Finite Group Databasebeta

D4×#88038 #16016127

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD4×#88038

Splittings

FittingD4×C13×C16 ⋊ C2
SylowC13 ⋊ D4×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D13
commutator, socleC22×C13C23×C8
FittingD4×C13×C16C2
prime radicalC2×D4×D13C8
cosocleC2×C8×C13C24
hypercenterD4×C16D13
hypocenterC13D4×M32
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ D4×C16

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322776);