Finite Group Databasebeta

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C3×C7×C11×A4 #14583943

order2772
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C7×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×C11×A4
unambiguous semidirect productC22⋊(C32×C7×C11)
unambiguous semidirect product(C22×C3)⋊(C3×C7×C11)
unambiguous semidirect product(C22×C11)⋊(C32×C7)
unambiguous semidirect product(C22×C3×C11)⋊(C3×C7)

Splittings

Fitting, socleC22×C3×C7×C11 ⋊ C3
derived, SylowC22 ⋊ C32×C7×C11
HallC22×C7×C11 ⋊ C32
HallC22×C11 ⋊ C32×C7
HallC22×C7 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11A4
commutator, cosocle, hypocenterC22C32×C7×C11
FrattiniC1G
Fitting, socleC22×C3×C7×C11C3
LCSG ▷ C22
UCSC1 ◁ C3×C7×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 924

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C7×A4×C11⋊C5, C3×C5×C7×C11×A4, C3×C7×C11×A5, …
maximal normal subgroup ofC3×C7×A4×C11⋊C5, C3×C5×C7×C11×A4, C3×C11×A4×C49, …
maximal quotient ofC3×C5×C7×C11×A4, C3×C11×A4×C49, C7×C11×A4×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2772, 99);