Finite Group Databasebeta

C3×#26010702 #45684005

order33129
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#26010702

Splittings

FittingC3×C9×C409 ⋊ C3
SylowC409 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C409⋊C3
commutator, cosocleC3×C409C33
FrattiniC3C32×C409⋊C3
FittingC3×C9×C409C3
socleC32×C409C32
prime radicalC32×C409⋊C3C3
hypercenterC3×C9C409⋊C3
hypocenterC409C3×3−1+2
LCSG ▷ C3×C409 ▷ C409
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11043

Conjugacy classes & character table

3705 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33129, 43);