Finite Group Databasebeta

D4×C3⋊(C9⋊C8) #13144398

order1728
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3

Aliases

direct productD4×C3⋊(C9⋊C8)

Splittings

SylowC3×C9 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C4C22×C3⋊D9
commutatorC2×C3×C9C22×C8
FrattiniC2×C3×C4C22×C3⋊D3
FittingC3×C4×D4×C9C2
socleC22×C32C22×Dic3
prime radicalC2×C32×D4Dic3
cosocleC2×C3×C4×C9C23
hypercenterC4×D4C3⋊D9
hypocenterC3×C9C8×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C4×D4

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 864

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10461);