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#15691697

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

Aliases

No aliases for this group.

Splittings

FittingC3×C13×3−1+2 ⋊ C3
SylowC13 ⋊ 3−1+4

Subgroups

subgroupG/H
center, FrattiniC3C33×C13⋊C3
commutator, socle, cosocleC3×C13C34
FittingC3×C13×3−1+2C3
prime radicalC3×C32⋊(C13⋊C3)C3
hypercenterC3×3−1+2C13⋊C3
hypocenterC133−1+4
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×3−1+2

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 351

Polycyclic presentation:

3^5,13|a^3=e,b^a=be,d^a=de,c^b=ce,f^c=f^3

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 307);