Properties

Label 31T11
Degree $31$
Order $4.111\times 10^{33}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $A_{31}$

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Group action invariants

Degree $n$:  $31$
Transitive number $t$:  $11$
Group:  $A_{31}$
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), (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 3,451 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4111419327088961408862781440000000=2^{25} \cdot 3^{14} \cdot 5^{7} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.