Finite Group Databasebeta

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C32×D3×2−1+4 #13181726

order1728
automorphism?
homologyAbelianization (H1) = C25×C32 · Schur multiplier (H2) = C29×C3

Aliases

direct productC32×D3×2−1+4

Splittings

FittingC33×2−1+4 ⋊ C2
SylowC33 ⋊ C2×2−1+4

Subgroups

subgroupG/H
centerC2×C32C24×D3
commutator, cosocleC2×C3C25×C32
FrattiniC2C24×C32×D3
FittingC33×2−1+4C2
socleC2×C33C25
hypercenterC32×2−1+4D3
hypocenterC3C2×C32×2−1+4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C32 ◁ C32×2−1+4

5348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47789);