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C11⋊(ΓL(1,𝔽8)⋊D43) #34090944

order19866
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(ΓL(1,𝔽8)⋊D43)
unambiguous semidirect productΓL(1,𝔽8)⋊D473

Splittings

Fitting, socle, derived, HallC7×C11×C43 ⋊ C2×C3
HallC11×ΓL(1,𝔽8)×C43 ⋊ C2
HallD3311 ⋊ C3
HallΓL(1,𝔽8)×C43 ⋊ D11
HallC11×C43 ⋊ AGL(1,𝔽7)
HallC7×C43 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ D43
HallC7×C11 ⋊ C3×D43
SylowC43 ⋊ C11⋊AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D473
SylowC11 ⋊ ΓL(1,𝔽8)⋊D43
SylowC7 ⋊ C3×D473

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C11×C43C2×C3
LCSG ▷ C7×C11×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,11,43|c^a=c^6,d^a=d^10,e^a=e^42,c^b=c^2

Conjugacy classes & character table

1187 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19866, 55);