Finite Group Databasebeta

C2×D11×#559 #15660820

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

Aliases

direct productC2×D11×#559

Splittings

FittingC2×C11×#559 ⋊ C2
SylowC11 ⋊ C22×#559

Subgroups

subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#559C2
socleC23×C11C25
prime radicalC2×D11×#127C2
hypercenterC2×#559D11
hypocenterC11C22×#559
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#559

8710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076615);