Properties

Label 37T11
Degree $37$
Order $1.376\times 10^{43}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{37}$

Related objects

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Group action invariants

Degree $n$:  $37$
Transitive number $t$:  $11$
Group:  $S_{37}$
Parity:  $-1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,2), (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)

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 21,637 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $13763753091226345046315979581580902400000000=2^{34} \cdot 3^{17} \cdot 5^{8} \cdot 7^{5} \cdot 11^{3} \cdot 13^{2} \cdot 17^{2} \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.