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C3×3−1+2×C13⋊C3 #15691686

order3159
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×3−1+2×C13⋊C3

Splittings

FittingC3×C13×3−1+2 ⋊ C3
SylowC13 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC32C32×C13⋊C3
commutator, cosocleC3×C13C34
FrattiniC3C33×C13⋊C3
FittingC3×C13×3−1+2C3
socleC32×C13C33
prime radicalC33×C13⋊C3C3
hypercenterC3×3−1+2C13⋊C3
hypocenterC13C32×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C3×3−1+2

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 351

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 296);