Finite Group Databasebeta

C9×#4958 #13142486

order1728
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#4958

Splittings

FittingC2×C3×C9×C22⋊C4 ⋊ C2
SylowC3×C9 ⋊ #386

Subgroups

subgroupG/H
centerC23×C9C22×D3
commutatorC22×C3C22×C4×C9
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C9×C22⋊C4C2
socle, cosocleC23×C32C23×C3
prime radicalC22×C3×#67C2×C3
hypercenterC2×C9×C22⋊C4D3
hypocenterC3C9×#386
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C9 ◁ C2×C9×C22⋊C4

990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8549);