Finite Group Databasebeta

SD16×#6129 #16744328

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productSD16×#6129

Splittings

FittingD4×C13×SD16 ⋊ C2
SylowC13 ⋊ SD16×#41

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingD4×C13×SD16C2
socleC22×C13C23×D4
prime radicalD4×#6129C2
hypercenterD4×SD16D13
hypocenterC13SD16×#41
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×SD16

2116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1050977);