Finite Group Databasebeta

C9×#5144 #13143254

order1728
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C22

Aliases

direct productC9×#5144

Splittings

FittingC3×C9×#131 ⋊ C2
SylowC3×C9 ⋊ #443

Subgroups

subgroupG/H
centerC8×C9#67
commutatorC3×C4C22×C4×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#131C2
socleC2×C32C3×C4×D4
prime radicalC3×#950C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#131D3
hypocenterC3C9×#443
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C8×C9 ◁ C2×C8×C9 ◁ C9×#131

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 9317);