Finite Group Databasebeta

C9×#5822 #13153691

order1728
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#5822

Splittings

FittingC2×C3×C9×#41 ⋊ C2
SylowC3×C9 ⋊ #575

Subgroups

subgroupG/H
centerC4×C9C2×#67
commutatorC3×C4C24×C9
FrattiniC3×C4C23×C3×D3
FittingC2×C3×C9×#41C2
socleC2×C32C22×C3×D4
prime radicalC3×#5822C3
cosocleC32×C4C24×C3
hypercenterC2×C9×#41D3
hypocenterC3C9×#575
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C9 ◁ C22×C4×C9 ◁ C2×C9×#41

950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19754);