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Cayley diagram

C9×C11⋊C5 #92462

order495
isoclinismisoclinic class of C11⋊C5
automorphismAut(G) = C2×C3×AGL(1,𝔽11) (order 660) · Inn(G) = C11⋊C5 · Out(G) = C22×C3
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11⋊C5
unambiguous semidirect productC11⋊(C5×C9)
unambiguous semidirect product(C9×C11)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC9C11⋊C5
commutator, hypocenterC11C5×C9
FrattiniC3C3×C11⋊C5
FittingC9×C11C5
socle, cosocleC3×C11C3×C5
prime radicalC3×C11⋊C5C3
LCSG ▷ C11
UCSC1 ◁ C9

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 99

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×AGL(1,𝔽11), D9×C11⋊C5, C9⋊AGL(1,𝔽11), …
maximal normal subgroup ofC9×AGL(1,𝔽11), D9×C11⋊C5, C9⋊AGL(1,𝔽11), …
maximal quotient ofC2×C9×C11⋊C5, C27×C11⋊C5, C3×C9×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(495, 1);