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C9×C32⋊(C139⋊C3) #46798544

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

Aliases

direct productC9×C32⋊(C139⋊C3)

Splittings

FittingC32×C9×C139 ⋊ C3
SylowC139 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
centerC3×C9C3×C139⋊C3
commutatorC3×C139C32×C9
FrattiniC32C32×C139⋊C3
FittingC32×C9×C139C3
socle, cosocleC32×C139C33
prime radicalC3×C32⋊(C139⋊C3)C3
hypercenterC32×C9C139⋊C3
hypocenterC139C9×H(3,𝔽3)
LCSG ▷ C3×C139 ▷ C139
UCSC1 ◁ C3×C9 ◁ C32×C9

202 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, 168);