Finite Group Databasebeta

C3×#10619833 #14518587

order1944
automorphism?
homologyAbelianization (H1) = C32×C8 · Schur multiplier (H2) = C3

Aliases

direct productC3×#10619833

Splittings

SylowC3×#737 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C3×C9#157
commutator, hypocenterH(3,𝔽3)C32×C8
FrattiniC2×C3C32×#157
FittingC2×C3×#737C4
socleC2×C32C3×#157
prime radicalC2×C3×H(3,𝔽3)C3×C4
cosocle#1084C2×C32
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3×C9

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2981);