Galois group: 32T5586

• Label: 32T5586
• Degree: $32$
• Order: $256$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: yes
• Group: $C_2^5:D_4$

Group invariants

Abstract group:		$C_2^5:D_4$
Order:		$256=2^{8}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		$2$

Group action invariants

Degree $n$:		$32$
Transitive number $t$:		$5586$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$16$
Generators:		$(1,32)(2,31)(3,30)(4,29)(5,20)(6,19)(7,18)(8,17)(9,22)(10,21)(11,24)(12,23)(13,28)(14,27)(15,26)(16,25)$, $(17,31)(18,32)(19,29)(20,30)(21,27)(22,28)(23,25)(24,26)$, $(1,13)(2,14)(3,15)(4,16)(5,11)(6,12)(7,9)(8,10)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)$, $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,23)(18,24)(19,21)(20,22)(25,31)(26,32)(27,29)(28,30)$, $(1,17,11,25)(2,18,12,26)(3,19,9,27)(4,20,10,28)(5,29,13,21)(6,30,14,22)(7,31,15,23)(8,32,16,24)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 31
$4$:	$C_2^2$ x 155
$8$:	$D_{4}$ x 56, $C_2^3$ x 155
$16$:	$D_4\times C_2$ x 196, $C_2^4$ x 31
$32$:	$C_2^2 \wr C_2$ x 112, $C_2^2 \times D_4$ x 98, 32T39
$64$:	16T105 x 84, 32T273 x 7
$128$:	16T325 x 8, 32T1369 x 7

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$, $D_{4}$ x 14

Degree 8: $D_4\times C_2$ x 7, $C_2^2 \wr C_2$ x 28

Degree 16: 16T105 x 7, 16T325 x 8

Low degree siblings

32T5586 x 2047

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

88 x 88 character table

Regular extensions

Data not computed