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A4×ΓL(1,𝔽8)×C47 #26044916

order11844
automorphism?
homologyAbelianization (H1) = C32×C47 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×ΓL(1,𝔽8)×C47
unambiguous semidirect product(C22×ΓL(1,𝔽8))⋊(C3×C47)
unambiguous semidirect product(C7×A4)⋊(C3×C47)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8))⋊(C3×C47)
unambiguous semidirect product(C22×ΓL(1,𝔽8)×C47)⋊C3
unambiguous semidirect product(C7×A4×C47)⋊C3
unambiguous semidirect product(C47×C22⋊ΓL(1,𝔽8))⋊C3

Splittings

Fitting, socle, HallC22×C7×C47 ⋊ C32
derived, HallC22×C7 ⋊ C32×C47
HallC7×C47 ⋊ C3×A4
HallC22×C47 ⋊ C3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×A4×C47
SylowC22 ⋊ C3×ΓL(1,𝔽8)×C47

Subgroups

subgroupG/H
center, hypercenterC47A4×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C47
FrattiniC1G
Fitting, socleC22×C7×C47C32
LCSG ▷ C22×C7
UCSC1 ◁ C47

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

940 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 63);