Finite Group Databasebeta

C3×(C3×C139⋊C3)⋊C9 #46798533

order33777
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×(C3×C139⋊C3)⋊C9

Splittings

FittingC32×C9×C139 ⋊ C3
SylowC139 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC33C3×C139⋊C3
commutatorC3×C139C32×C9
FrattiniC32C32×C139⋊C3
FittingC32×C9×C139C3
socleC33×C139C32
prime radicalC33×C139⋊C3C3
cosocleC32×C139C33
hypercenterC32×C9C139⋊C3
hypocenterC139C3×C32⋊C9
LCSG ▷ C3×C139 ▷ C139
UCSC1 ◁ C33 ◁ C32×C9

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11259

Conjugacy classes & character table

3825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 157);