Group action invariants
| Degree $n$ : | $31$ | |
| Transitive number $t$ : | $10$ | |
| Group : | $\PSL(5,2)$ | |
| Parity: | $1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,19)(6,12)(9,24)(11,18)(15,16)(17,26)(23,27)(28,30), (1,5,4,3,2)(6,31,30,8,7)(9,29,28,23,10)(11,22,21,20,19)(12,18,26,14,13)(15,25,24,27,17) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
NoneResolvents shown for degrees $\leq 47$
Subfields
Prime degree - none
Low degree siblings
31T10Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
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 $ | $1$ | $1$ | $()$ |
| $ 7, 7, 7, 7, 1, 1, 1 $ | $238080$ | $7$ | $( 1,31,22,16,28,23,21)( 2, 4,24,17, 6,14,11)( 3,13,30,15,19,10,27) ( 7,12, 8,25,26, 9,18)$ |
| $ 7, 7, 7, 7, 1, 1, 1 $ | $238080$ | $7$ | $( 1,21,23,28,16,22,31)( 2,11,14, 6,17,24, 4)( 3,27,10,19,15,30,13) ( 7,18, 9,26,25, 8,12)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $465$ | $2$ | $( 1,27)( 3,31)( 5,20)(10,21)(13,22)(15,28)(16,30)(19,23)$ |
| $ 14, 7, 7, 2, 1 $ | $714240$ | $14$ | $( 1,10,23,15,16,13,31,27,21,19,28,30,22, 3)( 2,11,14, 6,17,24, 4)( 5,20) ( 7,18, 9,26,25, 8,12)$ |
| $ 14, 7, 7, 2, 1 $ | $714240$ | $14$ | $( 1,15,31,19,22,10,16,27,28, 3,23,13,21,30)( 2, 6, 4,14,24,11,17)( 5,20) ( 7,26,12, 9, 8,18,25)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1 $ | $19840$ | $3$ | $( 2,31,11)( 4,28,22)( 5,19,18)( 7,26,30)( 8,12,27)( 9,13,15)(14,21,24) (20,29,23)$ |
| $ 21, 7, 3 $ | $476160$ | $21$ | $( 1,16,17,10, 6,25, 3)( 2,21,28,26,29,13,12,31,24,22,30,23,15,27,11,14, 4, 7, 20, 9, 8)( 5,19,18)$ |
| $ 21, 7, 3 $ | $476160$ | $21$ | $( 1,10, 3,17,25,16, 6)( 2,30, 8,22, 9,24,20,31, 7,12, 4,13,14,29,11,26,27,28, 15,21,23)( 5,19,18)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1 $ | $6510$ | $2$ | $( 1,30)( 2,22)( 3,29)( 5, 7)( 6,16)( 8,14)( 9,27)(11,19)(13,20)(17,18)(21,25) (26,28)$ |
| $ 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 1 $ | $312480$ | $4$ | $( 1,25,30,21)( 2, 5,22, 7)( 3,18,29,17)( 4,31)( 6, 9,16,27)( 8,28,14,26) (11,20,19,13)(12,15)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1 $ | $55552$ | $3$ | $( 1,25, 2)( 3, 7,18)( 4,31,10)( 5,17,29)( 6, 8,11)( 9,20,28)(12,23,24) (13,26,27)(14,19,16)(21,22,30)$ |
| $ 6, 6, 6, 6, 3, 3, 1 $ | $833280$ | $6$ | $( 1, 5,25,17, 2,29)( 3,30, 7,21,18,22)( 4,10,31)( 6,26, 8,27,11,13) ( 9,19,20,16,28,14)(12,24,23)$ |
| $ 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ | $78120$ | $4$ | $( 1, 8)( 2, 3,16,26)( 5,25, 9,19)( 6,28,22,29)( 7,21,27,11)(10,31)(12,24) (13,18)(14,30)(17,20)$ |
| $ 4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1 $ | $26040$ | $4$ | $( 1,24,14,31)( 2,16)( 3,26)( 4,23)( 5,25, 9,19)( 6,29,22,28)( 8,12,30,10) (13,18)$ |
| $ 6, 6, 3, 3, 3, 3, 2, 2, 1, 1, 1 $ | $416640$ | $6$ | $( 2, 9, 4, 8,17,25)( 3,15,13)( 5,20)( 6,14,24)( 7,26,18)(10,16,19,21,30,23) (11,12)(22,31,28)$ |
| $ 8, 8, 4, 4, 4, 2, 1 $ | $624960$ | $8$ | $( 1,12,30,31)( 2, 6,21,25,16,22,11,19)( 3,28,27, 9,26,29, 7, 5)( 4,23) ( 8,24,14,10)(13,17,18,20)$ |
| $ 5, 5, 5, 5, 5, 5, 1 $ | $666624$ | $5$ | $( 1,24,17, 3,21)( 2,23, 5,18,30)( 4, 9,13, 8,16)( 6,19,10,28,27) ( 7,22,25,12,29)(11,14,31,20,26)$ |
| $ 15, 15, 1 $ | $666624$ | $15$ | $( 1, 5,22,24,18,25,17,30,12, 3, 2,29,21,23, 7)( 4,27,14, 9, 6,31,13,19,20, 8, 10,26,16,28,11)$ |
| $ 15, 15, 1 $ | $666624$ | $15$ | $( 1,29,30,24, 7, 2,17,22,23, 3,25, 5,21,12,18)( 4,26,19, 9,11,10,13,14,28, 8, 31,27,16,20, 6)$ |
| $ 12, 6, 4, 3, 3, 2, 1 $ | $833280$ | $12$ | $( 1,30, 9,23,17,26,12,24,28,18,15,16)( 2,25, 4, 3,22,13)( 5, 7,10) ( 6,11,19,27)( 8,31)(14,29,21)$ |
| $ 31 $ | $322560$ | $31$ | $( 1,20,22, 4,17,30,15,11,23, 7,14,27, 9, 2,12,25, 5,18,31, 8,21, 3,16,29,28, 10,24, 6,26,13,19)$ |
| $ 31 $ | $322560$ | $31$ | $( 1,10, 8, 2,11,20,24,21,12,23,22, 6, 3,25, 7, 4,26,16, 5,14,17,13,29,18,27, 30,19,28,31, 9,15)$ |
| $ 31 $ | $322560$ | $31$ | $( 1,30,14,25,21,10,19,17, 7,12, 8,28,13, 4,23, 2,31,29,26,22,11, 9,18,16, 6, 20,15,27, 5, 3,24)$ |
| $ 31 $ | $322560$ | $31$ | $( 1,19,13,26, 6,24,10,28,29,16, 3,21, 8,31,18, 5,25,12, 2, 9,27,14, 7,23,11, 15,30,17, 4,22,20)$ |
| $ 31 $ | $322560$ | $31$ | $( 1,15, 9,31,28,19,30,27,18,29,13,17,14, 5,16,26, 4, 7,25, 3, 6,22,23,12,21, 24,20,11, 2, 8,10)$ |
| $ 31 $ | $322560$ | $31$ | $( 1,24, 3, 5,27,15,20, 6,16,18, 9,11,22,26,29,31, 2,23, 4,13,28, 8,12, 7,17, 19,10,21,25,14,30)$ |
Group invariants
| Order: | $9999360=2^{10} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 31$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |