Properties

Label 35T39
Order \(24010\)
n \(35\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $35$
Transitive number $t$ :  $39$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,4,11,6,13,2,9,5,12,7,14,3,10)(15,34,18,31,20,30,16,29,19,33,21,32,17,35)(22,28)(23,27)(25,26), (1,17,29,13,25)(2,19,32,10,28)(3,20,34,9,27)(4,16,35,11,22)(5,18,31,14,26)(6,15,30,8,24)(7,21,33,12,23)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
10:  $D_{5}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $D_{5}$

Degree 7: None

Low degree siblings

35T38 x 8, 35T39 x 7

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 316 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $24010=2 \cdot 5 \cdot 7^{4}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.