Finite Group Databasebeta

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C9×C11⋊C5×#595 #46777860

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11⋊C5×#595
unambiguous semidirect product(C11×#595)⋊(C5×C9)
unambiguous semidirect product(C9×C11×#595)⋊C5

Splittings

Fitting, HallC9×C11×C17 ⋊ C4×C5
derived, HallC11×C17 ⋊ C4×C5×C9
HallC9×C17×C11⋊C5 ⋊ C4
HallC9×C11×#595 ⋊ C5
HallC17×C11⋊C5 ⋊ C4×C9
HallC11×#595 ⋊ C5×C9
HallC9×C17 ⋊ C4×C11⋊C5
HallC9×C11 ⋊ C5×#595
SylowC17 ⋊ C4×C9×C11⋊C5
SylowC11 ⋊ C5×C9×#595

Subgroups

subgroupG/H
center, hypercenterC9C11⋊C5×#595
commutator, hypocenterC11×C17C4×C5×C9
FrattiniC3C3×C11⋊C5×#595
FittingC9×C11×C17C4×C5
socleC3×C11×C17C3×C4×C5
prime radicalC3×D17×C11⋊C5C2×C3
cosocleC3×C11×D17C2×C3×C5
LCSG ▷ C11×C17
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1683

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 28);