Finite Group Databasebeta

C9×#5727 #13153290

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

Aliases

direct productC9×#5727

Splittings

FittingC3×C9×C4⋊Q8 ⋊ C2
SylowC3×C9 ⋊ D4×Q8

Subgroups

subgroupG/H
centerC22×C9C23×D3
commutatorC22×C3C24×C9
FrattiniC22×C3C23×C3×D3
FittingC3×C9×C4⋊Q8C2
socle, cosocleC22×C32C24×C3
prime radicalC2×C3×D12C22×C3
hypercenterC9×C4⋊Q8D3
hypocenterC3D4×Q8×C9
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C9×C4⋊Q8

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19353);