Finite Group Databasebeta

C3×#21419259 #36382070

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

Aliases

direct productC3×#21419259

Splittings

SylowC31 ⋊ C3×#6878

Subgroups

subgroupG/H
centerC32#14578899
commutator, cosocleC3×C9×C31C33
FrattiniC3×C9C32×C31⋊C3
Fitting, prime radicalC3×C31×#732C3
socleC32×C31#732
hypercenterC3×#732C31⋊C3
hypocenterC31C3×#6878
LCSG ▷ C3×C9×C31 ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9 ◁ C3×#732

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2511

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3091);