Finite Group Databasebeta

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C3×C5×C11×A4 #14520483

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11A4
commutator, cosocle, hypocenterC22C32×C5×C11
FrattiniC1G
Fitting, socleC22×C3×C5×C11C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C11×A4×ΓL(1,𝔽8), C3×C5×C11×C22⋊ΓL(1,𝔽8), C3×C5×C7×C11×A4, …
maximal normal subgroup ofC3×C5×C7×C11×A4, C3×C5×A4×C121, C3×C5×C112×A4, …
maximal quotient ofC5×C11×A4×ΓL(1,𝔽8), C3×C5×C11×C22⋊ΓL(1,𝔽8), C3×C5×C7×C11×A4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 108);