Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $230$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,7,5,14)(2,10,8,6,13)(3,12,20,18,16)(4,11,19,17,15), (1,10,14,11,20,4)(2,9,13,12,19,3)(5,15)(6,16)(7,17)(8,18) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 60: $A_5$ 120: $A_5\times C_2$ 960: $C_2^4 : A_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $A_5$
Degree 10: $A_5\times C_2$, $C_2^4 : A_5$, $C_2 \wr A_5$
Low degree siblings
10T36, 20T224, 20T225, 30T344, 30T354, 32T97741, 40T1576, 40T1578, 40T1585, 40T1586, 40T1597, 40T1598, 40T1644Siblings are shown 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 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $10$ | $2$ | $( 7,18)( 8,17)( 9,20)(10,19)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ | $5$ | $2$ | $( 3,14)( 4,13)( 5,16)( 6,15)( 7,18)( 8,17)( 9,20)(10,19)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $10$ | $2$ | $( 1,11)( 2,12)( 3, 4)( 5,15)( 6,16)( 7, 8)( 9,19)(10,20)(13,14)(17,18)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $5$ | $2$ | $( 1,11)( 2,12)( 3, 4)( 5, 6)( 7, 8)( 9,10)(13,14)(15,16)(17,18)(19,20)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $1$ | $2$ | $( 1,11)( 2,12)( 3,13)( 4,14)( 5,15)( 6,16)( 7,17)( 8,18)( 9,19)(10,20)$ |
| $ 4, 4, 2, 2, 2, 2, 2, 2 $ | $120$ | $4$ | $( 1,20,12, 9)( 2,19,11,10)( 3, 7)( 4, 8)( 5,16)( 6,15)(13,17)(14,18)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ | $60$ | $2$ | $( 1, 9)( 2,10)( 3, 7)( 4, 8)(11,19)(12,20)(13,17)(14,18)$ |
| $ 4, 4, 4, 4, 1, 1, 1, 1 $ | $60$ | $4$ | $( 1,20,12, 9)( 2,19,11,10)( 3,18,14, 7)( 4,17,13, 8)$ |
| $ 4, 4, 2, 2, 2, 2, 2, 2 $ | $120$ | $4$ | $( 1,10,12,19)( 2, 9,11,20)( 3, 8)( 4, 7)( 5, 6)(13,18)(14,17)(15,16)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $60$ | $2$ | $( 1,19)( 2,20)( 3, 8)( 4, 7)( 5,15)( 6,16)( 9,11)(10,12)(13,18)(14,17)$ |
| $ 4, 4, 4, 4, 2, 2 $ | $60$ | $4$ | $( 1,10,12,19)( 2, 9,11,20)( 3,17,14, 8)( 4,18,13, 7)( 5,15)( 6,16)$ |
| $ 3, 3, 3, 3, 2, 2, 2, 2 $ | $80$ | $6$ | $( 1, 9, 7)( 2,10, 8)( 3,14)( 4,13)( 5,16)( 6,15)(11,19,17)(12,20,18)$ |
| $ 6, 6, 2, 2, 1, 1, 1, 1 $ | $80$ | $6$ | $( 1,20,18,12, 9, 7)( 2,19,17,11,10, 8)( 3,14)( 4,13)$ |
| $ 6, 6, 2, 2, 1, 1, 1, 1 $ | $80$ | $6$ | $( 1,20,18,12, 9, 7)( 2,19,17,11,10, 8)( 5,16)( 6,15)$ |
| $ 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $80$ | $3$ | $( 1, 9, 7)( 2,10, 8)(11,19,17)(12,20,18)$ |
| $ 6, 6, 2, 2, 2, 2 $ | $80$ | $6$ | $( 1,19,18, 2,20,17)( 3,13)( 4,14)( 5, 6)( 7,11, 9, 8,12,10)(15,16)$ |
| $ 6, 6, 2, 2, 2, 2 $ | $80$ | $6$ | $( 1,10, 7,11,20,17)( 2, 9, 8,12,19,18)( 3,13)( 4,14)( 5,15)( 6,16)$ |
| $ 6, 6, 2, 2, 2, 2 $ | $80$ | $6$ | $( 1,10, 7,11,20,17)( 2, 9, 8,12,19,18)( 3, 4)( 5, 6)(13,14)(15,16)$ |
| $ 6, 6, 2, 2, 2, 2 $ | $80$ | $6$ | $( 1,19,18, 2,20,17)( 3, 4)( 5,15)( 6,16)( 7,11, 9, 8,12,10)(13,14)$ |
| $ 10, 10 $ | $192$ | $10$ | $( 1,19, 7, 4, 5,11, 9,17,14,15)( 2,20, 8, 3, 6,12,10,18,13,16)$ |
| $ 5, 5, 5, 5 $ | $192$ | $5$ | $( 1, 9,18,14, 5)( 2,10,17,13, 6)( 3,16,12,20, 7)( 4,15,11,19, 8)$ |
| $ 5, 5, 5, 5 $ | $192$ | $5$ | $( 1, 9, 7,16, 3)( 2,10, 8,15, 4)( 5,14,12,20,18)( 6,13,11,19,17)$ |
| $ 10, 10 $ | $192$ | $10$ | $( 1,19,18,15, 3,11, 9, 8, 5,13)( 2,20,17,16, 4,12,10, 7, 6,14)$ |
Group invariants
| Order: | $1920=2^{7} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |