Finite Group Databasebeta

C2×#28380766 #43244387

order28096
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28380766

Splittings

FittingC2×Q16×C439 ⋊ C2
SylowC439 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingC2×Q16×C439C2
socleC22×C439C2×D4
hypercenterC2×Q16D439
hypocenterC439C2×#135
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

3094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 1332);