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C3×ΓL(1,𝔽8)⋊D257 #44569213

order32382
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊D257
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D257)
unambiguous semidirect productC257⋊(C3×AGL(1,𝔽7))
unambiguous semidirect productD1799⋊C32
unambiguous semidirect product(C3×D1799)⋊C3

Splittings

Fitting, socleC3×C7×C257 ⋊ C2×C3
derived, HallC7×C257 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)×C257 ⋊ C2
HallD1799 ⋊ C32
SylowC257 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ D257
SylowC7 ⋊ C32×D257

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)⋊D257
commutator, cosocle, hypocenterC7×C257C2×C32
FrattiniC1G
Fitting, socleC3×C7×C257C2×C3
LCSG ▷ C7×C257
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5397

Conjugacy classes & character table

1941 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32382, 15);