Properties

Label 35T49
Order \(50400\)
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 $t$ :  $49$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,29,16,34,6,24,11,4,26,19,31,9,21,14)(2,28,17,33,7,23,12,3,27,18,32,8,22,13)(5,30,20,35,10,25,15), (1,33,6,23,11,3,31,8,21,13)(2,32,7,22,12)(4,35,9,25,14,5,34,10,24,15)(16,28)(17,27)(18,26)(19,30)(20,29)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
10:  $D_{5}$
20:  $D_{10}$
5040:  $S_7$
10080:  $S_7\times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $D_{5}$

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 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $50400=2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.