Finite Group Databasebeta

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C3×D4×GO+(4,𝔽2) #13181036

order1728
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC3×D4×GO+(4,𝔽2)

Splittings

FittingC33×D4 ⋊ D4
SylowC33 ⋊ D42

Subgroups

subgroupG/H
centerC2×C3C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C24×C3
FrattiniC2C22×C3×GO+(4,𝔽2)
FittingC33×D4D4
socleC2×C33C22×D4
hypercenterC3×D4GO+(4,𝔽2)
hypocenterC32C3×D42
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×D4

1436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47099);