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C3×(C13⋊C3)⋊D137 #44545393

order32058
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C13⋊C3)⋊D137
unambiguous semidirect product(C13⋊C3)⋊(C3×D137)
unambiguous semidirect productC137⋊(C3×D13⋊C3)
unambiguous semidirect productD1781⋊C32
unambiguous semidirect product(C3×D1781)⋊C3

Splittings

Fitting, socleC3×C13×C137 ⋊ C2×C3
derived, HallC13×C137 ⋊ C2×C32
HallC3×C13⋊C3×C137 ⋊ C2
HallD1781 ⋊ C32
SylowC137 ⋊ C3×D13⋊C3
HallC3×C13⋊C3 ⋊ D137
SylowC13 ⋊ C32×D137

Subgroups

subgroupG/H
center, hypercenterC3(C13⋊C3)⋊D137
commutator, cosocle, hypocenterC13×C137C2×C32
FrattiniC1G
Fitting, socleC3×C13×C137C2×C3
LCSG ▷ C13×C137
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5343

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32058, 15);