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C3×A4×C11⋊C5 #14520441

order1980
isoclinismisoclinic class of A4×C11⋊C5
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C11⋊C5
unambiguous semidirect productC22⋊(C32×C11⋊C5)
unambiguous semidirect productC11⋊(C3×C5×A4)
unambiguous semidirect product(C22×C3)⋊(C3×C11⋊C5)
unambiguous semidirect product(C3×C11)⋊(C5×A4)
unambiguous semidirect product(C11×A4)⋊(C3×C5)
unambiguous semidirect product(C22×C11⋊C5)⋊C32
unambiguous semidirect product(C3×C11×A4)⋊C5
unambiguous semidirect product(C22×C3×C11⋊C5)⋊C3

Splittings

Fitting, socleC22×C3×C11 ⋊ C3×C5
derived, HallC22×C11 ⋊ C32×C5
HallC3×C11×A4 ⋊ C5
HallC22×C11⋊C5 ⋊ C32
SylowC11 ⋊ C3×C5×A4
SylowC22 ⋊ C32×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C32×C5
FrattiniC1G
Fitting, socleC22×C3×C11C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×ΓL(1,𝔽8)×C11⋊C5, C3×C7×A4×C11⋊C5, C3×C11⋊C5×C22⋊ΓL(1,𝔽8), …
maximal normal subgroup ofC3×C7×A4×C11⋊C5, C3×C11×A4×C11⋊C5, C3×A4×C13×C11⋊C5, …
maximal quotient ofA4×ΓL(1,𝔽8)×C11⋊C5, C3×C7×A4×C11⋊C5, C3×C11⋊C5×C22⋊ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 66);