Finite Group Databasebeta

C4×C9×#239 #13152694

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

Aliases

direct productC4×C9×#239

Splittings

FittingC3×C4×Q8×C9 ⋊ C2
SylowC3×C9 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4×C9C22×D3
commutatorC2×C3C23×C4×C9
FrattiniC22×C3C23×C3×D3
FittingC3×C4×Q8×C9C2
socle, cosocleC22×C32C24×C3
prime radicalC2×C3×#239C2×C3
hypercenterC4×Q8×C9D3
hypocenterC3C4×C9×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C4×Q8×C9

1000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18757);