Properties

Label 35T45
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 $t$:  $45$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,23)(2,22)(3,26)(4,27)(5,24)(6,25)(7,28)(8,21,10,20,14,17,12,16,9,15,13,19,11,18)(29,34,33,31,32,30,35), (1,12)(2,8)(3,9)(4,14)(5,11)(6,10)(7,13)(15,31,16,33,17,34,20,29,21,35,18,30,19,32)(22,23)(24,26)(25,27)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$10$:  $D_{5}$
$20$:  $D_{10}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $D_{5}$

Degree 7: None

Low degree siblings

35T45 x 15

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 200 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.