Finite Group Databasebeta

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D3×#63644 #13159541

order1728
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productD3×#63644

Splittings

SylowC33 ⋊ C2×#106

Subgroups

subgroupG/H
centerC22D3×C4⋊(C3⋊D3)
commutatorC33×C4C22×C4
FrattiniC2×C4C2×D3×C3⋊D3
FittingC2×C33×C8C22
socleC22×C33C2×D4
prime radicalC22×C32×D3D4
cosocleC2×C33×C4C23
hypercenterC2×C8D3×C3⋊D3
hypocenterC33C2×#106
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊D3×#106, D3×#10592410, D3×#10592851
maximal normal subgroup ofD3×C3⋊D3×#106, D3×#10592410, D3×#10592851

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 25604);