Galois group: 24T2458

• Label: 24T2458
• Degree: $24$
• Order: $768$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_2^7:C_6$

Group invariants

Abstract group:		$C_2^7:C_6$
Order:		$768=2^{8} \cdot 3$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$2458$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$4$
Generators:		$(1,7,18,23,10,16)(2,8,17,24,9,15)(3,11,20)(4,12,19)(5,14,22)(6,13,21)$, $(1,12)(2,11)(3,15,6,17)(4,16,5,18)(7,20,10,21)(8,19,9,22)(13,24)(14,23)$, $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 7
$3$:	$C_3$
$4$:	$C_2^2$ x 7
$6$:	$C_6$ x 7
$8$:	$D_{4}$ x 2, $C_2^3$
$12$:	$A_4$, $C_6\times C_2$ x 7
$16$:	$D_4\times C_2$
$24$:	$A_4\times C_2$ x 7, $D_4 \times C_3$ x 2, 24T3
$48$:	$C_2^2 \times A_4$ x 7, 24T38
$96$:	$C_2^4:C_6$, 12T51 x 2, 24T135
$192$:	12T87 x 3, 24T411
$384$:	12T134 x 2, 24T1078

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $C_3$

Degree 4: None

Degree 6: $C_6$, $A_4\times C_2$ x 2

Degree 8: None

Degree 12: $C_2^2 \times A_4$, 12T134 x 2

Low degree siblings

24T2447 x 32, 24T2448 x 16, 24T2451 x 16, 24T2453 x 16, 24T2454 x 8, 24T2457 x 32, 24T2458 x 15, 24T2461 x 8, 24T2462 x 16, 24T2504 x 16, 24T2505 x 16, 32T34747 x 8

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

56 x 56 character table

Regular extensions

Data not computed