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C9×C19⋊AGL(1,𝔽11) #34037829

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C19⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C9×D19)
unambiguous semidirect product(C9×D209)⋊C5

Splittings

Fitting, HallC9×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C5×C9
HallC9×C19×C11⋊C5 ⋊ C2
HallC9×D209 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C9
HallC9×C11⋊C5 ⋊ D19
HallD209 ⋊ C5×C9
HallC9×C19 ⋊ AGL(1,𝔽11)
HallC9×C11 ⋊ C5×D19
HallC11⋊C5 ⋊ C9×D19
SylowC19 ⋊ C9×AGL(1,𝔽11)
SylowC11 ⋊ C5×C9×D19

Subgroups

subgroupG/H
center, hypercenterC9C19⋊AGL(1,𝔽11)
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC3C3×C19⋊AGL(1,𝔽11)
FittingC9×C11×C19C2×C5
socle, cosocleC3×C11×C19C2×C3×C5
prime radicalC3×C19⋊AGL(1,𝔽11)C3
LCSG ▷ C11×C19
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×D19×AGL(1,𝔽11), D9×C19⋊AGL(1,𝔽11), D171⋊AGL(1,𝔽11), …
maximal normal subgroup ofC9×D19×AGL(1,𝔽11), D9×C19⋊AGL(1,𝔽11), D171⋊AGL(1,𝔽11), …
maximal quotient ofC9×C19⋊(Dic11⋊C5), C2×C9×C19⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 22);