Finite Group Databasebeta

C8×C9×D12 #13141427

order1728
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C8×C9 · Schur multiplier (H2) = C23

Aliases

direct productC8×C9×D12

Splittings

FittingC3×C4×C8×C9 ⋊ C2
SylowC3×C9 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C8×C9C2×D3
commutatorC2×C3C22×C8×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C4×C8×C9C2
socleC22×C32C22×C3×C4
prime radicalC2×C3×D12C3×C4
cosocleC2×C32×C4C23×C3
hypercenterC4×C8×C9D3
hypocenterC3C8×D4×C9
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C8×C9 ◁ C4×C8×C9

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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, 7490);