Finite Group Databasebeta

C22×D9×H(3,𝔽3) #14518461

order1944
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32

Aliases

direct productC22×D9×H(3,𝔽3)

Splittings

FittingC22×C9×H(3,𝔽3) ⋊ C2
SylowC9×H(3,𝔽3) ⋊ C23

Subgroups

subgroupG/H
centerC22×C3C32×D9
commutator, cosocleC3×C9C23×C32
FrattiniC32C22×C32×D3
FittingC22×C9×H(3,𝔽3)C2
socleC22×C32C32×D3
hypercenterC22×H(3,𝔽3)D9
hypocenterC9C23×H(3,𝔽3)
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C22×H(3,𝔽3)

698 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2855);