Finite Group Databasebeta

C3×#66359 #11757826

order972
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C2×C33

Aliases

direct productC3×#66359

Splittings

SylowC22 ⋊ C3×#733

Subgroups

subgroupG/H
centerC32C22⋊H(3,𝔽3)
commutator, cosocleC22×C32C33
FrattiniC32C32×A4
FittingC22×C32×C9C3
socleC22×C32H(3,𝔽3)
prime radicalC22×C33C32
hypercenterC32×C9A4
hypocenterC22C3×#733
LCSG ▷ C22×C32 ▷ C22×C3 ▷ C22
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9

182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC3⋊(#66359⋊C2)
maximal subgroup ofC3×#66359⋊C2, C3⋊(#66359⋊C2), D3×#66359, …
maximal normal subgroup ofC3×#66359⋊C2, C3⋊(#66359⋊C2), D3×#66359, …
maximal quotient ofC3×#10619576, C2×C3×#66359

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 551);