Galois group: 24T6428

• Label: 24T6428
• Degree: $24$
• Order: $3072$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^7:S_4$

Group invariants

Abstract group:		$C_2^7:S_4$
Order:		$3072=2^{10} \cdot 3$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$6428$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$2$
Generators:		$(1,23,6,17,2,24,5,18)(3,22,8,20,4,21,7,19)(9,10)(13,14)$, $(1,12,20)(2,11,19)(3,9,18)(4,10,17)(5,15,21,6,16,22)(7,14,23,8,13,24)$, $(1,21,12,3,23,9)(2,22,11,4,24,10)(5,20,16,7,18,13)(6,19,15,8,17,14)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 7
$4$:	$C_2^2$ x 7
$6$:	$S_3$
$8$:	$C_2^3$
$12$:	$D_{6}$ x 3
$24$:	$S_4$ x 3, $S_3 \times C_2^2$
$48$:	$S_4\times C_2$ x 9
$96$:	$V_4^2:S_3$, 12T48 x 3
$192$:	12T100 x 3
$384$:	12T139, 16T751 x 2
$768$:	16T1063, 32T34928
$1536$:	24T3330

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_4$, $S_4\times C_2$ x 2

Degree 8: None

Degree 12: 12T103

Low degree siblings

24T5377 x 4, 24T5384 x 4, 24T5435 x 4, 24T5444 x 4, 24T5591 x 4, 24T5593 x 4, 24T5731 x 4, 24T5744 x 4, 24T6285 x 4, 24T6428 x 3, 24T6790 x 4, 24T6812 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

62 x 62 character table

Regular extensions

Data not computed