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C2×C9×C11⋊C5 #11758355

order990
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC2×C9×C11 ⋊ C5
derived, SylowC11 ⋊ C2×C5×C9
HallC9×C11 ⋊ C2×C5
HallC2×C11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C11⋊C5
commutator, hypocenterC11C2×C5×C9
FrattiniC3C2×C3×C11⋊C5
FittingC2×C9×C11C5
socleC2×C3×C11C3×C5
prime radicalC2×C3×C11⋊C5C3
cosocleC3×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 198

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×Dic11⋊C5, Dic9×C11⋊C5, C9⋊(Dic11⋊C5), …
maximal normal subgroup ofC9×Dic11⋊C5, Dic9×C11⋊C5, C9⋊(Dic11⋊C5), …
maximal quotient ofC4×C9×C11⋊C5, C22×C9×C11⋊C5, C2×C9×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(990, 4);