Properties

Label 35T45
Order \(48020\)
n \(35\)
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)
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)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.