Finite Group Databasebeta

C32×#14578887 #36382242

order22599
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C36

Aliases

direct productC32×#14578887

Splittings

SylowC31 ⋊ C32×C9⋊C9

Subgroups

subgroupG/H
centerC34C3×C31⋊C3
commutatorC3×C31C33×C9
FrattiniC32C33×C31⋊C3
FittingC33×C9×C31C3
socle, prime radicalC34×C31C32
cosocleC32×C31C34
hypercenterC33×C9C31⋊C3
hypocenterC31C32×C9⋊C9
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C34 ◁ C33×C9

1484 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, 3263);