Finite Group Databasebeta

D4×#88131 #16022312

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

Aliases

direct productD4×#88131

Splittings

SylowC13 ⋊ D4×#117

Subgroups

subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingD4×C13×C22⋊C4C2
socle, cosocleC23×C13C25
prime radicalC23×D4×C13C22
hypercenterD4×C22⋊C4D13
hypocenterC13D4×#117
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ D4×C22⋊C4

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328961);