Finite Group Databasebeta

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C3×C11×C361⋊C3 #49088309

order35739
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C361⋊C3
unambiguous semidirect productC361⋊(C32×C11)
unambiguous semidirect product(C3×C361)⋊(C3×C11)
unambiguous semidirect product(C11×C361)⋊C32
unambiguous semidirect product(C3×C11×C361)⋊C3

Splittings

FittingC3×C11×C361 ⋊ C3
derived, SylowC361 ⋊ C32×C11
HallC11×C361 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C11C361⋊C3
commutator, cosocle, hypocenterC361C32×C11
FrattiniC19C3×C11×C19⋊C3
FittingC3×C11×C361C3
socleC3×C11×C19C19⋊C3
LCSG ▷ C361
UCSC1 ◁ C3×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11913

Conjugacy classes & character table

4059 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35739, 5);