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D141⋊AGL(1,𝔽11) #44526628

order31020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD141⋊AGL(1,𝔽11)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊D47
unambiguous semidirect product(C47⋊AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D33⋊D47)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C47 ⋊ C22×C5
HallC3×C47×C11⋊C5 ⋊ C22
HallD33⋊D47 ⋊ C5
HallC47×C11⋊C5 ⋊ C2×D3
HallC11×C47 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D47
HallC3×C47 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D3×D47
SylowC47 ⋊ D3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D47
SylowC11 ⋊ C5×D3×D47
SylowC3 ⋊ D47×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C47C22×C5
LCSG ▷ C3×C11×C47
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1551

Polycyclic presentation:

2^2,5,3,11,47|e^a=e^10,f^a=f^46,d^b=d^2,e^b=e^10,e^c=e^4

Conjugacy classes & character table

447 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 31);