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C9⋊(C19⋊AGL(1,𝔽11)) #34037833

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

Aliases

unambiguous semidirect productC9⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect productC19⋊(C9⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊D171
unambiguous semidirect productD1881⋊C5

Splittings

Fitting, derived, HallC9×C11×C19 ⋊ C2×C5
HallC9×C19×C11⋊C5 ⋊ C2
HallD1881 ⋊ C5
HallC19×C11⋊C5 ⋊ D9
HallC9×C11⋊C5 ⋊ D19
HallC11×C19 ⋊ C5×D9
HallC9×C19 ⋊ AGL(1,𝔽11)
HallC9×C11 ⋊ C5×D19
HallC11⋊C5 ⋊ D171
SylowC19 ⋊ C9⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D171
SylowC9 ⋊ C19⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C11×C19C2×C5
FrattiniC3C3⋊(C19⋊AGL(1,𝔽11))
socleC3×C11×C19C5×D3
LCSG ▷ C9×C11×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Polycyclic presentation:

2,3,5,11,19,3|b^3=f^2,b^a=b^2f,d^a=d^10,e^a=e^18,f^a=f^2,d^c=d^4

Conjugacy classes & character table

606 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×C9⋊AGL(1,𝔽11), AGL(1,𝔽11)×D171, D9×C19⋊AGL(1,𝔽11), …
maximal normal subgroup ofD19×C9⋊AGL(1,𝔽11), AGL(1,𝔽11)×D171, D9×C19⋊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, 26);