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C3×ΓL(1,𝔽8)⋊(D41⋊C5) #38788934

order25830
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊(D41⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(C3×AGL(1,𝔽7))
unambiguous semidirect product(ΓL(1,𝔽8)⋊D41)⋊(C3×C5)
unambiguous semidirect product(C7⋊(D41⋊C5))⋊C32
unambiguous semidirect product(C3×ΓL(1,𝔽8)⋊D41)⋊C5
unambiguous semidirect product(C3×C7⋊(D41⋊C5))⋊C3

Splittings

Fitting, socleC3×C7×C41 ⋊ C2×C3×C5
derived, HallC7×C41 ⋊ C2×C32×C5
HallC3×ΓL(1,𝔽8)×C41⋊C5 ⋊ C2
HallC3×ΓL(1,𝔽8)⋊D41 ⋊ C5
HallC7⋊(D41⋊C5) ⋊ C32
HallC3×ΓL(1,𝔽8)×C41 ⋊ C2×C5
HallC7×C41⋊C5 ⋊ C2×C32
HallD287 ⋊ C32×C5
HallC41⋊C5 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ D41⋊C5
SylowC41 ⋊ C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C32×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)⋊(D41⋊C5)
commutator, cosocle, hypocenterC7×C41C2×C32×C5
FrattiniC1G
Fitting, socleC3×C7×C41C2×C3×C5
LCSG ▷ C7×C41
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 861

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 38);