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C3⋊(C43⋊AGL(1,𝔽11)) #28382009

order14190
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C43⋊AGL(1,𝔽11))
unambiguous semidirect productC43⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊D129
unambiguous semidirect productD1419⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C43 ⋊ C2×C5
HallC3×C43×C11⋊C5 ⋊ C2
HallD1419 ⋊ C5
HallC43×C11⋊C5 ⋊ D3
HallC11×C43 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D43
HallC3×C43 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ D129
SylowC43 ⋊ C3⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D43
SylowC11 ⋊ C5×D129
SylowC3 ⋊ C43⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C43C2×C5
LCSG ▷ C3×C11×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1419

Polycyclic presentation:

2,3,5,11,43|b^a=b^2,d^a=d^10,e^a=e^42,d^c=d^4

Conjugacy classes & character table

459 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD43×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×D129, D3×C43⋊AGL(1,𝔽11), …
maximal normal subgroup ofD43×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×D129, D3×C43⋊AGL(1,𝔽11), …
maximal quotient ofC3⋊(C43⋊(Dic11⋊C5)), C2×C3⋊(C43⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 26);