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C2×C9×(C11⋊C5)⋊D11 #36344887

order21780
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×(C11⋊C5)⋊D11
unambiguous semidirect product(C2×C11⋊C5)⋊(C9×D11)

Splittings

FittingC2×C9×C112 ⋊ C2×C5
derived, SylowC112 ⋊ C22×C5×C9
HallC9×C11×C11⋊C5 ⋊ C22
HallC2×C9×C11⋊D11 ⋊ C5
HallC9×C112 ⋊ C22×C5
HallC11×C11⋊C5 ⋊ C22×C9
HallC2×C11⋊D11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9(C11⋊C5)⋊D11
commutator, hypocenterC112C22×C5×C9
FrattiniC3C2×C3×(C11⋊C5)⋊D11
FittingC2×C9×C112C2×C5
socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×(C11⋊C5)⋊D11C3
cosocleC3×C112C22×C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C9

150 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 54 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

828 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 236);