Galois group: 24T6012

• Label: 24T6012
• Degree: $24$
• Order: $3072$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^8:D_6$

Group invariants

Abstract group:		$C_2^8:D_6$
Order:		$3072=2^{10} \cdot 3$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$6012$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,2)(5,8,6,7)(9,11,10,12)(15,16)(17,20,18,19)(21,24,22,23)$, $(1,19)(2,20)(3,17)(4,18)(5,24,6,23)(7,22,8,21)(9,14,10,13)(11,16,12,15)$, $(1,21,2,22)(3,24,4,23)(5,14,8,16)(6,13,7,15)(9,18,11,19)(10,17,12,20)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_2^2$
$6$:	$S_3$
$12$:	$D_{6}$
$24$:	$S_4$ x 3
$48$:	$S_4\times C_2$ x 3
$96$:	$V_4^2:S_3$
$192$:	$V_4^2:(S_3\times C_2)$ x 6, 12T100
$768$:	16T1068 x 3

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_3$

Degree 8: None

Degree 12: 12T69

Low degree siblings

16T1526 x 8, 24T5340 x 8, 24T6012 x 7, 24T6021 x 16, 24T6028 x 48, 24T6030 x 48, 32T205521 x 16, 32T205529 x 4

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

58 x 58 character table

Regular extensions

Data not computed