Finite Group Databasebeta

C2×C9×#805 #13142399

order1728
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23

Aliases

direct productC2×C9×#805

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ C2×#104

Subgroups

subgroupG/H
centerC2×C4×C9D12
commutatorC3×C4C22×C4×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C42×C9C2
socleC22×C32C3×C22⋊C4
prime radicalC2×C3×#235C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC2×C42×C9D3
hypocenterC3C2×C9×#104
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C22×C4×C9 ◁ C2×C42×C9

618 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, 8462);