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AΣL(1,𝔽27)×C139⋊C3 #46798619

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

Aliases

direct productAΣL(1,𝔽27)×C139⋊C3

Splittings

FittingAΣL(1,𝔽27)×C139 ⋊ C3
SylowC139 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC3H(3,𝔽3)×C139⋊C3
commutator, cosocleC32×C139C33
FrattiniC32C32×C139⋊C3
FittingAΣL(1,𝔽27)×C139C3
socleC3×C139C3×H(3,𝔽3)
hypercenterAΣL(1,𝔽27)C139⋊C3
hypocenterC139C3×AΣL(1,𝔽27)
LCSG ▷ C32×C139 ▷ C3×C139 ▷ C139
UCSC1 ◁ C3 ◁ C32 ◁ AΣL(1,𝔽27)

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1251

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 243);