Properties

Label 35T37
Order \(24010\)
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 $t$ :  $37$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,18,31,11,26)(2,17,29,10,24)(3,19,32,12,25)(4,21,33,14,22)(5,16,35,9,27)(6,20,34,13,23)(7,15,30,8,28), (1,28,9,34,16,3,25,10,29,17)(2,23,11,32,18)(4,27,8,33,15,7,26,13,35,20)(5,22,14,30,21,6,24,12,31,19)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
5:  $C_5$
10:  $C_{10}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $C_5$

Degree 7: None

Low degree siblings

35T37 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 250 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $24010=2 \cdot 5 \cdot 7^{4}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.