Finite Group Databasebeta

C2×#13115833 #15889702

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13115833

Splittings

FittingC22×C13×#102 ⋊ C2
SylowC13 ⋊ C2×#1999

Subgroups

subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#102C2
socleC24×C13C2×D4
hypercenterC22×#102D13
hypocenterC13C2×#1999
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

2870 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, 196351);