Finite Group Databasebeta

C3×D3×D4×C9 #13048847

order1296
automorphism?
homologyAbelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C23×C3

Aliases

direct productC3×D3×D4×C9

Splittings

FittingC32×D4×C9 ⋊ C2
SylowC32×C9 ⋊ C2×D4

Subgroups

subgroupG/H
centerC2×C3×C9C22×D3
commutatorC2×C3C23×C3×C9
FrattiniC2×C3C22×C32×D3
FittingC32×D4×C9C2
socleC2×C33C23×C3
prime radicalC32×D3×D4C3
cosocleC2×C32C23×C32
hypercenterC3×D4×C9D3
hypocenterC3C2×C3×D4×C9
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C9 ◁ C3×D4×C9

660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2565);