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C4×C9×C11⋊C5 #14520379

order1980
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C9)
unambiguous semidirect product(C4×C9×C11)⋊C5

Splittings

Fitting, HallC4×C9×C11 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C9
HallC9×C11 ⋊ C4×C5
HallC4×C11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC4×C9C11⋊C5
commutator, hypocenterC11C4×C5×C9
FrattiniC2×C3C2×C3×C11⋊C5
FittingC4×C9×C11C5
socle, cosocleC2×C3×C11C2×C3×C5
prime radicalC2×C3×C11⋊C5C2×C3
LCSG ▷ C11
UCSC1 ◁ C4×C9

36 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:

(1,2,3,4)(5,6,7,8,9,10,11,12,13)(15,16,18,21,20)(17,19,23,24,22);(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 ofC4×C7×C9×C11⋊C5, C4×C11⋊C5×C7⋊C9, C9×Dic7×C11⋊C5, …
maximal normal subgroup ofC4×C7×C9×C11⋊C5, C4×C9×C11×C11⋊C5, C4×C9×C13×C11⋊C5, …
maximal quotient ofC4×C7×C9×C11⋊C5, C4×C11⋊C5×C7⋊C9, C9×Dic7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 4);