Finite Group Databasebeta

C22×D9×C3⋊C8 #13150014

order1728
isoclinismisoclinic class of D3×D9
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D9×C3⋊C8

Splittings

derived, SylowC3×C9 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4D3×D9
commutator, hypocenterC3×C9C23×C8
FrattiniC3×C4C22×D32
FittingC22×C3×C4×C9C22
socleC23×C32C4×D3
prime radicalC23×C3×D9C4
cosocleC3×C4×C9C24
LCSG ▷ C3×C9
UCSC1 ◁ C22×C4

1090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 16077);