Finite Group Databasebeta

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C3×D13⋊C3×C137 #44545392

order32058
automorphism?
homologyAbelianization (H1) = C2×C32×C137 · Schur multiplier (H2) = C3

Aliases

direct productC3×D13⋊C3×C137
unambiguous semidirect productD13⋊(C32×C137)
unambiguous semidirect product(C13⋊C3)⋊(C2×C3×C137)
unambiguous semidirect product(C3×D13)⋊(C3×C137)
unambiguous semidirect product(D13×C137)⋊C32
unambiguous semidirect product(C3×D13×C137)⋊C3

Splittings

Fitting, socleC3×C13×C137 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C32×C137
HallC3×C13⋊C3×C137 ⋊ C2
HallD13×C137 ⋊ C32
HallC13×C137 ⋊ C2×C32
HallC3×C13⋊C3 ⋊ C2×C137
HallD13 ⋊ C32×C137

Subgroups

subgroupG/H
center, hypercenterC3×C137D13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C137
FrattiniC1G
Fitting, socleC3×C13×C137C2×C3
LCSG ▷ C13
UCSC1 ◁ C3×C137

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5343

Conjugacy classes & character table

3288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32058, 14);