Properties

Label 33T162
Degree $33$
Order $8.683\times 10^{36}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{33}$

Related objects

Learn more about

Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $162$
Group:  $S_{33}$
Parity:  $-1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33), (1,2)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 11: None

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 10,143 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $8683317618811886495518194401280000000=2^{31} \cdot 3^{15} \cdot 5^{7} \cdot 7^{4} \cdot 11^{3} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.