Finite Group Databasebeta

C22×#20296317 #43244377

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

Aliases

direct productC22×#20296317

Splittings

SylowC439 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
Fitting, prime radicalC22×D4×C439C2
socleC23×C439D4
hypercenterC22×D4D439
hypocenterC439C22×SD16
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

4408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 1322);