Properties

Label 22T37
Degree $22$
Order $225280$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $37$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,3,14,19,6)(2,4,13,20,5)(7,11,9,21,16)(8,12,10,22,15)(17,18), (1,11,3,5,22,18,7,16,13,20)(2,12,4,6,21,17,8,15,14,19)(9,10)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5$:  $C_5$
$10$:  $C_{10}$ x 3
$20$:  20T3
$110$:  $F_{11}$
$220$:  22T6
$112640$:  22T34

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $F_{11}$

Low degree siblings

22T37, 44T333, 44T336, 44T339 x 2, 44T340 x 2, 44T341

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 88 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $225280=2^{12} \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.