Finite Group Databasebeta

← Prev (#44525196) Next (#44525198) →

H(3,𝔽3)×#11765919 #44525197

order30861
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×#11765919

Splittings

FittingH(3,𝔽3)×C127 ⋊ C9
SylowC127 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC3C32×#11765919
commutator, socleC3×C127C32×C9
FittingH(3,𝔽3)×C127C9
prime radicalH(3,𝔽3)×C127⋊C3C3
cosocleC3×C127⋊C3C33
hypercenterH(3,𝔽3)#11765919
hypocenterC127C9×H(3,𝔽3)
LCSG ▷ C3×C127 ▷ C127
UCSC1 ◁ C3 ◁ H(3,𝔽3)

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1143

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 351);