Finite Group Databasebeta

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D9×C19×C11⋊C5 #34037830

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productD9×C19×C11⋊C5
unambiguous semidirect productC9⋊(C2×C19×C11⋊C5)
unambiguous semidirect product(C11×D9)⋊(C5×C19)
unambiguous semidirect product(C11×D9×C19)⋊C5

Splittings

Fitting, HallC9×C11×C19 ⋊ C2×C5
derived, HallC9×C11 ⋊ C2×C5×C19
HallC9×C19×C11⋊C5 ⋊ C2
HallC11×D9×C19 ⋊ C5
HallC9×C11⋊C5 ⋊ C2×C19
HallC11×C19 ⋊ C5×D9
HallC11×D9 ⋊ C5×C19
HallC9×C19 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×D9×C19
SylowC9 ⋊ C2×C19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC19D9×C11⋊C5
commutator, cosocle, hypocenterC9×C11C2×C5×C19
FrattiniC3D3×C19×C11⋊C5
FittingC9×C11×C19C2×C5
socleC3×C11×C19C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD9×C19×AGL(1,𝔽11), D9×C19⋊AGL(1,𝔽11), D9×D19×C11⋊C5, …
maximal normal subgroup ofD9×C19×AGL(1,𝔽11), D9×C19⋊AGL(1,𝔽11), D9×D19×C11⋊C5, …
maximal quotient ofC19×Dic9×C11⋊C5, C2×D9×C19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 23);