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C9×C29×C11⋊C5 #28385156

order14355
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC9×C29×C11⋊C5
unambiguous semidirect productC11⋊(C5×C9×C29)
unambiguous semidirect product(C9×C11)⋊(C5×C29)
unambiguous semidirect product(C11×C29)⋊(C5×C9)
unambiguous semidirect product(C9×C11×C29)⋊C5

Splittings

Fitting, HallC9×C11×C29 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C29
HallC11×C29 ⋊ C5×C9
HallC9×C11 ⋊ C5×C29

Subgroups

subgroupG/H
center, hypercenterC9×C29C11⋊C5
commutator, hypocenterC11C5×C9×C29
FrattiniC3C3×C29×C11⋊C5
FittingC9×C11×C29C5
socleC3×C11×C29C3×C5
prime radicalC3×C29×C11⋊C5C3
cosocleC3×C11C3×C5×C29
LCSG ▷ C11
UCSC1 ◁ C9×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2871

Conjugacy classes & character table

1827 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C9×C29×C11⋊C5, C9×C11⋊C5×D29, C9×C29×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C9×C29×C11⋊C5, C9×C11⋊C5×D29, C9×C29×AGL(1,𝔽11), …
maximal quotient ofC2×C9×C29×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14355, 2);