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C11×C9⋊#66774 #46777908

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

Aliases

direct productC11×C9⋊#66774
unambiguous semidirect productC9⋊(C11×#66774)

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C4
derived, HallC5×C9×C17 ⋊ C4×C11
HallC9×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C11 ⋊ Dic17
HallC11×C17 ⋊ C9⋊AGL(1,𝔽5)
HallC9×C17 ⋊ C11×AGL(1,𝔽5)
HallC9×C11 ⋊ #66774
HallC5×C17 ⋊ C11×Dic9
HallC5×C11 ⋊ Dic153
HallC5×C9 ⋊ C11×Dic17
SylowC17 ⋊ C11×C9⋊AGL(1,𝔽5)
SylowC9 ⋊ C11×#66774
SylowC5 ⋊ C11×Dic153

Subgroups

subgroupG/H
center, hypercenterC11C9⋊#66774
commutator, hypocenterC5×C9×C17C4×C11
FrattiniC3C11×C3⋊#66774
FittingC5×C9×C11×C17C4
socleC3×C5×C11×C17Dic3
prime radicalC3×D5×C11×C17D3
cosocleC9×D5×C17C2×C11
LCSG ▷ C5×C9×C17
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3399 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 76);