Finite Group Databasebeta

D3×C9×C4⋊C8 #13142027

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

Aliases

direct productD3×C9×C4⋊C8

Splittings

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

Subgroups

subgroupG/H
centerC2×C4×C9C22×D3
commutatorC2×C3C22×C8×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×C4⋊C8C2
socleC22×C32C22×C3×C4
prime radicalC22×C3×D3C2×C3×C4
cosocleC2×C32×C4C23×C3
hypercenterC9×C4⋊C8D3
hypocenterC3C2×C9×C4⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C9×C4⋊C8

452 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, 8090);