Finite Group Databasebeta

D13×#3312 #16739517

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD13×#3312

Splittings

FittingC13×#3312 ⋊ C2
SylowC13 ⋊ C2×#3312

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3312C2
socleC22×C13C23×D4
prime radicalC2×D4×D13D4
hypercenter#3312D13
hypocenterC13C2×#3312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3312

2094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1046166);