Galois group: 22T44

• Label: 22T44
• Degree: $22$
• Order: $16220160$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: no
• $p$-group: no
• Group: $C_2^{11}.M_{11}$

Group invariants

Abstract group:		$C_2^{11}.M_{11}$
Order:		$16220160=2^{15} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$22$
Transitive number $t$:		$44$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,21,10,18,11,15,5,4,2,22,9,17,12,16,6,3)(7,8)(13,19)(14,20)$, $(1,15,7,13,11,10,17,4,2,16,8,14,12,9,18,3)(5,19)(6,20)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$
$7920$:	$M_{11}$
$15840$:	22T26
$8110080$:	22T43

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $M_{11}$

Low degree siblings

22T44, 44T613, 44T615 x 2, 44T617 x 2

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

104 x 104 character table

Regular extensions

Data not computed