Finite Group Databasebeta

C2×#13116840 #16016952

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116840

Splittings

FittingC2×C13×#458 ⋊ C2
SylowC13 ⋊ C2×#2200

Subgroups

subgroupG/H
centerC22#11718693
commutator, cosocleC2×D4×C13C24
FrattiniC2×D4C23×D13
FittingC2×C13×#458C2
socleC22×C13B(4,𝔽2)
hypercenterC2×#458D13
hypocenterC13C2×#2200
LCSG ▷ C2×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#458

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

226 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323601);