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C43×C3⋊AGL(1,𝔽11) #28382008

order14190
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C43×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D3×C43)
unambiguous semidirect productD33⋊(C5×C43)
unambiguous semidirect product(C43×D33)⋊C5

Splittings

Fitting, socle, HallC3×C11×C43 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C43
HallC3×C43×C11⋊C5 ⋊ C2
HallC43×D33 ⋊ C5
HallC43×C11⋊C5 ⋊ D3
HallC11×C43 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C43
HallC3×C43 ⋊ AGL(1,𝔽11)
HallD33 ⋊ C5×C43
HallC11⋊C5 ⋊ D3×C43
SylowC11 ⋊ C5×D3×C43
SylowC3 ⋊ C43×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC43C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C5×C43
FrattiniC1G
Fitting, socleC3×C11×C43C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1419

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD43×C3⋊AGL(1,𝔽11), D3×C43×AGL(1,𝔽11), D129⋊AGL(1,𝔽11), …
maximal normal subgroup ofD43×C3⋊AGL(1,𝔽11), D3×C43×AGL(1,𝔽11), D129⋊AGL(1,𝔽11), …
maximal quotient ofC43×C3⋊(Dic11⋊C5), C2×C43×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 25);