Galois group: 22T32

• Label: 22T32
• Degree: $22$
• Order: $45056$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^{10}.D_{22}$

Group invariants

Abstract group:		$C_2^{10}.D_{22}$
Order:		$45056=2^{12} \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$22$
Transitive number $t$:		$32$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,6)(2,5)(7,22)(8,21)(9,20,10,19)(11,17)(12,18)(13,16)(14,15)$, $(1,4)(2,3)(5,21)(6,22)(7,19,8,20)(9,18,10,17)(11,16,12,15)(13,14)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_2^2$
$22$:	$D_{11}$
$44$:	$D_{22}$
$22528$:	22T29

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $D_{11}$

Low degree siblings

22T32 x 61, 44T236 x 31, 44T239 x 31, 44T240 x 62, 44T241 x 62, 44T266 x 310, 44T267 x 310, 44T268 x 310, 44T269 x 31, 44T270 x 155, 44T271 x 155, 44T272 x 155, 44T273 x 310, 44T274 x 310, 44T275 x 310

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Conjugacy classes not computed

Character table

Character table not computed

Regular extensions

Data not computed