Finite Group Databasebeta

C32×#5615 #13178978

order1728
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C24×C3

Aliases

direct productC32×#5615

Splittings

FittingC33×#121 ⋊ C2
SylowC33 ⋊ #540

Subgroups

subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#121C2
socleC22×C33C24
hypercenterC32×#121D3
hypocenterC3C32×#540
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#121

1816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 45041);