Properties

Label 11T8
Order \(39916800\)
n \(11\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No
Group: $S_{11}$

Related objects

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Group action invariants

Degree $n$ :  $11$
Transitive number $t$ :  $8$
Group :  $S_{11}$
CHM label :  $S11$
Parity:  $-1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2), (1,2,3,4,5,6,7,8,9,10,11)
$|\Aut(F/K)|$:  $1$

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

22T45

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 56 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $39916800=2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.