Finite Group Databasebeta

C22×#10622824 #14912037

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#10622824

Splittings

SylowC11 ⋊ C22×#381

Subgroups

subgroupG/H
centerC25C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC25×C4×C11C2
socleC25×C11C23
prime radicalC26×C11C22
cosocleC23×C11C25
hypercenterC25×C4D11
hypocenterC11C22×#381
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C25 ◁ C25×C4

8062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 327832);