Properties

Label 35T38
Order \(24010\)
n \(35\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $35$
Transitive number $t$ :  $38$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,35,2,31,3,29,6,32,7,34,4,30,5,33)(8,28,12,27,11,24,14,23,13,22,10,26,9,25)(15,19,18,21,20,17,16), (1,7,2,4,3,5,6)(8,35,12,31,11,29,14,32,13,34,10,30,9,33)(15,23,16,26,17,28,20,24,21,22,18,25,19,27)
$|\Aut(F/K)|$:  $7$

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 7, 35T39 x 8

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.