Finite Group Databasebeta

C9×#15688521 #41006391

order26973
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC9×#15688521

Splittings

SylowC37 ⋊ C9×#733

Subgroups

subgroupG/H
centerC3×C9C32⋊(C37⋊C3)
commutatorC32×C37C32×C9
FrattiniC33C32×C37⋊C3
FittingC3×C92×C37C3
socleC32×C37C3×H(3,𝔽3)
prime radical, cosocleC33×C37C33
hypercenterC3×C92C37⋊C3
hypocenterC37C9×#733
LCSG ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C32×C9 ◁ C3×C92

274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

3069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 2162);