋊C4, C22×C4, C2×D4 [×3], Dic5, C20 [×2], C20 [×2], D10 [×10], C2×C10, C4×S3 [×2], C2×Dic3 [×2], C2×Dic3, C3⋊D4 [×4], C2×C12, C3×D4 [×2], C22×S3, C22×C6 [×2], C3×D5 [×2], D15 [×2], C30 [×3], C4⋊D4, C4×D5 [×2], D20 [×6], C2×Dic5, C2×C20, C2×C20 [×2], C22×D5 [×2], C22×D5, C4⋊Dic3, C6.D4 [×2], S3×C2×C4, C2×C3⋊D4 [×2], C6×D4, C5×Dic3 [×2], Dic15, C60 [×2], C6×D5 [×6], D30 [×2], D30 [×2], C2×C30, D10⋊C4 [×2], C5×C4⋊C4, C2×C4×D5, C2×D20, C2×D20 [×2], D6⋊3D4, C3⋊D20 [×4], C3×D20 [×2], C10×Dic3 [×2], C4×D15 [×2], C2×Dic15, C2×C60, D5×C2×C6 [×2], C22×D15, C4⋊2D20, D10⋊Dic3 [×2], C5×C4⋊Dic3, C2×C3⋊D20 [×2], C6×D20, C2×C4×D15, C60⋊11D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×4], C23, D5, D6 [×3], C2×D4 [×2], C4○D4, D10 [×3], C3⋊D4 [×2], C22×S3, C4⋊D4, D20 [×2], C22×D5, S3×D4, D4⋊2S3, C2×C3⋊D4, S3×D5, C2×D20, D4×D5, Q8⋊2D5, D6⋊3D4, C3⋊D20 [×2], C2×S3×D5, C4⋊2D20, D20⋊S3, C20⋊D6, C2×C3⋊D20, C60⋊11D4
►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)
(1 161 71 230)(2 172 72 181)(3 123 73 192)(4 134 74 203)(5 145 75 214)(6 156 76 225)(7 167 77 236)(8 178 78 187)(9 129 79 198)(10 140 80 209)(11 151 81 220)(12 162 82 231)(13 173 83 182)(14 124 84 193)(15 135 85 204)(16 146 86 215)(17 157 87 226)(18 168 88 237)(19 179 89 188)(20 130 90 199)(21 141 91 210)(22 152 92 221)(23 163 93 232)(24 174 94 183)(25 125 95 194)(26 136 96 205)(27 147 97 216)(28 158 98 227)(29 169 99 238)(30 180 100 189)(31 131 101 200)(32 142 102 211)(33 153 103 222)(34 164 104 233)(35 175 105 184)(36 126 106 195)(37 137 107 206)(38 148 108 217)(39 159 109 228)(40 170 110 239)(41 121 111 190)(42 132 112 201)(43 143 113 212)(44 154 114 223)(45 165 115 234)(46 176 116 185)(47 127 117 196)(48 138 118 207)(49 149 119 218)(50 160 120 229)(51 171 61 240)(52 122 62 191)(53 133 63 202)(54 144 64 213)(55 155 65 224)(56 166 66 235)(57 177 67 186)(58 128 68 197)(59 139 69 208)(60 150 70 219)
(1 71)(2 100)(3 69)(4 98)(5 67)(6 96)(7 65)(8 94)(9 63)(10 92)(11 61)(12 90)(13 119)(14 88)(15 117)(16 86)(17 115)(18 84)(19 113)(20 82)(21 111)(22 80)(23 109)(24 78)(25 107)(26 76)(27 105)(28 74)(29 103)(30 72)(31 101)(32 70)(33 99)(34 68)(35 97)(36 66)(37 95)(38 64)(39 93)(40 62)(41 91)(42 120)(43 89)(44 118)(45 87)(46 116)(47 85)(48 114)(49 83)(50 112)(51 81)(52 110)(53 79)(54 108)(55 77)(56 106)(57 75)(58 104)(59 73)(60 102)(121 141)(122 170)(123 139)(124 168)(125 137)(126 166)(127 135)(128 164)(129 133)(130 162)(132 160)(134 158)(136 156)(138 154)(140 152)(142 150)(143 179)(144 148)(145 177)(147 175)(149 173)(151 171)(153 169)(155 167)(157 165)(159 163)(172 180)(174 178)(181 189)(182 218)(183 187)(184 216)(186 214)(188 212)(190 210)(191 239)(192 208)(193 237)(194 206)(195 235)(196 204)(197 233)(198 202)(199 231)(201 229)(203 227)(205 225)(207 223)(209 221)(211 219)(213 217)(220 240)(222 238)(224 236)(226 234)(228 232)
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), (1,161,71,230)(2,172,72,181)(3,123,73,192)(4,134,74,203)(5,145,75,214)(6,156,76,225)(7,167,77,236)(8,178,78,187)(9,129,79,198)(10,140,80,209)(11,151,81,220)(12,162,82,231)(13,173,83,182)(14,124,84,193)(15,135,85,204)(16,146,86,215)(17,157,87,226)(18,168,88,237)(19,179,89,188)(20,130,90,199)(21,141,91,210)(22,152,92,221)(23,163,93,232)(24,174,94,183)(25,125,95,194)(26,136,96,205)(27,147,97,216)(28,158,98,227)(29,169,99,238)(30,180,100,189)(31,131,101,200)(32,142,102,211)(33,153,103,222)(34,164,104,233)(35,175,105,184)(36,126,106,195)(37,137,107,206)(38,148,108,217)(39,159,109,228)(40,170,110,239)(41,121,111,190)(42,132,112,201)(43,143,113,212)(44,154,114,223)(45,165,115,234)(46,176,116,185)(47,127,117,196)(48,138,118,207)(49,149,119,218)(50,160,120,229)(51,171,61,240)(52,122,62,191)(53,133,63,202)(54,144,64,213)(55,155,65,224)(56,166,66,235)(57,177,67,186)(58,128,68,197)(59,139,69,208)(60,150,70,219), (1,71)(2,100)(3,69)(4,98)(5,67)(6,96)(7,65)(8,94)(9,63)(10,92)(11,61)(12,90)(13,119)(14,88)(15,117)(16,86)(17,115)(18,84)(19,113)(20,82)(21,111)(22,80)(23,109)(24,78)(25,107)(26,76)(27,105)(28,74)(29,103)(30,72)(31,101)(32,70)(33,99)(34,68)(35,97)(36,66)(37,95)(38,64)(39,93)(40,62)(41,91)(42,120)(43,89)(44,118)(45,87)(46,116)(47,85)(48,114)(49,83)(50,112)(51,81)(52,110)(53,79)(54,108)(55,77)(56,106)(57,75)(58,104)(59,73)(60,102)(121,141)(122,170)(123,139)(124,168)(125,137)(126,166)(127,135)(128,164)(129,133)(130,162)(132,160)(134,158)(136,156)(138,154)(140,152)(142,150)(143,179)(144,148)(145,177)(147,175)(149,173)(151,171)(153,169)(155,167)(157,165)(159,163)(172,180)(174,178)(181,189)(182,218)(183,187)(184,216)(186,214)(188,212)(190,210)(191,239)(192,208)(193,237)(194,206)(195,235)(196,204)(197,233)(198,202)(199,231)(201,229)(203,227)(205,225)(207,223)(209,221)(211,219)(213,217)(220,240)(222,238)(224,236)(226,234)(228,232)>;
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), (1,161,71,230)(2,172,72,181)(3,123,73,192)(4,134,74,203)(5,145,75,214)(6,156,76,225)(7,167,77,236)(8,178,78,187)(9,129,79,198)(10,140,80,209)(11,151,81,220)(12,162,82,231)(13,173,83,182)(14,124,84,193)(15,135,85,204)(16,146,86,215)(17,157,87,226)(18,168,88,237)(19,179,89,188)(20,130,90,199)(21,141,91,210)(22,152,92,221)(23,163,93,232)(24,174,94,183)(25,125,95,194)(26,136,96,205)(27,147,97,216)(28,158,98,227)(29,169,99,238)(30,180,100,189)(31,131,101,200)(32,142,102,211)(33,153,103,222)(34,164,104,233)(35,175,105,184)(36,126,106,195)(37,137,107,206)(38,148,108,217)(39,159,109,228)(40,170,110,239)(41,121,111,190)(42,132,112,201)(43,143,113,212)(44,154,114,223)(45,165,115,234)(46,176,116,185)(47,127,117,196)(48,138,118,207)(49,149,119,218)(50,160,120,229)(51,171,61,240)(52,122,62,191)(53,133,63,202)(54,144,64,213)(55,155,65,224)(56,166,66,235)(57,177,67,186)(58,128,68,197)(59,139,69,208)(60,150,70,219), (1,71)(2,100)(3,69)(4,98)(5,67)(6,96)(7,65)(8,94)(9,63)(10,92)(11,61)(12,90)(13,119)(14,88)(15,117)(16,86)(17,115)(18,84)(19,113)(20,82)(21,111)(22,80)(23,109)(24,78)(25,107)(26,76)(27,105)(28,74)(29,103)(30,72)(31,101)(32,70)(33,99)(34,68)(35,97)(36,66)(37,95)(38,64)(39,93)(40,62)(41,91)(42,120)(43,89)(44,118)(45,87)(46,116)(47,85)(48,114)(49,83)(50,112)(51,81)(52,110)(53,79)(54,108)(55,77)(56,106)(57,75)(58,104)(59,73)(60,102)(121,141)(122,170)(123,139)(124,168)(125,137)(126,166)(127,135)(128,164)(129,133)(130,162)(132,160)(134,158)(136,156)(138,154)(140,152)(142,150)(143,179)(144,148)(145,177)(147,175)(149,173)(151,171)(153,169)(155,167)(157,165)(159,163)(172,180)(174,178)(181,189)(182,218)(183,187)(184,216)(186,214)(188,212)(190,210)(191,239)(192,208)(193,237)(194,206)(195,235)(196,204)(197,233)(198,202)(199,231)(201,229)(203,227)(205,225)(207,223)(209,221)(211,219)(213,217)(220,240)(222,238)(224,236)(226,234)(228,232) );
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)], [(1,161,71,230),(2,172,72,181),(3,123,73,192),(4,134,74,203),(5,145,75,214),(6,156,76,225),(7,167,77,236),(8,178,78,187),(9,129,79,198),(10,140,80,209),(11,151,81,220),(12,162,82,231),(13,173,83,182),(14,124,84,193),(15,135,85,204),(16,146,86,215),(17,157,87,226),(18,168,88,237),(19,179,89,188),(20,130,90,199),(21,141,91,210),(22,152,92,221),(23,163,93,232),(24,174,94,183),(25,125,95,194),(26,136,96,205),(27,147,97,216),(28,158,98,227),(29,169,99,238),(30,180,100,189),(31,131,101,200),(32,142,102,211),(33,153,103,222),(34,164,104,233),(35,175,105,184),(36,126,106,195),(37,137,107,206),(38,148,108,217),(39,159,109,228),(40,170,110,239),(41,121,111,190),(42,132,112,201),(43,143,113,212),(44,154,114,223),(45,165,115,234),(46,176,116,185),(47,127,117,196),(48,138,118,207),(49,149,119,218),(50,160,120,229),(51,171,61,240),(52,122,62,191),(53,133,63,202),(54,144,64,213),(55,155,65,224),(56,166,66,235),(57,177,67,186),(58,128,68,197),(59,139,69,208),(60,150,70,219)], [(1,71),(2,100),(3,69),(4,98),(5,67),(6,96),(7,65),(8,94),(9,63),(10,92),(11,61),(12,90),(13,119),(14,88),(15,117),(16,86),(17,115),(18,84),(19,113),(20,82),(21,111),(22,80),(23,109),(24,78),(25,107),(26,76),(27,105),(28,74),(29,103),(30,72),(31,101),(32,70),(33,99),(34,68),(35,97),(36,66),(37,95),(38,64),(39,93),(40,62),(41,91),(42,120),(43,89),(44,118),(45,87),(46,116),(47,85),(48,114),(49,83),(50,112),(51,81),(52,110),(53,79),(54,108),(55,77),(56,106),(57,75),(58,104),(59,73),(60,102),(121,141),(122,170),(123,139),(124,168),(125,137),(126,166),(127,135),(128,164),(129,133),(130,162),(132,160),(134,158),(136,156),(138,154),(140,152),(142,150),(143,179),(144,148),(145,177),(147,175),(149,173),(151,171),(153,169),(155,167),(157,165),(159,163),(172,180),(174,178),(181,189),(182,218),(183,187),(184,216),(186,214),(188,212),(190,210),(191,239),(192,208),(193,237),(194,206),(195,235),(196,204),(197,233),(198,202),(199,231),(201,229),(203,227),(205,225),(207,223),(209,221),(211,219),(213,217),(220,240),(222,238),(224,236),(226,234),(228,232)])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 10A | ··· | 10F | 12A | 12B | 15A | 15B | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 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 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 20 | 20 | 30 | 30 | 2 | 2 | 2 | 12 | 12 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 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 | C3⋊D4 | D20 | S3×D4 | D4⋊2S3 | S3×D5 | D4×D5 | Q8⋊2D5 | C3⋊D20 | C2×S3×D5 | D20⋊S3 | C20⋊D6 |
| kernel | C60⋊11D4 | D10⋊Dic3 | C5×C4⋊Dic3 | C2×C3⋊D20 | C6×D20 | C2×C4×D15 | C2×D20 | C60 | D30 | C4⋊Dic3 | C2×C20 | C22×D5 | C30 | C2×Dic3 | C2×C12 | C20 | C12 | C10 | C10 | C2×C4 | C6 | C6 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 4 | 2 | 4 | 8 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of C60⋊11D4 ►in GL6(𝔽61)
| 1 | 60 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 50 | 30 | 0 | 0 |
| 0 | 0 | 0 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 18 |
| 0 | 0 | 0 | 0 | 43 | 60 |
| 9 | 9 | 0 | 0 | 0 | 0 |
| 18 | 52 | 0 | 0 | 0 | 0 |
| 0 | 0 | 35 | 37 | 0 | 0 |
| 0 | 0 | 46 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 60 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 36 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 43 | 60 |
G:=sub<GL(6,GF(61))| [1,1,0,0,0,0,60,0,0,0,0,0,0,0,50,0,0,0,0,0,30,11,0,0,0,0,0,0,18,43,0,0,0,0,18,60],[9,18,0,0,0,0,9,52,0,0,0,0,0,0,35,46,0,0,0,0,37,26,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[60,0,0,0,0,0,1,1,0,0,0,0,0,0,60,0,0,0,0,0,36,1,0,0,0,0,0,0,1,43,0,0,0,0,0,60] >;
C60⋊11D4 in GAP, Magma, Sage, TeX
C_{60}\rtimes_{11}D_4 % in TeX
G:=Group("C60:11D4"); // GroupNames label
G:=SmallGroup(480,541);
// by ID
G=gap.SmallGroup(480,541);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,64,422,219,100,1356,18822]);
// Polycyclic
G:=Group<a,b,c|a^60=b^4=c^2=1,b*a*b^-1=a^11,c*a*c=a^29,c*b*c=b^-1>;
// generators/relations