Finite Group Databasebeta

C3×#22582518 #41007368

order26973
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#22582518

Splittings

SylowC37 ⋊ C3×#6882

Subgroups

subgroupG/H
centerC32#15688519
commutator, cosocleC3×C9×C37C33
FrattiniC3×C9C32×C37⋊C3
FittingC3×C37×C9⋊C9C3
socleC32×C37#732
prime radicalC33×C37H(3,𝔽3)
hypercenterC3×C9⋊C9C37⋊C3
hypocenterC37C3×#6882
LCSG ▷ C3×C9×C37 ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9 ◁ C3×C9⋊C9

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

1245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3139);