Finite Group Databasebeta

C3×#10588686 #13142681

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#10588686

Splittings

FittingC3×C9×#117 ⋊ C2
SylowC3×C9 ⋊ #410

Subgroups

subgroupG/H
centerC3×C4(C2×D9)⋊C4
commutatorC22×C9C22×C3×C4
FrattiniC23×C3C22×C3×D3
FittingC3×C9×#117C2
socleC2×C32C2×(C2×D3)⋊C4
prime radicalC2×C3×#3697C2
cosocleC23×C9C23×C3
hypercenterC3×#117D9
hypocenterC9C3×#410
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#117

550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8744);