Finite Group Databasebeta

C22×#20296313 #43244364

order28096
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#20296313

Splittings

SylowC439 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D439
commutatorC2×C439C23×C4
FrattiniC4C23×D439
FittingC23×C4×C439C2
socleC23×C439C2×C4
prime radicalC24×C439C4
cosocleC4×C439C24
hypercenterC23×C4D439
hypocenterC439C22×M16
LCSG ▷ C2×C439 ▷ C439
UCSC1 ◁ C22×C4 ◁ C23×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

7048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 1309);