Finite Group Databasebeta

C22×#10623074 #15660745

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

Aliases

direct productC22×#10623074

Splittings

SylowC11 ⋊ C22×#554

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11C22×#554
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

8454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076540);