Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $547$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,6,13)(2,17,5,14)(3,20,8,16)(4,19,7,15)(9,10), (1,19,10,3,6,15,13,8,17,12,2,20,9,4,5,16,14,7,18,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 14400: $(A_5^2 : C_2):C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: None
Degree 10: $(A_5^2 : C_2):C_2$
Low degree siblings
20T547, 24T13991 x 2, 40T14354, 40T14367 x 2, 40T14368 x 2Siblings 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, 2, 2, 2, 2, 2, 2 $ | $1$ | $2$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $200$ | $2$ | $( 1,10)( 2, 9)( 5, 6)(11,20)(12,19)(13,14)(17,18)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $225$ | $2$ | $( 1,10)( 2, 9)( 3,15)( 4,16)( 5,14)( 6,13)( 7, 8)(11,19)(12,20)(17,18)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ | $225$ | $2$ | $( 1, 9)( 2,10)( 3,16)( 4,15)( 5,13)( 6,14)(11,20)(12,19)$ |
| $ 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $400$ | $3$ | $( 1, 9, 6)( 2,10, 5)( 3,11,20)( 4,12,19)$ |
| $ 6, 6, 2, 2, 2, 2 $ | $400$ | $6$ | $( 1,10, 6, 2, 9, 5)( 3,12,20, 4,11,19)( 7, 8)(13,14)(15,16)(17,18)$ |
| $ 6, 3, 3, 2, 2, 2, 2 $ | $800$ | $6$ | $( 1, 9, 6)( 2,10, 5)( 3,12,20, 4,11,19)( 7,16)( 8,15)(13,18)(14,17)$ |
| $ 4, 4, 4, 4, 2, 1, 1 $ | $1800$ | $4$ | $( 1, 9, 6,14)( 2,10, 5,13)( 3,15,11,19)( 4,16,12,20)( 7, 8)$ |
| $ 5, 5, 5, 5 $ | $288$ | $5$ | $( 1, 9, 6,14,17)( 2,10, 5,13,18)( 3,16, 8,11,20)( 4,15, 7,12,19)$ |
| $ 10, 10 $ | $288$ | $10$ | $( 1,10, 6,13,17, 2, 9, 5,14,18)( 3,15, 8,12,20, 4,16, 7,11,19)$ |
| $ 5, 5, 5, 5 $ | $288$ | $5$ | $( 1, 9, 6,14,17)( 2,10, 5,13,18)( 3, 8,16,11,20)( 4, 7,15,12,19)$ |
| $ 10, 10 $ | $288$ | $10$ | $( 1,10, 6,13,17, 2, 9, 5,14,18)( 3, 7,16,12,20, 4, 8,15,11,19)$ |
| $ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $30$ | $2$ | $( 3,16)( 4,15)(11,20)(12,19)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $30$ | $2$ | $( 1, 2)( 3,15)( 4,16)( 5, 6)( 7, 8)( 9,10)(11,19)(12,20)(13,14)(17,18)$ |
| $ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $40$ | $3$ | $( 3,11,20)( 4,12,19)$ |
| $ 6, 2, 2, 2, 2, 2, 2, 2 $ | $40$ | $6$ | $( 1, 2)( 3,12,20, 4,11,19)( 5, 6)( 7, 8)( 9,10)(13,14)(15,16)(17,18)$ |
| $ 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $48$ | $5$ | $( 3,16, 8,11,20)( 4,15, 7,12,19)$ |
| $ 10, 2, 2, 2, 2, 2 $ | $48$ | $10$ | $( 1, 2)( 3,15, 8,12,20, 4,16, 7,11,19)( 5, 6)( 9,10)(13,14)(17,18)$ |
| $ 3, 3, 2, 2, 2, 2, 2, 2, 2 $ | $400$ | $6$ | $( 1,10)( 2, 9)( 3,11,20)( 4,12,19)( 5, 6)( 7,15)( 8,16)(13,14)(17,18)$ |
| $ 6, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $400$ | $6$ | $( 1, 9)( 2,10)( 3,12,20, 4,11,19)( 7,16)( 8,15)$ |
| $ 4, 4, 2, 2, 2, 2, 2, 1, 1 $ | $600$ | $4$ | $( 1,10)( 2, 9)( 3,16,11,20)( 4,15,12,19)( 5, 6)(13,14)(17,18)$ |
| $ 4, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $600$ | $4$ | $( 1, 9)( 2,10)( 3,15,11,19)( 4,16,12,20)( 7, 8)$ |
| $ 6, 2, 2, 2, 2, 2, 2, 2 $ | $600$ | $6$ | $( 1,10)( 2, 9)( 3,12,20, 4,11,19)( 5,14)( 6,13)( 7, 8)(15,16)(17,18)$ |
| $ 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $600$ | $6$ | $( 1, 9)( 2,10)( 3,11,20)( 4,12,19)( 5,13)( 6,14)$ |
| $ 10, 2, 2, 2, 2, 2 $ | $720$ | $10$ | $( 1,10)( 2, 9)( 3,15, 8,12,20, 4,16, 7,11,19)( 5,14)( 6,13)(17,18)$ |
| $ 5, 5, 2, 2, 2, 2, 1, 1 $ | $720$ | $10$ | $( 1, 9)( 2,10)( 3,16, 8,11,20)( 4,15, 7,12,19)( 5,13)( 6,14)$ |
| $ 5, 5, 3, 3, 1, 1, 1, 1 $ | $960$ | $15$ | $( 1, 9, 6)( 2,10, 5)( 3,16, 8,11,20)( 4,15, 7,12,19)$ |
| $ 10, 6, 2, 2 $ | $960$ | $30$ | $( 1,10, 6, 2, 9, 5)( 3,15, 8,12,20, 4,16, 7,11,19)(13,14)(17,18)$ |
| $ 4, 4, 3, 3, 2, 2, 2 $ | $1200$ | $12$ | $( 1, 9, 6)( 2,10, 5)( 3,15,11,19)( 4,16,12,20)( 7, 8)(13,18)(14,17)$ |
| $ 6, 4, 4, 2, 2, 1, 1 $ | $1200$ | $12$ | $( 1,10, 6, 2, 9, 5)( 3,16,11,20)( 4,15,12,19)(13,17)(14,18)$ |
| $ 4, 4, 4, 4, 4 $ | $120$ | $4$ | $( 1,11, 2,12)( 3, 5, 4, 6)( 7,17, 8,18)( 9,20,10,19)(13,15,14,16)$ |
| $ 4, 4, 4, 4, 4 $ | $1800$ | $4$ | $( 1,20,10,12)( 2,19, 9,11)( 3, 5,15,14)( 4, 6,16,13)( 7,17, 8,18)$ |
| $ 12, 4, 4 $ | $2400$ | $12$ | $( 1,19,10, 3, 6,12, 2,20, 9, 4, 5,11)( 7,18, 8,17)(13,16,14,15)$ |
| $ 20 $ | $1440$ | $20$ | $( 1,19,10, 3, 6,15,13, 8,17,12, 2,20, 9, 4, 5,16,14, 7,18,11)$ |
| $ 20 $ | $1440$ | $20$ | $( 1,20,10, 4, 6,16,13, 7,17,11, 2,19, 9, 3, 5,15,14, 8,18,12)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $120$ | $2$ | $( 1,20)( 2,19)( 3, 6)( 4, 5)( 7,18)( 8,17)( 9,11)(10,12)(13,15)(14,16)$ |
| $ 6, 6, 2, 2, 2, 2 $ | $2400$ | $6$ | $( 1,20)( 2,19)( 3, 6,16,14, 8,17)( 4, 5,15,13, 7,18)( 9,11)(10,12)$ |
| $ 4, 4, 4, 4, 2, 2 $ | $1800$ | $4$ | $( 1,11, 9,20)( 2,12,10,19)( 3, 6,16,14)( 4, 5,15,13)( 7,18)( 8,17)$ |
| $ 10, 10 $ | $1440$ | $10$ | $( 1, 4, 6,15,14,12, 9, 7,17,19)( 2, 3, 5,16,13,11,10, 8,18,20)$ |
| $ 10, 10 $ | $1440$ | $10$ | $( 1, 3, 6,16,14,11, 9, 8,17,20)( 2, 4, 5,15,13,12,10, 7,18,19)$ |
Group invariants
| Order: | $28800=2^{7} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |