Finite Group Databasebeta

C3×#19152732 #30685281

order17091
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#19152732

Splittings

FittingC3×C9×C211 ⋊ C3
SylowC211 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C211⋊C3
commutator, cosocleC3×C211C33
FrattiniC3C32×C211⋊C3
FittingC3×C9×C211C3
socleC32×C211C32
prime radicalC32×C211⋊C3C3
hypercenterC3×C9C211⋊C3
hypocenterC211C3×3−1+2
LCSG ▷ C3×C211 ▷ C211
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5697

Conjugacy classes & character table

1923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17091, 44);