Group action invariants
| Degree $n$ : | $38$ | |
| Transitive number $t$ : | $33$ | |
| Group : | $\PSL(2,37)$ | |
| Parity: | $1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,20,23,11,9,13,22,14,16,24,34,12,33,15,6,31,37,36)(4,10,35,26,8,29,7,17,25,27,19,28,32,30,18,21,38,5), (1,21,2)(3,7,20)(5,13,11)(6,30,37)(8,9,36)(10,26,18)(12,14,17)(15,35,34)(16,29,33)(19,22,24)(23,31,25)(27,28,38) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
NoneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 19: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
| Cycle Type | Size | Order | Representative |
| $ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $703$ | $2$ | $( 1,32)( 2,15)( 3,13)( 4,25)( 5, 6)( 7,27)( 8,34)( 9,22)(10,26)(11,21)(12,31) (14,36)(16,28)(17,35)(18,19)(20,37)(23,30)(29,33)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ | $1406$ | $3$ | $( 1, 7,16)( 2, 5,20)( 3,11,29)( 4,19,22)( 6,37,15)( 8,17,23)( 9,25,18) (10,31,14)(12,36,26)(13,21,33)(27,28,32)(30,34,35)$ |
| $ 6, 6, 6, 6, 6, 6, 1, 1 $ | $1406$ | $6$ | $( 1,28, 7,32,16,27)( 2,37, 5,15,20, 6)( 3,33,11,13,29,21)( 4, 9,19,25,22,18) ( 8,30,17,34,23,35)(10,36,31,26,14,12)$ |
| $ 9, 9, 9, 9, 1, 1 $ | $1406$ | $9$ | $( 1,12,23,16,26,17, 7,36, 8)( 2,11,25,20, 3, 9, 5,29,18)( 4,37,13,22, 6,33,19, 15,21)(10,35,27,14,34,32,31,30,28)$ |
| $ 9, 9, 9, 9, 1, 1 $ | $1406$ | $9$ | $( 1,23,26, 7, 8,12,16,17,36)( 2,25, 3, 5,18,11,20, 9,29)( 4,13, 6,19,21,37,22, 33,15)(10,27,34,31,28,35,14,32,30)$ |
| $ 9, 9, 9, 9, 1, 1 $ | $1406$ | $9$ | $( 1,26, 8,16,36,23, 7,12,17)( 2, 3,18,20,29,25, 5,11, 9)( 4, 6,21,22,15,13,19, 37,33)(10,34,28,14,30,27,31,35,32)$ |
| $ 18, 18, 1, 1 $ | $1406$ | $18$ | $( 1,35,12,27,23,14,16,34,26,32,17,31, 7,30,36,28, 8,10)( 2,22,11, 6,25,33,20, 19, 3,15, 9,21, 5, 4,29,37,18,13)$ |
| $ 18, 18, 1, 1 $ | $1406$ | $18$ | $( 1,31,23,28,26,35, 7,14, 8,32,12,30,16,10,17,27,36,34)( 2,21,25,37, 3,22, 5, 33,18,15,11, 4,20,13, 9, 6,29,19)$ |
| $ 18, 18, 1, 1 $ | $1406$ | $18$ | $( 1,30,26,27, 8,31,16,35,36,32,23,10, 7,34,12,28,17,14)( 2, 4, 3, 6,18,21,20, 22,29,15,25,13, 5,19,11,37, 9,33)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1,34,29, 3,23, 4,28, 6,13,10,32,36,20,17,24, 2,26, 7,27)( 5,22,18,19,21,35, 38,15,30,33, 9,11,12, 8,25,16,37,31,14)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1,36, 3,24,28, 7,10,34,20,23, 2, 6,27,32,29,17, 4,26,13)( 5,11,19,25,38,31, 33,22,12,21,16,15,14, 9,18, 8,35,37,30)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1, 6,24,29,10,26,23,36,27,28,17,34,13, 2, 3,32, 7, 4,20)( 5,15,25,18,33,37, 21,11,14,38, 8,22,30,16,19, 9,31,35,12)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1, 4,32, 2,34,28,36,26,29, 6,20, 7, 3,13,17,27,23,10,24)( 5,35, 9,16,22,38, 11,37,18,15,12,31,19,30, 8,14,21,33,25)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1, 7, 2,17,36,10, 6, 4, 3,34,27,26,24,20,32,13,28,23,29)( 5,31,16, 8,11,33, 15,35,19,22,14,37,25,12, 9,30,38,21,18)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1,26,17,32, 6,23,34, 7,24,36,13, 4,29,27, 2,20,10,28, 3)( 5,37, 8, 9,15,21, 22,31,25,11,30,35,18,14,16,12,33,38,19)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1,28,20,27, 4,36, 7,23,32,26, 3,10, 2,29,13,24,34, 6,17)( 5,38,12,14,35,11, 31,21, 9,37,19,33,16,18,30,25,22,15, 8)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1,10,27,13, 7, 6,26,28, 2, 4,24,23,17, 3,20,29,36,34,32)( 5,33,14,30,31,15, 37,38,16,35,25,21, 8,19,12,18,11,22, 9)$ |
| $ 19, 19 $ | $1332$ | $19$ | $( 1,23,13,20,26,34, 4,10,17, 7,29,28,32,24,27, 3, 6,36, 2)( 5,21,30,12,37,22, 35,33, 8,31,18,38, 9,25,14,19,15,11,16)$ |
| $ 37, 1 $ | $684$ | $37$ | $( 1,28, 9,13,21,15,23,27, 8,35,25,32,14,30, 5,29,26,38,33,20,19,24,34,18, 2, 12,17,16, 3,36,10, 7,31, 6,22, 4,11)$ |
| $ 37, 1 $ | $684$ | $37$ | $( 1,23,14,33, 2,10,11,15,32,38,18,36, 4,21,25,26,34, 3,22,13,35,29,24,16, 6, 9, 8, 5,19,17,31,28,27,30,20,12, 7)$ |
Group invariants
| Order: | $25308=2^{2} \cdot 3^{2} \cdot 19 \cdot 37$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |