Finite Group Databasebeta

C2×#13115836 #15889706

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115836

Splittings

FittingC23×C13×SD16 ⋊ C2
SylowC13 ⋊ C2×#2000

Subgroups

subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC23×C13×SD16C2
socleC24×C13C2×D4
prime radicalC22×#88192C2
hypercenterC23×SD16D13
hypocenterC13C2×#2000
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×SD16

2526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 196355);