Properties

Label 35T49
Degree $35$
Order $50400$
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)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.