Finite Group Databasebeta

C2×#13125029 #16731160

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13125029

Splittings

FittingC2×C13×#540 ⋊ C2
SylowC13 ⋊ C2×#3119

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#540C2
socleC23×C13C22×D4
hypercenterC2×#540D13
hypocenterC13C2×#3119
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

2198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1037809);