Finite Group Databasebeta

C2×#13081549 #15634287

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13081549

Splittings

SylowC11 ⋊ C2×#3387

Subgroups

subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#441C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#441D11
hypocenterC11C2×#3387
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

1778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1050082);