Properties

Label 22T42
Degree $22$
Order $1351680$
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 $t$:  $42$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,8)(2,7)(3,14)(4,13)(5,10)(6,9)(15,20,16,19)(17,18)(21,22), (3,9,17,19,22,4,10,18,20,21)(5,14,16,11,7)(6,13,15,12,8)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$660$:  $\PSL(2,11)$
$1320$:  22T13
$675840$:  22T39

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

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

Low degree siblings

22T42, 44T433 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 112 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1351680=2^{13} \cdot 3 \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.