Finite Group Databasebeta

← Prev (#14520392) Next (#14520394) →

C22×C9×C11⋊C5 #14520393

order1980
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C9×C11⋊C5
unambiguous semidirect product(C22×C9×C11)⋊C5

Splittings

Fitting, HallC22×C9×C11 ⋊ C5
derived, SylowC11 ⋊ C22×C5×C9
HallC9×C11 ⋊ C22×C5
HallC22×C11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC22×C9C11⋊C5
commutator, hypocenterC11C22×C5×C9
FrattiniC3C22×C3×C11⋊C5
FittingC22×C9×C11C5
socleC22×C3×C11C3×C5
prime radicalC22×C3×C11⋊C5C3
cosocleC3×C11C22×C3×C5
LCSG ▷ C11
UCSC1 ◁ C22×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 396

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2)(5,6,7,8,9,10,11,12,13)(15,16,18,21,20)(17,19,23,24,22);(3,4)(14,15,17,20,16,18,22,24,19,21,23)

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×D7⋊C9, C22×C11⋊C5×C7⋊C9, C2×C9×D7×C11⋊C5, …
maximal normal subgroup ofC22×C7×C9×C11⋊C5, C22×C9×C11×C11⋊C5, C22×C9×C13×C11⋊C5, …
maximal quotient ofC2×C11⋊C5×D7⋊C9, C22×C11⋊C5×C7⋊C9, C2×C9×D7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 18);