Finite Group Databasebeta

D13×#3020 #16729560

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productD13×#3020

Splittings

FittingC13×#3020 ⋊ C2
SylowC13 ⋊ C2×#3020

Subgroups

subgroupG/H
centerC2C2×D13×#120
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3020C2
socleC2×C13C22×#120
hypercenter#3020D13
hypocenterC13C2×#3020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3020

4710 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, 1036209);