Properties

Label 35T46
Degree $35$
Order $48020$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $35$
Transitive number $t$:  $46$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $7$
Generators:  (1,34,12,16)(2,30,11,18)(3,33,14,17)(4,29,9,15)(5,32,8,21)(6,35,13,19)(7,31,10,20), (1,21,26,13,4,20,23,11,6,17,27,8,2,16,25,10,5,15,22,14,7,19,24,12,3,18,28,9)(29,34,33,31,32,30,35)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$20$:  $F_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $F_5$

Degree 7: None

Low degree siblings

35T47

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 179 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $48020=2^{2} \cdot 5 \cdot 7^{4}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.