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C9⋊(C11⋊#66775) #46777910

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

Aliases

unambiguous semidirect productC9⋊(C11⋊#66775)
unambiguous semidirect productC11⋊(C9⋊#66775)

Splittings

Fitting, derived, HallC5×C9×C11×C17 ⋊ C4
HallC9×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ #595
HallC11×C17 ⋊ C9⋊AGL(1,𝔽5)
HallC9×C17 ⋊ C11⋊AGL(1,𝔽5)
HallC9×C11 ⋊ #66775
HallC5×C17 ⋊ Dic99
HallC5×C11 ⋊ C9⋊#595
HallC5×C9 ⋊ C11⋊#595
SylowC17 ⋊ C9⋊(C11⋊AGL(1,𝔽5))
SylowC11 ⋊ C9⋊#66775
SylowC9 ⋊ C11⋊#66775
SylowC5 ⋊ C9⋊(C11⋊#595)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC5×C9×C11×C17C4
FrattiniC3C3⋊(C11⋊#66775)
socleC3×C5×C11×C17Dic3
prime radicalC3×C11×D85D3
cosocleC9×C11×D85C2
LCSG ▷ C5×C9×C11×C17
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Polycyclic presentation:

2^2,3,5,11,17,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^10,f^a=f^13,g^a=g^2,d^b=d^4,f^b=f^16

Conjugacy classes & character table

2181 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 78);