Finite Group Databasebeta

C9×#14578887 #36379844

order22599
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C32×C9

Aliases

direct productC9×#14578887

Splittings

SylowC31 ⋊ C9×C9⋊C9

Subgroups

subgroupG/H
centerC32×C9C3×C31⋊C3
commutatorC3×C31C3×C92
FrattiniC33C32×C31⋊C3
FittingC3×C92×C31C3
socle, prime radical, cosocleC33×C31C33
hypercenterC3×C92C31⋊C3
hypocenterC31C9×C9⋊C9
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C32×C9 ◁ C3×C92

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22599

Conjugacy classes & character table

2727 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 865);