Properties

Label 35T39
Degree $35$
Order $24010$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $35$
Transitive number $t$:  $39$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.