Finite Group Databasebeta

C2×#13116647 #16016040

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13116647

Splittings

FittingC2×C13×#364 ⋊ C2
SylowC13 ⋊ C2×#2165

Subgroups

subgroupG/H
centerC2×C4#88146
commutatorC2×C4×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C13×#364C2
socleC22×C13#432
prime radicalC23×D13M16
cosocleC2×C8×C13C24
hypercenterC2×#364D13
hypocenterC13C2×#2165
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#364

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322689);