Finite Group Databasebeta

C3×#22582058 #40999788

order26811
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#22582058

Splittings

FittingC3×C9×C331 ⋊ C3
SylowC331 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C331⋊C3
commutator, cosocleC3×C331C33
FrattiniC3C32×C331⋊C3
FittingC3×C9×C331C3
socleC32×C331C32
prime radicalC32×C331⋊C3C3
hypercenterC3×C9C331⋊C3
hypocenterC331C3×3−1+2
LCSG ▷ C3×C331 ▷ C331
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8937

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26811, 44);