Finite Group Databasebeta

C22×C9×#208 #13153526

order1728
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C4×C9 · Schur multiplier (H2) = C25

Aliases

direct productC22×C9×#208

Splittings

SylowC3×C9 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4×C9C2×D3
commutatorC2×C3C23×C4×C9
FrattiniC3×C4C23×C3×D3
FittingC23×C3×C4×C9C2
socleC23×C32C2×C3×C4
prime radicalC24×C32C3×C4
cosocleC32×C4C24×C3
hypercenterC23×C4×C9D3
hypocenterC3C22×C9×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C9 ◁ C23×C4×C9

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19589);