Finite Group Databasebeta

D4×#88163 #16738598

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

Aliases

direct productD4×#88163

Splittings

FittingD4×C13×M16 ⋊ C2
SylowC13 ⋊ D4×#137

Subgroups

subgroupG/H
centerC22C23×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingD4×C13×M16C2
socleC22×C13C23×D4
prime radicalD4×#6127C2
hypercenterD4×M16D13
hypocenterC13D4×#137
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

2746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1045247);