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C3⋊(C11⋊(C17⋊AGL(1,𝔽7))) #37555642

order23562
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C11⋊(C17⋊AGL(1,𝔽7)))
unambiguous semidirect productC11⋊(C3⋊(C17⋊AGL(1,𝔽7)))
unambiguous semidirect productC17⋊(C3⋊(C11⋊AGL(1,𝔽7)))
unambiguous semidirect productΓL(1,𝔽8)⋊D561
unambiguous semidirect productD3927⋊C3

Splittings

Fitting, socle, derivedC3×C7×C11×C17 ⋊ C2×C3
HallC3×C11×C17×ΓL(1,𝔽8) ⋊ C2
HallC7×C11×C17 ⋊ C3×D3
HallC3×C17×ΓL(1,𝔽8) ⋊ D11
HallC3×C11×ΓL(1,𝔽8) ⋊ D17
HallC11×C17 ⋊ C3⋊AGL(1,𝔽7)
HallC7×C17 ⋊ C3×D33
HallC7×C11 ⋊ C3×D51
HallC3×ΓL(1,𝔽8) ⋊ D187
SylowC17 ⋊ C3⋊(C11⋊AGL(1,𝔽7))
SylowC11 ⋊ C3⋊(C17⋊AGL(1,𝔽7))
SylowC7 ⋊ C3×D561

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C17C2×C3
LCSG ▷ C3×C7×C11×C17
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Polycyclic presentation:

2,3^2,7,11,17|c^a=c^2,d^a=d^6,e^a=e^10,f^a=f^16,d^b=d^2

Conjugacy classes & character table

1407 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 36);