Finite Group Databasebeta

C3×#26014619 #46798632

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

Aliases

direct productC3×#26014619

Splittings

SylowC139 ⋊ C3×#733

Subgroups

subgroupG/H
centerC32C32⋊(C139⋊C3)
commutator, cosocleC32×C139C33
FrattiniC32C32×C139⋊C3
FittingC32×C9×C139C3
socleC32×C139H(3,𝔽3)
prime radicalC33×C139C32
hypercenterC32×C9C139⋊C3
hypocenterC139C3×#733
LCSG ▷ C32×C139 ▷ C3×C139 ▷ C139
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11259

Conjugacy classes & character table

3777 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 256);