Finite Group Databasebeta

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C3×#10596510 #13181029

order1728
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10596510

Splittings

FittingC2×C33×C4 ⋊ D4
SylowC33 ⋊ #525

Subgroups

subgroupG/H
centerC3×C4C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C24×C3
FrattiniC2C22×C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socleC2×C33C22×D4
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#525
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47092);