Finite Group Databasebeta

C22×C11⋊#564 #15660669

order2816
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×C11⋊#564

Splittings

SylowC11 ⋊ C22×#564

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#125C2
socle, prime radicalC24×C11C24
hypercenterC22×#125D11
hypocenterC11C22×#564
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

6374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076464);