Galois group: 24T9055

• Label: 24T9055
• Degree: $24$
• Order: $6144$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^8.S_4$

Group invariants

Abstract group:		$C_2^8.S_4$
Order:		$6144=2^{11} \cdot 3$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$9055$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,23,9,7,19,12)(2,24,10,8,20,11)(3,18,14,5,21,15)(4,17,13,6,22,16)$, $(1,17,4,19)(2,18,3,20)(5,24,7,22)(6,23,8,21)(9,16,11,13)(10,15,12,14)$, $(1,23,10,2,24,9)(3,18,13,4,17,14)(5,21,16,6,22,15)(7,19,11,8,20,12)$

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 7
$48$:	$S_4\times C_2$ x 7
$96$:	$V_4^2:S_3$ x 7
$192$:	$C_2^3:S_4$ x 2, 12T100 x 7
$384$:	16T747, 24T1056
$768$:	16T1063 x 2, 24T1691 x 2, 24T2359
$3072$:	32T205603

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_4$

Degree 8: None

Degree 12: 12T100

Low degree siblings

24T7929 x 8, 24T8169 x 8, 24T9055 x 15, 32T397916 x 16

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

78 x 78 character table

Regular extensions

Data not computed