Galois group: 22T23

• Label: 22T23
• Degree: $22$
• Order: $11264$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^{10}:C_{11}$

Group invariants

Abstract group:		$C_2^{10}:C_{11}$
Order:		$11264=2^{10} \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$22$
Transitive number $t$:		$23$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,11,21,10,19,8,18,6,15,3,14)(2,12,22,9,20,7,17,5,16,4,13)$, $(1,4,6,8,10,12,14,15,17,20,21)(2,3,5,7,9,11,13,16,18,19,22)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$11$:	$C_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $C_{11}$

Low degree siblings

22T23 x 92, 44T116 x 31, 44T117 x 465, 44T118 x 465, 44T119 x 465, 44T120 x 465, 44T121 x 930, 44T122 x 930, 44T123 x 930, 44T124 x 930, 44T125 x 930, 44T126 x 930, 44T127 x 930, 44T128 x 930, 44T129 x 930, 44T130 x 930, 44T131 x 930, 44T132 x 930, 44T133 x 930, 44T134 x 930, 44T135 x 930

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