Finite Group Databasebeta

C9×#4939 #13142404

order1728
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23×C4

Aliases

direct productC9×#4939

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ #390

Subgroups

subgroupG/H
centerC23×C9C22×D3
commutatorC22×C3C22×C4×C9
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C42×C9C2
socle, cosocleC23×C32C23×C3
prime radicalC22×C3×D12C2×C3
hypercenterC2×C42×C9D3
hypocenterC3C9×#390
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C9 ◁ C2×C42×C9

882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8467);