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(C11⋊AGL(1,𝔽7))⋊D19 #31798250

order17556
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C11⋊AGL(1,𝔽7))⋊D19
unambiguous semidirect product(ΓL(1,𝔽8)⋊D19)⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C22×C3
HallD77⋊D19 ⋊ C3
HallC11×C19×ΓL(1,𝔽8) ⋊ C22
HallC19×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D19
HallC11×C19 ⋊ C2×AGL(1,𝔽7)
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D19
HallΓL(1,𝔽8) ⋊ D11×D19
SylowC19 ⋊ D11×AGL(1,𝔽7)
SylowC11 ⋊ D19×AGL(1,𝔽7)
SylowC7 ⋊ C3×D11×D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C19C22×C3
LCSG ▷ C7×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Polycyclic presentation:

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

Conjugacy classes & character table

337 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 65);