Finite Group Databasebeta

← Prev (#13181745) Next (#13181747) →

C3×C3⋊D3×2−1+4 #13181746

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

Aliases

direct productC3×C3⋊D3×2−1+4

Splittings

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

Subgroups

subgroupG/H
centerC2×C3C24×C3⋊D3
commutator, cosocleC2×C32C25×C3
FrattiniC2C24×C3×C3⋊D3
FittingC33×2−1+4C2
socleC2×C33C25
hypercenterC3×2−1+4C3⋊D3
hypocenterC32C2×C3×2−1+4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×2−1+4

5348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47809);