Finite Group Databasebeta

C3×#10589415 #13145973

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×#10589415

Splittings

SylowC33 ⋊ C22⋊C16

Subgroups

subgroupG/H
centerC2×C3×C8C2×C3⋊D3
commutatorC2×C32C2×C3×C16
FrattiniC2×C8C2×C3×C3⋊D3
FittingC22×C33×C8C2
socleC22×C33C2×C8
prime radicalC23×C33C8
cosocleC2×C32×C8C22×C3
hypercenterC22×C3×C8C3⋊D3
hypocenterC32C3×C22⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C8 ◁ C22×C3×C8

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 12036);