Finite Group Databasebeta

C32×#14578890 #36382866

order22599
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC32×#14578890

Splittings

FittingC32×C27×C31 ⋊ C3
SylowC31 ⋊ C32×C27⋊C3

Subgroups

subgroupG/H
centerC32×C9C3×C31⋊C3
commutatorC3×C31C33×C9
FrattiniC9C33×C31⋊C3
FittingC32×C27×C31C3
socleC33×C31C3×C9
prime radicalC33×C31⋊C3C9
cosocleC9×C31C34
hypercenterC32×C27C31⋊C3
hypocenterC31C32×C27⋊C3
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C32×C9 ◁ C32×C27

944 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, 3887);