Finite Group Databasebeta

C3⋊D3×#733 #13091602

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

Aliases

direct productC3⋊D3×#733
unambiguous semidirect productC3⋊(D3×#733)

Splittings

Fitting, SylowC32×#733 ⋊ C2

Subgroups

subgroupG/H
centerC3C3⋊D3×H(3,𝔽3)
commutator, cosocleC34C2×C32
FrattiniC32C32×C3⋊D3
FittingC32×#733C2
socleC33C2×H(3,𝔽3)
prime radicalC32×C3⋊D3C32
hypercenter#733C3⋊D3
hypocenterC32C2×#733
LCSG ▷ C34 ▷ C33 ▷ C32
UCSC1 ◁ C3 ◁ C32 ◁ #733

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1676);