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C2×C11×C9⋊AGL(1,𝔽11) #36344890

order21780
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C9⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C9)⋊(C11×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C11×D9)
unambiguous semidirect product(C2×D99)⋊(C5×C11)

Splittings

FittingC2×C9×C112 ⋊ C2×C5
derivedC9×C11 ⋊ C22×C5×C11
HallC9×C11×C11⋊C5 ⋊ C22
HallC2×C11×D99 ⋊ C5
HallC9×C112 ⋊ C22×C5
HallC11×C11⋊C5 ⋊ C2×D9
SylowC112 ⋊ C2×C5×D9
SylowC9 ⋊ C2×C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C11C9⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC9×C11C22×C5×C11
FrattiniC3C2×C11×C3⋊AGL(1,𝔽11)
FittingC2×C9×C112C2×C5
socleC2×C3×C112C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C2×C11

126 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

858 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 239);