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C5×C9⋊(C11⋊#595) #46777899

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

Aliases

direct productC5×C9⋊(C11⋊#595)
unambiguous semidirect productC9⋊(C5×C11⋊#595)

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C4
derived, HallC9×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ #595
HallC11×C17 ⋊ C5×Dic9
HallC9×C17 ⋊ C5×Dic11
HallC9×C11 ⋊ C5×#595
HallC5×C17 ⋊ Dic99
HallC5×C11 ⋊ C9⋊#595
HallC5×C9 ⋊ C11⋊#595
SylowC17 ⋊ C5×Dic99
SylowC11 ⋊ C5×C9⋊#595
SylowC9 ⋊ C5×C11⋊#595

Subgroups

subgroupG/H
center, hypercenterC5C9⋊(C11⋊#595)
commutator, hypocenterC9×C11×C17C4×C5
FrattiniC3C5×C3⋊(C11⋊#595)
FittingC5×C9×C11×C17C4
socleC3×C5×C11×C17Dic3
prime radicalC3×C5×C11×D17D3
cosocleC9×C11×D17C2×C5
LCSG ▷ C9×C11×C17
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

2490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 67);