Finite Group Databasebeta

C4×C9×D24 #13141433

order1728
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23

Aliases

direct productC4×C9×D24

Splittings

FittingC3×C4×C8×C9 ⋊ C2
SylowC3×C9 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2×C4×C9D12
commutatorC3×C4C22×C4×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C4×C8×C9C2
socleC22×C32C2×C3×D4
prime radicalC2×C3×D24C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC4×C8×C9D3
hypocenterC3C4×C9×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C42×C9 ◁ C4×C8×C9

446 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, 7496);