Finite Group Databasebeta

← Prev (#36344668) Next (#36344670) →

C2×C9⋊(D121⋊C5) #36344669

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

Aliases

direct productC2×C9⋊(D121⋊C5)
unambiguous semidirect product(C2×C9)⋊(D121⋊C5)
unambiguous semidirect product(C2×C121⋊C5)⋊D9
unambiguous semidirect product(C2×D1089)⋊C5

Splittings

FittingC2×C9×C121 ⋊ C2×C5
derived, HallC9×C121 ⋊ C22×C5
HallC9×C121⋊C5 ⋊ C22
HallC2×D1089 ⋊ C5
HallC121⋊C5 ⋊ C2×D9
SylowC121 ⋊ C2×C5×D9
SylowC9 ⋊ C2×D121⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(D121⋊C5)
commutator, cosocle, hypocenterC9×C121C22×C5
FrattiniC3×C11C2×C3⋊AGL(1,𝔽11)
FittingC2×C9×C121C2×C5
socleC2×C3×C11C3⋊AGL(1,𝔽11)
LCSG ▷ C9×C121
UCSC1 ◁ C2

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 18);