Finite Group Databasebeta

C3×#10592638 #13162977

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3×C4

Aliases

direct productC3×#10592638

Splittings

FittingC2×C33×C42 ⋊ C2
SylowC33 ⋊ #390

Subgroups

subgroupG/H
centerC23×C3C22×C3⋊D3
commutatorC22×C32C22×C3×C4
FrattiniC23C22×C3×C3⋊D3
FittingC2×C33×C42C2
socleC23×C33C23
prime radicalC22×C3×C4⋊(C3⋊D3)C2
cosocleC23×C32C23×C3
hypercenterC2×C3×C42C3⋊D3
hypocenterC32C3×#390
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C2×C3×C42

1980 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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, 29040);