Finite Group Databasebeta

C3×D9×#97 #13141499

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23

Aliases

direct productC3×D9×#97

Splittings

FittingC3×C9×#97 ⋊ C2
SylowC3×C9 ⋊ C2×#97

Subgroups

subgroupG/H
centerC2×C3×C4C22×D9
commutatorC2×C9C2×C3×C42
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#97C2
socleC22×C32C2×C4×D3
prime radicalC22×C3×D9C2×C4
cosocleC2×C4×C9C23×C3
hypercenterC3×#97D9
hypocenterC9C2×C3×#97
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C3×#97

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7562);