Finite Group Databasebeta

D3×#6882 #13091307

order1458
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productD3×#6882
unambiguous semidirect productC3⋊(C2×#6882)

Splittings

Fitting, SylowC3×#6882 ⋊ C2

Subgroups

subgroupG/H
centerC3D3×#732
commutator, cosocleC32×C9C2×C32
FrattiniC3×C9C32×D3
FittingC3×#6882C2
socleC32C2×#732
prime radicalC32×D3H(3,𝔽3)
hypercenter#6882D3
hypocenterC3C2×#6882
LCSG ▷ C32×C9 ▷ C33 ▷ C32 ▷ C3
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6882

107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 54

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1381);