Finite Group Databasebeta

C2×C9×#953 #13153762

order1728
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C27

Aliases

direct productC2×C9×#953

Splittings

FittingC25×C3×C9 ⋊ C2
SylowC3×C9 ⋊ C2×#120

Subgroups

subgroupG/H
centerC23×C9C22×D3
commutatorC22×C3C24×C9
FrattiniC22×C3C23×C3×D3
FittingC25×C3×C9C2
socleC23×C32C23×C3
prime radicalC2×C3×#953C3
cosocleC22×C32C24×C3
hypercenterC25×C9D3
hypocenterC3C2×C9×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C9 ◁ C25×C9

2734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

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, 19825);