Finite Group Databasebeta

Q32×D439 #43244030

order28096
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D439

Splittings

FittingQ32×C439 ⋊ C2
SylowC439 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D439
commutator, cosocleC8×C439C23
FrattiniC8C22×D439
FittingQ32×C439C2
socleC2×C439C2×D8
prime radicalC2×D439D8
hypercenterQ32D439
hypocenterC439C2×Q32
LCSG ▷ C8×C439 ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

2431 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 975);