Finite Group Databasebeta

← Prev (#44525088) Next (#44525090) →

AΣL(1,𝔽27)×C127⋊C3 #44525089

order30861
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productAΣL(1,𝔽27)×C127⋊C3

Splittings

FittingAΣL(1,𝔽27)×C127 ⋊ C3
SylowC127 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC3H(3,𝔽3)×C127⋊C3
commutator, cosocleC32×C127C33
FrattiniC32C32×C127⋊C3
FittingAΣL(1,𝔽27)×C127C3
socleC3×C127C3×H(3,𝔽3)
hypercenterAΣL(1,𝔽27)C127⋊C3
hypocenterC127C3×AΣL(1,𝔽27)
LCSG ▷ C32×C127 ▷ C3×C127 ▷ C127
UCSC1 ◁ C3 ◁ C32 ◁ AΣL(1,𝔽27)

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1143

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 243);