Group action invariants
Degree $n$: | $10$ | |
Transitive number $t$: | $44$ | |
Group: | $A_{10}$ | |
CHM label: | $A10$ | |
Parity: | $1$ | |
Primitive: | yes | |
Nilpotency class: | $-1$ (not nilpotent) | |
$\card{\Aut(F/K)}$: | $1$ | |
Generators: | (1,2)(3,4,5,6,7,8,9,10), (1,2,3) |
Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 5: None
Low degree siblings
45T1982Siblings 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 $ | $1$ | $1$ | $()$ |
$ 3, 1, 1, 1, 1, 1, 1, 1 $ | $240$ | $3$ | $( 4, 8,10)$ |
$ 7, 1, 1, 1 $ | $86400$ | $7$ | $(1,6,7,9,3,2,5)$ |
$ 7, 3 $ | $86400$ | $21$ | $( 1, 2, 9, 6, 5, 3, 7)( 4, 8,10)$ |
$ 7, 3 $ | $86400$ | $21$ | $( 1, 2, 9, 6, 5, 3, 7)( 4,10, 8)$ |
$ 3, 3, 3, 1 $ | $22400$ | $3$ | $( 2, 8, 3)( 4, 7,10)( 5, 6, 9)$ |
$ 9, 1 $ | $201600$ | $9$ | $( 2, 5, 7, 8, 6,10, 3, 9, 4)$ |
$ 2, 2, 1, 1, 1, 1, 1, 1 $ | $630$ | $2$ | $( 2,10)( 3, 6)$ |
$ 4, 2, 1, 1, 1, 1 $ | $18900$ | $4$ | $( 2, 6,10, 3)( 4, 7)$ |
$ 3, 2, 2, 1, 1, 1 $ | $25200$ | $6$ | $( 1, 9, 5)( 2,10)( 3, 6)$ |
$ 4, 3, 2, 1 $ | $151200$ | $12$ | $( 1, 5, 9)( 2, 3,10, 6)( 4, 7)$ |
$ 2, 2, 2, 2, 1, 1 $ | $4725$ | $2$ | $( 1, 3)( 4, 9)( 5, 8)( 6,10)$ |
$ 3, 3, 1, 1, 1, 1 $ | $8400$ | $3$ | $( 1,10, 5)( 3, 6, 8)$ |
$ 6, 2, 1, 1 $ | $151200$ | $6$ | $( 1, 8,10, 3, 5, 6)( 4, 9)$ |
$ 4, 4, 1, 1 $ | $56700$ | $4$ | $( 1, 7, 5, 6)( 2,10, 3, 8)$ |
$ 8, 2 $ | $226800$ | $8$ | $( 1, 8, 7, 2, 5,10, 6, 3)( 4, 9)$ |
$ 4, 2, 2, 2 $ | $18900$ | $4$ | $( 1, 9, 3, 4)( 2, 7)( 5, 6)( 8,10)$ |
$ 3, 3, 2, 2 $ | $25200$ | $6$ | $( 1, 3)( 2, 8, 6)( 4, 9)( 5, 7,10)$ |
$ 6, 4 $ | $151200$ | $12$ | $( 1, 9, 3, 4)( 2, 5, 8, 7, 6,10)$ |
$ 5, 1, 1, 1, 1, 1 $ | $6048$ | $5$ | $(2,6,7,3,9)$ |
$ 5, 3, 1, 1 $ | $120960$ | $15$ | $( 2, 7, 9, 6, 3)( 4, 8,10)$ |
$ 5, 5 $ | $72576$ | $5$ | $( 1, 8, 4,10, 5)( 2, 9, 3, 7, 6)$ |
$ 9, 1 $ | $201600$ | $9$ | $( 2, 8,10, 5, 9, 7, 6, 4, 3)$ |
$ 5, 2, 2, 1 $ | $90720$ | $10$ | $( 1,10)( 2, 3, 6, 9, 7)( 5, 8)$ |
Group invariants
Order: | $1814400=2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7$ | |
Cyclic: | no | |
Abelian: | no | |
Solvable: | no | |
Label: | not available |
Character table: not available. |