Finite Group Databasebeta

D13×#1915 #15864944

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD13×#1915

Splittings

FittingC13×#1915 ⋊ C2
SylowC13 ⋊ C2×#1915

Subgroups

subgroupG/H
centerC2D13×#386
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1915C2
socleC2×C13C2×#386
prime radicalC2×#41×D13C22
cosocleC22×C4×C13C24
hypercenter#1915D13
hypocenterC13C2×#1915
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1915

1670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171593);