Finite Group Databasebeta

C3×#19129016 #30633149

order16119
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#19129016

Splittings

FittingC3×C9×C199 ⋊ C3
SylowC199 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C199⋊C3
commutator, cosocleC3×C199C33
FrattiniC3C32×C199⋊C3
FittingC3×C9×C199C3
socleC32×C199C32
prime radicalC32×C199⋊C3C3
hypercenterC3×C9C199⋊C3
hypocenterC199C3×3−1+2
LCSG ▷ C3×C199 ▷ C199
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5373

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16119, 44);