Finite Group Databasebeta

C3×C9×#11765919 #44525192

order30861
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C32×C9

Aliases

direct productC3×C9×#11765919
unambiguous semidirect product(C127⋊C3)⋊C92

Splittings

FittingC3×C9×C127 ⋊ C9
derived, SylowC127 ⋊ C3×C92

Subgroups

subgroupG/H
center, hypercenterC3×C9#11765919
commutator, hypocenterC127C3×C92
FrattiniC3C32×#11765919
FittingC3×C9×C127C9
socleC32×C127C3×C9
prime radicalC32×C127⋊C3C32
cosocleC3×C127⋊C3C33
LCSG ▷ C127
UCSC1 ◁ C3×C9

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3429

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 346);