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C9×D19×C11⋊C5 #34037827

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

Aliases

direct productC9×D19×C11⋊C5
unambiguous semidirect product(C9×C11×D19)⋊C5

Splittings

Fitting, HallC9×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C5×C9
HallC9×C19×C11⋊C5 ⋊ C2
HallC9×C11×D19 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C9
HallC11×D19 ⋊ C5×C9
HallC9×C19 ⋊ C2×C11⋊C5
HallC9×C11 ⋊ C5×D19
SylowC19 ⋊ C2×C9×C11⋊C5
SylowC11 ⋊ C5×C9×D19

Subgroups

subgroupG/H
center, hypercenterC9D19×C11⋊C5
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC3C3×D19×C11⋊C5
FittingC9×C11×C19C2×C5
socle, cosocleC3×C11×C19C2×C3×C5
prime radicalC3×D19×C11⋊C5C3
LCSG ▷ C11×C19
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×D19×AGL(1,𝔽11), D19×C9⋊AGL(1,𝔽11), D9×D19×C11⋊C5, …
maximal normal subgroup ofC9×D19×AGL(1,𝔽11), D19×C9⋊AGL(1,𝔽11), D9×D19×C11⋊C5, …
maximal quotient ofC9×C11⋊C5×Dic19, C2×C9×D19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 20);