Finite Group Databasebeta

← Prev (#36344898) Next (#36344900) →

C2×C9⋊((C11⋊C5)⋊D11) #36344899

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

Aliases

direct productC2×C9⋊((C11⋊C5)⋊D11)
unambiguous semidirect product(C2×C9)⋊((C11⋊C5)⋊D11)
unambiguous semidirect product(C2×C11⋊C5)⋊D99

Splittings

FittingC2×C9×C112 ⋊ C2×C5
derived, HallC9×C112 ⋊ C22×C5
HallC9×C11×C11⋊C5 ⋊ C22
HallC2×C9⋊(C11⋊D11) ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D9
SylowC112 ⋊ C2×C5×D9
SylowC9 ⋊ C2×(C11⋊C5)⋊D11

Subgroups

subgroupG/H
center, hypercenterC2C9⋊((C11⋊C5)⋊D11)
commutator, cosocle, hypocenterC9×C112C22×C5
FrattiniC3C2×C3⋊((C11⋊C5)⋊D11)
FittingC2×C9×C112C2×C5
socleC2×C3×C112C5×D3
LCSG ▷ C9×C112
UCSC1 ◁ C2

150 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 42 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

708 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 248);