Finite Group Databasebeta

C2×#28380737 #43244129

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

Aliases

direct productC2×#28380737

Splittings

FittingC2×C42×C439 ⋊ C2
SylowC439 ⋊ C2×#126

Subgroups

subgroupG/H
centerC23C22×D439
commutator, cosocleC22×C439C24
FrattiniC22C23×D439
FittingC2×C42×C439C2
socleC23×C439C23
prime radicalC23×D439C22
hypercenterC2×C42D439
hypocenterC439C2×#126
LCSG ▷ C22×C439 ▷ C439
UCSC1 ◁ C23 ◁ C2×C42

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

7036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 1074);