Finite Group Databasebeta

C2×#13127988 #16769444

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13127988

Splittings

FittingC2×C13×#510 ⋊ C2
SylowC13 ⋊ C2×#3417

Subgroups

subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC2×C13×#510C2
socleC22×C13C22×D8
hypercenterC2×#510D13
hypocenterC13C2×#3417
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076093);