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C3×H(3,𝔽3)×C139⋊C3 #46798670

order33777
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C37

Aliases

direct productC3×H(3,𝔽3)×C139⋊C3

Splittings

FittingC3×H(3,𝔽3)×C139 ⋊ C3
SylowC139 ⋊ C32×H(3,𝔽3)

Subgroups

subgroupG/H
centerC32C32×C139⋊C3
commutator, cosocleC3×C139C34
FrattiniC3C33×C139⋊C3
FittingC3×H(3,𝔽3)×C139C3
socleC32×C139C33
hypercenterC3×H(3,𝔽3)C139⋊C3
hypocenterC139C32×H(3,𝔽3)
LCSG ▷ C3×C139 ▷ C139
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3753

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 294);