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C3×#66366 #11757858

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

Aliases

direct productC3×#66366

Splittings

FittingC22×C3×3−1+2 ⋊ C3
SylowC22 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C22⋊H(3,𝔽3)
commutator, cosocleC22×C32C33
FrattiniC32C32×A4
FittingC22×C3×3−1+2C3
socleC22×C32H(3,𝔽3)
hypercenterC3×3−1+2A4
hypocenterC22C3×AΣL(1,𝔽27)
LCSG ▷ C22×C32 ▷ C22×C3 ▷ C22
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC3⋊(#66366⋊C2)
maximal subgroup ofC3×#66366⋊C2, C3⋊(#66366⋊C2), D3×#66366, …
maximal normal subgroup ofC3×#66366⋊C2, C3⋊(#66366⋊C2), D3×#66366, …
maximal quotient ofC3×#10619583, C2×C3×#66366

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 583);