Finite Group Databasebeta

C27×C32⋊(C31⋊C3) #36381110

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

Aliases

direct productC27×C32⋊(C31⋊C3)

Splittings

FittingC32×C27×C31 ⋊ C3
SylowC31 ⋊ C27×H(3,𝔽3)

Subgroups

subgroupG/H
centerC3×C27C3×C31⋊C3
commutatorC3×C31C32×C27
FrattiniC3×C9C32×C31⋊C3
FittingC32×C27×C31C3
socleC32×C31C32×C9
prime radicalC3×C32⋊(C31⋊C3)C9
cosocleC3×C9×C31C33
hypercenterC32×C27C31⋊C3
hypocenterC31C27×H(3,𝔽3)
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C3×C27 ◁ C32×C27

292 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, 2131);