Properties

Label 37T10
Degree $37$
Order $6.882\times 10^{42}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $A_{37}$

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Group action invariants

Degree $n$:  $37$
Transitive number $t$:  $10$
Group:  $A_{37}$
Parity:  $1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (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), (1,2,3)

Low degree resolvents

none

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 10,871 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $6881876545613172523157989790790451200000000=2^{33} \cdot 3^{17} \cdot 5^{8} \cdot 7^{5} \cdot 11^{3} \cdot 13^{2} \cdot 17^{2} \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.