Finite Group Databasebeta

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C9×#14578913 #36382264

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

Aliases

direct productC9×#14578913

Splittings

FittingC9×3−1+2×C31 ⋊ C3
SylowC31 ⋊ C9×#737

Subgroups

subgroupG/H
centerC3×C9C32×C31⋊C3
commutatorC3×C31C33×C9
FrattiniC32C33×C31⋊C3
FittingC9×3−1+2×C31C3
socle, cosocleC32×C31C34
prime radicalC3×C32⋊(C31⋊C3)C32
hypercenterC9×3−1+2C31⋊C3
hypocenterC31C9×#737
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3285);