Properties

Label 35T41
Order \(25200\)
n \(35\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $35$
Transitive number $t$ :  $41$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,21,6,26,16)(2,22,7,27,17)(3,23,8,28,18)(4,24,9,29,19)(5,25,10,30,20)(11,31)(12,32)(13,33)(14,34)(15,35), (1,14,22,20,8,31,29,2,15,23,16,9,32,30,3,11,24,17,10,33,26,4,12,25,18,6,34,27,5,13,21,19,7,35,28)
$|\Aut(F/K)|$:  $5$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
5:  $C_5$
10:  $C_{10}$
5040:  $S_7$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $C_5$

Degree 7: $S_7$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 75 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $25200=2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.