Finite Group Databasebeta

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C5×C9×C11⋊#595 #46777879

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

Aliases

direct productC5×C9×C11⋊#595

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C4
derived, HallC11×C17 ⋊ C4×C5×C9
HallC9×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ C4×C9
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ #595
HallC9×C17 ⋊ C5×Dic11
HallC9×C11 ⋊ C5×#595
HallC5×C17 ⋊ C9×Dic11
HallC5×C11 ⋊ C9×#595
SylowC17 ⋊ C5×C9×Dic11
SylowC11 ⋊ C5×C9×#595

Subgroups

subgroupG/H
center, hypercenterC5×C9C11⋊#595
commutator, hypocenterC11×C17C4×C5×C9
FrattiniC3C3×C5×C11⋊#595
FittingC5×C9×C11×C17C4
socleC3×C5×C11×C17C3×C4
prime radicalC3×C5×C11×D17C2×C3
cosocleC3×C11×D17C2×C3×C5
LCSG ▷ C11×C17
UCSC1 ◁ C5×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

2610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 47);