Finite Group Databasebeta

← Prev (#14520397) Next (#14520399) →

C9×D5×D11 #14520398

order1980
isoclinismisoclinic class of D5×D11
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC9×D5×D11
unambiguous semidirect product(D5×C11)⋊(C2×C9)
unambiguous semidirect product(C5×D11)⋊(C2×C9)
unambiguous semidirect productD55⋊(C2×C9)

Splittings

Fitting, HallC5×C9×C11 ⋊ C22
derived, HallC5×C11 ⋊ C22×C9
HallC9×C11 ⋊ C2×D5
HallC5×C9 ⋊ C2×D11
SylowC11 ⋊ C2×C9×D5
SylowC5 ⋊ C2×C9×D11

Subgroups

subgroupG/H
center, hypercenterC9D5×D11
commutator, hypocenterC5×C11C22×C9
FrattiniC3C3×D5×D11
FittingC5×C9×C11C22
socle, cosocleC3×C5×C11C22×C3
prime radicalC3×D5×D11C3
LCSG ▷ C5×C11
UCSC1 ◁ C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 495

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C5⋊(D7⋊C9), D5×C11⋊(D7⋊C9), D55⋊(D7⋊C9), …
maximal normal subgroup ofC7×C9×D5×D11, C9×D5×C11×D11, C9×D5×C13×D11, …
maximal quotient ofD11×C5⋊(D7⋊C9), D5×C11⋊(D7⋊C9), D55⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 23);