Finite Group Databasebeta

C2×#13115872 #15889819

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

Aliases

direct productC2×#13115872

Splittings

FittingC22×C13×C4⋊Q8 ⋊ C2
SylowC13 ⋊ C2×#2005

Subgroups

subgroupG/H
centerC23#88191
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C4⋊Q8C2
socleC23×C13#120
prime radicalC22×#6127C22
hypercenterC22×C4⋊Q8D13
hypocenterC13C2×#2005
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊Q8

1998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 196468);