Finite Group Databasebeta

C3×#10619581 #14517253

order1944
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#10619581

Splittings

SylowQ8 ⋊ C3×#733

Subgroups

subgroupG/H
center, socleC2×C32C22⋊H(3,𝔽3)
commutator, cosocleC32×Q8C33
FrattiniC2×C32C32×A4
FittingC3×Q8×3−1+2C3
prime radicalC2×C33C3×A4
hypercenterC2×C3×3−1+2A4
hypocenterQ8C3×#733
LCSG ▷ C32×Q8 ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C32 ◁ C2×C33 ◁ C2×C3×3−1+2

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1647);