Finite Group Databasebeta

C2×#13115887 #15889910

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

Aliases

direct productC2×#13115887

Splittings

FittingC22×C13×AGL(1,ℤ/8) ⋊ C2
SylowC13 ⋊ C2×#2008

Subgroups

subgroupG/H
centerC22#11718884
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×AGL(1,ℤ/8)C2
socleC22×C13#392
hypercenterC22×AGL(1,ℤ/8)D13
hypocenterC13C2×#2008
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 196559);