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H(3,𝔽3)×C139⋊C9 #46798545

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

Aliases

direct productH(3,𝔽3)×C139⋊C9

Splittings

SylowC139 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C32×C139⋊C3
commutatorC3×C139C32×C9
Fitting, prime radicalC3×H(3,𝔽3)×C139C3
socle, cosocleC32×C139C33
hypercenterC3×H(3,𝔽3)C139⋊C3
hypocenterC139C9×H(3,𝔽3)
LCSG ▷ C3×C139 ▷ C139
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11259

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, 169);