Properties

Label 47T6
Degree $47$
Order $2.586\times 10^{59}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{47}$

Related objects

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Group action invariants

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

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:  not available
Character table: not available.