Finite Group Databasebeta

D13×#2264 #16021055

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

Aliases

direct productD13×#2264

Splittings

FittingC13×#2264 ⋊ C2
SylowC13 ⋊ C2×#2264

Subgroups

subgroupG/H
centerC2C2×D13×D16
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC13×#2264C2
socleC2×C13C22×D16
prime radicalD13×#508C2
hypercenter#2264D13
hypocenterC13C2×#2264
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

462 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, 327704);