Finite Group Databasebeta

C3×#10588388 #13141488

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#10588388

Splittings

FittingC3×C9×#97 ⋊ C2
SylowC3×C9 ⋊ C4×M16

Subgroups

subgroupG/H
centerC2×C3×C4C22×D9
commutatorC2×C9C2×C3×C42
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#97C2
socleC22×C32C2×C4×D3
prime radicalC22×C3×D9C2×C4
cosocleC2×C4×C9C23×C3
hypercenterC3×#97D9
hypocenterC9C3×C4×M16
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C3×#97

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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(1728, 7551);