Finite Group Databasebeta

D4×#88180 #16022324

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productD4×#88180

Splittings

SylowC13 ⋊ D4×#117

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socle, cosocleC23×C13C25
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13D4×#117
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

3562 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, 328973);