Group action invariants
| Degree $n$ : | $10$ | |
| Transitive number $t$ : | $41$ | |
| Group : | $(A_5^2 : C_2):C_2$ | |
| CHM label : | $[1/2.S(5)^{2}]2=[A(5):2]2$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (2,10)(5,7), (2,4,6,8,10), (1,6)(2,7)(3,8)(4,9)(5,10) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 5: None
Low degree siblings
12T279, 20T456, 20T459, 24T12117, 25T101, 30T819, 36T9862, 40T10506, 40T10507, 40T10508Siblings 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 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 1, 1, 1, 1, 1, 1 $ | $100$ | $2$ | $( 1, 3)( 6, 8)$ |
| $ 2, 2, 2, 2, 1, 1 $ | $225$ | $2$ | $( 1, 3)( 2,10)( 5, 7)( 6, 8)$ |
| $ 3, 3, 1, 1, 1, 1 $ | $400$ | $3$ | $( 1, 3, 5)( 6, 8,10)$ |
| $ 3, 3, 2, 2 $ | $400$ | $6$ | $( 1, 3, 5)( 2, 4)( 6, 8,10)( 7, 9)$ |
| $ 4, 4, 1, 1 $ | $900$ | $4$ | $( 1, 3, 5, 7)( 2, 6, 8,10)$ |
| $ 5, 5 $ | $288$ | $5$ | $( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)$ |
| $ 5, 5 $ | $288$ | $5$ | $( 1, 3, 5, 7, 9)( 2, 6, 8,10, 4)$ |
| $ 2, 2, 1, 1, 1, 1, 1, 1 $ | $30$ | $2$ | $( 2,10)( 6, 8)$ |
| $ 3, 1, 1, 1, 1, 1, 1, 1 $ | $40$ | $3$ | $( 6, 8,10)$ |
| $ 5, 1, 1, 1, 1, 1 $ | $48$ | $5$ | $( 2, 4, 6, 8,10)$ |
| $ 3, 2, 2, 1, 1, 1 $ | $400$ | $6$ | $( 1, 3)( 2, 4)( 6, 8,10)$ |
| $ 4, 2, 1, 1, 1, 1 $ | $600$ | $4$ | $( 1, 3)( 2, 6, 8,10)$ |
| $ 3, 2, 2, 1, 1, 1 $ | $600$ | $6$ | $( 1, 3)( 5, 7)( 6, 8,10)$ |
| $ 5, 2, 2, 1 $ | $720$ | $10$ | $( 1, 3)( 2, 4, 6, 8,10)( 5, 7)$ |
| $ 5, 3, 1, 1 $ | $960$ | $15$ | $( 1, 3, 5)( 2, 4, 6, 8,10)$ |
| $ 4, 3, 2, 1 $ | $1200$ | $12$ | $( 1, 3, 5)( 2, 6, 8,10)( 7, 9)$ |
| $ 2, 2, 2, 2, 2 $ | $60$ | $2$ | $( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)$ |
| $ 4, 4, 2 $ | $900$ | $4$ | $( 1, 8, 3, 6)( 2, 7,10, 5)( 4, 9)$ |
| $ 6, 2, 2 $ | $1200$ | $6$ | $( 1, 8, 3,10, 5, 6)( 2, 7)( 4, 9)$ |
| $ 10 $ | $1440$ | $10$ | $( 1, 8, 3,10, 5, 2, 7, 4, 9, 6)$ |
| $ 2, 2, 2, 2, 2 $ | $60$ | $2$ | $( 1, 8)( 2, 7)( 3, 6)( 4, 9)( 5,10)$ |
| $ 6, 2, 2 $ | $1200$ | $6$ | $( 1, 8)( 2, 7, 4, 9,10, 5)( 3, 6)$ |
| $ 4, 4, 2 $ | $900$ | $4$ | $( 1, 6, 3, 8)( 2, 7,10, 5)( 4, 9)$ |
| $ 10 $ | $1440$ | $10$ | $( 1,10, 5, 2, 7, 6, 3, 4, 9, 8)$ |
Group invariants
| Order: | $14400=2^{6} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |