Finite Group Databasebeta

C3×C32⋊(C31⋊C27) #36380959

order22599
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C34

Aliases

direct productC3×C32⋊(C31⋊C27)

Splittings

SylowC31 ⋊ C3×C32⋊C27

Subgroups

subgroupG/H
centerC32×C9C3×C31⋊C3
commutatorC3×C31C32×C27
FrattiniC3×C9C32×C31⋊C3
FittingC33×C9×C31C3
socleC33×C31C3×C9
prime radicalC34×C31C9
cosocleC3×C9×C31C33
hypercenterC33×C9C31⋊C3
hypocenterC31C3×C32⋊C27
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C32×C9 ◁ C33×C9

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

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, 1980);