Finite Group Databasebeta

← Prev (#14520408) Next (#14520410) →

C2×C5×C11×D9 #14520409

order1980
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D9
unambiguous semidirect productC9⋊(C22×C5×C11)
unambiguous semidirect product(C2×C9)⋊(C2×C5×C11)

Splittings

FittingC2×C5×C9×C11 ⋊ C2
derived, SylowC9 ⋊ C22×C5×C11
HallC5×C9×C11 ⋊ C22
HallC9×C11 ⋊ C22×C5
HallC5×C9 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D9
commutator, cosocle, hypocenterC9C22×C5×C11
FrattiniC3C2×C5×D3×C11
FittingC2×C5×C9×C11C2
socleC2×C3×C5×C11D3
LCSG ▷ C9
UCSC1 ◁ C2×C5×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 990

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C11×D7×D9, C2×C5×C7×C11×D9, C2×C5×C11×D63, …
maximal normal subgroup ofC2×C5×C7×C11×D9, C2×C5×D9×C121, C2×C5×C112×D9, …
maximal quotient ofC5×C11×D7×D9, C2×C5×C7×C11×D9, C2×C5×C11×D63, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 34);