Finite Group Databasebeta

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#36382957

order22599
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

No aliases for this group.

Splittings

SylowC31 ⋊ #10624933

Subgroups

subgroupG/H
centerC3C32×C32⋊(C31⋊C3)
commutator, cosocleC32×C31C34
FrattiniC32C33×C31⋊C3
FittingC31×3−1+4C3
socleC3×C31C32×H(3,𝔽3)
prime radicalC3×H(3,𝔽3)×C31C32
hypercenter3−1+4C31⋊C3
hypocenterC31#10624933
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3 ◁ C3×H(3,𝔽3) ◁ 3−1+4

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2511

Polycyclic presentation:

3^6,31|a^3=f,b^3=f^2,b^a=be,e^a=ef,g^b=g^25,d^c=df

Conjugacy classes & character table

935 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3978);