Finite Group Databasebeta

D4×#88186 #16738509

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

Aliases

direct productD4×#88186

Splittings

FittingC2×D42×C13 ⋊ C2
SylowC13 ⋊ D4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×D42×C13C2
socleC22×C13C23×D4
hypercenterC2×D42D13
hypocenterC13D4×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D42

3230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1045158);