Properties

Label 47T6
Order \(258623241511168180642964355153611979969197632389120000000000\)
n \(47\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No
Group: $S_{47}$

Related objects

Learn more about

Group action invariants

Degree $n$ :  $47$
Transitive number $t$ :  $6$
Group :  $S_{47}$
Parity:  $-1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47), (1,2)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - 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 124,754 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $258623241511168180642964355153611979969197632389120000000000=2^{42} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.