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C3⋊(C5⋊(C17⋊AGL(1,𝔽11))) #43242513

order28050
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C5⋊(C17⋊AGL(1,𝔽11)))
unambiguous semidirect productC5⋊(C3⋊(C17⋊AGL(1,𝔽11)))
unambiguous semidirect productC17⋊(C3⋊(C5⋊AGL(1,𝔽11)))
unambiguous semidirect product(C11⋊C5)⋊D255
unambiguous semidirect productD2805⋊C5

Splittings

Fitting, socle, derivedC3×C5×C11×C17 ⋊ C2×C5
HallC3×C5×C17×C11⋊C5 ⋊ C2
HallC5×C17×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ D17
HallC3×C11×C17 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D51
HallC11×C17 ⋊ C5×D15
HallC3×C17 ⋊ C5⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D85
SylowC17 ⋊ C3⋊(C5⋊AGL(1,𝔽11))
SylowC11 ⋊ C5×D255
SylowC3 ⋊ C5⋊(C17⋊AGL(1,𝔽11))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C17C2×C5
LCSG ▷ C3×C5×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2805

Polycyclic presentation:

2,5,3,5,11,17|c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^16,e^b=e^4

Conjugacy classes & character table

900 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 38);