Finite Group Databasebeta

D13×#1536 #15830954

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD13×#1536

Splittings

FittingC13×#1536 ⋊ C2
SylowC13 ⋊ C2×#1536

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1536C2
socleC22×C13C22×C22⋊C4
prime radicalD13×#532C2
cosocleC42×C13C24
hypercenter#1536D13
hypocenterC13C2×#1536
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1536

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 137603);