Properties

Label 35T38
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 $t$:  $38$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $7$
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)

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:  not available
Character table: not available.