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A4×ΓL(1,𝔽8)×C71 #31822075

order17892
automorphism?
homologyAbelianization (H1) = C32×C71 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×ΓL(1,𝔽8)×C71
unambiguous semidirect product(C22×ΓL(1,𝔽8))⋊(C3×C71)
unambiguous semidirect product(C7×A4)⋊(C3×C71)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8))⋊(C3×C71)
unambiguous semidirect product(C22×ΓL(1,𝔽8)×C71)⋊C3
unambiguous semidirect product(C7×A4×C71)⋊C3
unambiguous semidirect product(C71×C22⋊ΓL(1,𝔽8))⋊C3

Splittings

Fitting, socle, HallC22×C7×C71 ⋊ C32
derived, HallC22×C7 ⋊ C32×C71
HallC7×C71 ⋊ C3×A4
HallC22×C71 ⋊ C3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×A4×C71
SylowC22 ⋊ C3×ΓL(1,𝔽8)×C71

Subgroups

subgroupG/H
center, hypercenterC71A4×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C71
FrattiniC1G
Fitting, socleC22×C7×C71C32
LCSG ▷ C22×C7
UCSC1 ◁ C71

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1988

Conjugacy classes & character table

1420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 92);