Finite Group Databasebeta

C9×#14578891 #36380947

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

Aliases

direct productC9×#14578891

Splittings

FittingC9×C27×C31 ⋊ C3
SylowC31 ⋊ C9×C27⋊C3

Subgroups

subgroupG/H
centerC92C3×C31⋊C3
commutatorC3×C31C3×C92
FrattiniC3×C9C32×C31⋊C3
FittingC9×C27×C31C3
socleC32×C31C32×C9
prime radicalC32×C31⋊C3C3×C9
cosocleC3×C9×C31C33
hypercenterC9×C27C31⋊C3
hypocenterC31C9×C27⋊C3
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C92 ◁ C9×C27

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

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, 1968);