Finite Group Databasebeta

C32×C9×C139⋊C3 #46798668

order33777
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C36

Aliases

direct productC32×C9×C139⋊C3

Splittings

FittingC32×C9×C139 ⋊ C3
derived, SylowC139 ⋊ C33×C9

Subgroups

subgroupG/H
center, hypercenterC32×C9C139⋊C3
commutator, hypocenterC139C33×C9
FrattiniC3C33×C139⋊C3
FittingC32×C9×C139C3
socleC33×C139C32
prime radicalC33×C139⋊C3C3
cosocleC3×C139C34
LCSG ▷ C139
UCSC1 ◁ C32×C9

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11259

Conjugacy classes & character table

3969 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 292);