Finite Group Databasebeta

C9×#5504 #13152416

order1728
automorphism?
homologyAbelianization (H1) = C23×C4×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#5504

Splittings

FittingC2×C3×C9×C4⋊C4 ⋊ C2
SylowC3×C9 ⋊ #520

Subgroups

subgroupG/H
centerC22×C9C23×D3
commutatorC2×C3C23×C4×C9
FrattiniC22×C3C23×C3×D3
FittingC2×C3×C9×C4⋊C4C2
socle, cosocleC22×C32C24×C3
prime radicalC2×C3×#235C2×C3
hypercenterC2×C9×C4⋊C4D3
hypocenterC3C9×#520
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×C9×C4⋊C4

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18479);