Finite Group Databasebeta

C3×#10588380 #13141424

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

Aliases

direct productC3×#10588380

Splittings

FittingC3×C4×C8×C9 ⋊ C2
SylowC3×C9 ⋊ #443

Subgroups

subgroupG/H
centerC3×C8D36
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C4×C8×C9C2
socleC2×C32C4×D12
prime radicalC3×#63467C2
cosocleC2×C4×C9C23×C3
hypercenterC3×C4×C8D9
hypocenterC9C3×#443
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C3×C8 ◁ C2×C3×C8 ◁ C3×C4×C8

362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7487);