Finite Group Databasebeta

C23×C9×#67 #13164966

order1728
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C25×C9 · Schur multiplier (H2) = C210

Aliases

direct productC23×C9×#67

Splittings

FittingC25×C3×C9 ⋊ C2
SylowC3×C9 ⋊ C23×D4

Subgroups

subgroupG/H
centerC24×C9C2×D3
commutatorC2×C3C25×C9
FrattiniC2×C3C24×C3×D3
FittingC25×C3×C9C2
socleC24×C32C22×C3
prime radicalC23×C3×#67C3
cosocleC2×C32C25×C3
hypercenterC25×C9D3
hypocenterC3C23×D4×C9
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C9 ◁ C25×C9

4834 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, 31029);