Properties

Label 22T39
Degree $22$
Order $675840$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $39$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,9,12,13,17,2,10,11,14,18)(3,22,19,6,8)(4,21,20,5,7)(15,16), (1,7,6,2,8,5)(3,4)(9,21,18)(10,22,17)(11,15,13,12,16,14)(19,20)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$660$:  $\PSL(2,11)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $\PSL(2,11)$

Low degree siblings

22T39

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:  $675840=2^{12} \cdot 3 \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.