Finite Group Databasebeta

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C9×D19×AGL(1,𝔽11) #49178333

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC9×D19×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C9×D19)
unambiguous semidirect product(C9×D11×D19)⋊C5

Splittings

Fitting, HallC9×C11×C19 ⋊ C22×C5
derived, HallC11×C19 ⋊ C22×C5×C9
HallC9×C19×C11⋊C5 ⋊ C22
HallC9×D11×D19 ⋊ C5
HallC19×C11⋊C5 ⋊ C22×C9
HallD11×D19 ⋊ C5×C9
HallC9×C11⋊C5 ⋊ C2×D19
HallC9×C19 ⋊ C2×AGL(1,𝔽11)
HallC9×C11 ⋊ C2×C5×D19
HallC11⋊C5 ⋊ C2×C9×D19
SylowC19 ⋊ C2×C9×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C9×D19

Subgroups

subgroupG/H
center, hypercenterC9D19×AGL(1,𝔽11)
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC3C3×D19×AGL(1,𝔽11)
FittingC9×C11×C19C22×C5
socle, cosocleC3×C11×C19C22×C3×C5
prime radicalC3×D19×AGL(1,𝔽11)C3
LCSG ▷ C11×C19
UCSC1 ◁ C9

120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

1089 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 42);