Finite Group Databasebeta

C2×#13115943 #15890103

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

Aliases

direct productC2×#13115943

Splittings

FittingC23×C13×D8 ⋊ C2
SylowC13 ⋊ C2×#2018

Subgroups

subgroupG/H
centerC23#88192
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC23×C13×D8C2
socleC23×C13#121
hypercenterC23×D8D13
hypocenterC13C2×#2018
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

2158 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, 196752);