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C11⋊(ΓL(1,𝔽8)⋊(D19⋊C3)) #39911836

order26334
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC11⋊(ΓL(1,𝔽8)⋊(D19⋊C3))
unambiguous semidirect productΓL(1,𝔽8)⋊(C11⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C11⋊((C19⋊C3)⋊D7))⋊C3
unambiguous semidirect product(C11⋊(ΓL(1,𝔽8)⋊D19))⋊C3
unambiguous semidirect product(C11⋊#11716327)⋊C3
unambiguous semidirect product(C11⋊#11716328)⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C2×C32
HallC11×ΓL(1,𝔽8)×C19⋊C3 ⋊ C2
HallD1463 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C3×AGL(1,𝔽7)
HallC7×C19 ⋊ C32×D11
HallC7×C11 ⋊ C3×D19⋊C3
SylowC19 ⋊ C3×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ ΓL(1,𝔽8)⋊(D19⋊C3)
SylowC7 ⋊ C3×C11⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C19C2×C32
LCSG ▷ C7×C11×C19
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Polycyclic presentation:

2,3^2,7,11,19|d^a=d^6,e^a=e^10,f^a=f^18,f^b=f^7,d^c=d^2

Conjugacy classes & character table

261 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 63);