Properties

Label 30T5712
Degree $30$
Order $2.653\times 10^{32}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{30}$

Related objects

Learn more about

Group action invariants

Degree $n$:  $30$
Transitive number $t$:  $5712$
Group:  $S_{30}$
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), (1,2)

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 5: None

Degree 6: None

Degree 10: None

Degree 15: 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 5,604 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $265252859812191058636308480000000=2^{26} \cdot 3^{14} \cdot 5^{7} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23 \cdot 29$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.