Finite Group Databasebeta

D4×#88168 #16738512

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD4×#88168

Splittings

FittingD4×C13×SD16 ⋊ C2
SylowC13 ⋊ D4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingD4×C13×SD16C2
socleC22×C13C23×D4
hypercenterD4×SD16D13
hypocenterC13D4×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×SD16

3230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1045161);