Finite Group Databasebeta

D13×#1612 #15835157

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD13×#1612

Splittings

FittingC13×#1612 ⋊ C2
SylowC13 ⋊ C2×#1612

Subgroups

subgroupG/H
centerC22D13×#120
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1612C2
socleC22×C13C2×#120
prime radicalD13×#538C2
hypercenter#1612D13
hypocenterC13C2×#1612
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1612

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 141806);