Finite Group Databasebeta

C3×#22552076 #38733336

order24867
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#22552076

Splittings

FittingC3×C9×C307 ⋊ C3
SylowC307 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C307⋊C3
commutator, cosocleC3×C307C33
FrattiniC3C32×C307⋊C3
FittingC3×C9×C307C3
socleC32×C307C32
prime radicalC32×C307⋊C3C3
hypercenterC3×C9C307⋊C3
hypocenterC307C3×3−1+2
LCSG ▷ C3×C307 ▷ C307
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8289

Conjugacy classes & character table

2787 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24867, 44);