Finite Group Databasebeta

C2×#13116957 #16017477

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13116957

Splittings

FittingC2×C13×#368 ⋊ C2
SylowC13 ⋊ C2×#2221

Subgroups

subgroupG/H
centerC22#11718544
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#368C2
socleC22×C13#466
hypercenterC2×#368D13
hypocenterC13C2×#2221
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 324126);