Finite Group Databasebeta

C9×#5477 #13152294

order1728
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#5477

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ #532

Subgroups

subgroupG/H
centerC2×C4×C9C22×D3
commutatorC22×C3C24×C9
FrattiniC22×C3C23×C3×D3
FittingC2×C3×C42×C9C2
socle, cosocleC22×C32C24×C3
prime radicalC3×#5477C3
hypercenterC2×C42×C9D3
hypocenterC3C9×#532
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C2×C42×C9

1038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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, 18357);