Finite Group Databasebeta

C2×#28380686 #43244027

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

Aliases

direct productC2×#28380686

Splittings

FittingC2×Q16×C439 ⋊ C2
SylowC439 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#20296314
commutator, cosocleC8×C439C23
FrattiniC8C22×D439
FittingC2×Q16×C439C2
socleC22×C439D8
prime radicalC2×D3512C2
hypercenterC2×Q16D439
hypocenterC439C2×SD32
LCSG ▷ C8×C439 ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

3088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 972);