Finite Group Databasebeta

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C9×C11×#66772 #46777889

order33660
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×#66772

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C4
derived, HallC5×C17 ⋊ C4×C9×C11
HallC9×C11×C17 ⋊ Dic5
HallC5×C11×C17 ⋊ C4×C9
HallC5×C9×C17 ⋊ C4×C11
HallC5×C9×C11 ⋊ #595
HallC11×C17 ⋊ C9×Dic5
HallC9×C17 ⋊ C11×Dic5
HallC5×C11 ⋊ C9×#595
HallC5×C9 ⋊ C11×#595
SylowC17 ⋊ C9×C11×Dic5
SylowC5 ⋊ C9×C11×#595

Subgroups

subgroupG/H
center, hypercenterC9×C11#66772
commutator, hypocenterC5×C17C4×C9×C11
FrattiniC3C3×C11×#66772
FittingC5×C9×C11×C17C4
socleC3×C5×C11×C17C3×C4
prime radicalC3×C5×C11×D17C2×C3
cosocleC3×C5×D17C2×C3×C11
LCSG ▷ C5×C17
UCSC1 ◁ C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 57);