Finite Group Databasebeta

C22×#10622585 #14912117

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#10622585

Splittings

SylowC11 ⋊ C22×#389

Subgroups

subgroupG/H
centerC25C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC23×C11×C4⋊C4C2
socle, prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC23×C4⋊C4D11
hypocenterC11C22×#389
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C4⋊C4

4894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 327912);