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C3×#11760440 #15691642

order3159
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

direct productC3×#11760440

Splittings

FittingC3×C13×H(3,𝔽3) ⋊ C3
SylowC13 ⋊ C3×#732

Subgroups

subgroupG/H
centerC32C32⋊(C13⋊C3)
commutator, cosocleC32×C13C33
FrattiniC32C32×C13⋊C3
FittingC3×C13×H(3,𝔽3)C3
socleC32×C13H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C13⋊C3
hypocenterC13C3×#732
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1053

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 252);