Properties

Label 35T47
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 $t$:  $47$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,28,3,24,7,22,5,25,2,27,6,23,4,26)(8,19,9,17,10,18,13,16,14,21,11,15,12,20)(29,31,35,33,30,34,32), (1,11,32,28,5,14,29,27,4,13,31,24,7,10,35,23,6,9,33,22,3,8,30,26,2,12,34,25)(15,17)(18,21)(19,20)

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

35T46

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.