Finite Group Databasebeta

C3×#10588226 #13135644

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

Aliases

direct productC3×#10588226

Splittings

SylowC3×C9 ⋊ C22⋊C16

Subgroups

subgroupG/H
centerC2×C3×C8C2×D9
commutatorC2×C9C2×C3×C16
FrattiniC2×C3×C8C2×C3×D3
FittingC22×C3×C8×C9C2
socleC22×C32C2×C3⋊C8
prime radicalC23×C32C3⋊C8
cosocleC2×C8×C9C22×C3
hypercenterC22×C3×C8D9
hypocenterC9C3×C22⋊C16
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C8 ◁ C22×C3×C8

274 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, 1707);