Properties

Label 35T43
Order \(36015\)
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 $t$ :  $43$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,15,29,11,22)(2,21,32,10,27)(3,16,34,12,26)(4,19,35,14,23)(5,20,31,9,28)(6,18,30,13,24)(7,17,33,8,25), (1,23,11,32,20,5,27,14,29,16,7,22,10,35,21)(2,26,12,34,18)(3,28,8,30,15,6,24,9,33,17,4,25,13,31,19)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
5:  $C_5$
15:  $C_{15}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $C_5$

Degree 7: None

Low degree siblings

35T43 x 79

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 175 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $36015=3 \cdot 5 \cdot 7^{4}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.