Finite Group Databasebeta

#36380954

order22599
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C3×C9

Aliases

No aliases for this group.

Splittings

SylowC31 ⋊ #10624681

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C31⋊C3
commutatorC3×C31C3×C92
FittingC31×#6887C3
socleC32×C31C32×C9
prime radicalC33×C31C3×C9
cosocleC3×C9×C31C33
hypercenter#6887C31⋊C3
hypocenterC31#10624681
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C3×C9 ◁ #6887

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Polycyclic presentation:

3^6,31|a^3=d,b^3=e,d^3=f,g^a=g^25,c^b=cf

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, 1975);