Finite Group Databasebeta

D13×#2003 #15889807

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD13×#2003

Splittings

FittingC13×#2003 ⋊ C2
SylowC13 ⋊ C2×#2003

Subgroups

subgroupG/H
centerC22D13×#120
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2003C2
socleC22×C13C2×#120
prime radicalC2×D13×AGL(1,ℤ/8)C2
hypercenter#2003D13
hypocenterC13C2×#2003
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2003

2126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 196456);