Finite Group Databasebeta

C2×#13115948 #15890109

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

Aliases

direct productC2×#13115948

Splittings

FittingC23×C13×SD16 ⋊ C2
SylowC13 ⋊ C2×#2019

Subgroups

subgroupG/H
centerC23#88192
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC23×C13×SD16C2
socleC23×C13#121
prime radicalC22×#88186C2
hypercenterC23×SD16D13
hypocenterC13C2×#2019
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

2030 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, 196758);