Finite Group Databasebeta

C22×#10623118 #15660754

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

Aliases

direct productC22×#10623118

Splittings

SylowC11 ⋊ C22×#551

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
Fitting, prime radicalC22×C11×#120C2
socleC24×C11C24
hypercenterC22×#120D11
hypocenterC11C22×#551
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

9526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076549);