Finite Group Databasebeta

D4×C9×C3⋊C8 #13142721

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

Aliases

direct productD4×C9×C3⋊C8

Splittings

SylowC3×C9 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C4×C9C22×D3
commutatorC2×C3C22×C8×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C4×D4×C9C2
socleC22×C32C22×C3×C4
prime radicalC2×C32×D4C3×C4
cosocleC2×C32×C4C23×C3
hypercenterC4×D4×C9D3
hypocenterC3C8×D4×C9
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C4×D4×C9

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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, 8784);