Finite Group Databasebeta

D13×#2020 #15890115

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD13×#2020

Splittings

FittingC13×#2020 ⋊ C2
SylowC13 ⋊ C2×#2020

Subgroups

subgroupG/H
centerC22D13×#121
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2020C2
socleC22×C13C2×#121
prime radicalC2×#41×D13C22
hypercenter#2020D13
hypocenterC13C2×#2020
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2020

1902 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, 196764);