Finite Group Databasebeta

C3×#10619725 #14517874

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

Aliases

direct productC3×#10619725

Splittings

SylowC3×#737 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC3×C4×C9C3⋊D3
commutator, hypocenterH(3,𝔽3)C32×C8
FrattiniC3×C4C32×C3⋊D3
FittingC3×C4×#737C2
socleC2×C32C3×C3⋊Dic3
prime radicalC2×C3×H(3,𝔽3)C3×C4
cosocleC4×H(3,𝔽3)C2×C32
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C3×C4×C9

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2268);