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ΓL(1,𝔽8)×C3⋊(D41⋊C5) #38788939

order25830
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C3⋊(D41⋊C5)
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(D3×ΓL(1,𝔽8))
unambiguous semidirect productD123⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D123)⋊C5
unambiguous semidirect product(C7×C3⋊(D41⋊C5))⋊C3

Splittings

Fitting, socle, derivedC3×C7×C41 ⋊ C2×C3×C5
HallC3×ΓL(1,𝔽8)×C41⋊C5 ⋊ C2
HallΓL(1,𝔽8)×D123 ⋊ C5
HallC3×ΓL(1,𝔽8)×C41 ⋊ C2×C5
HallC7×C41⋊C5 ⋊ C3×D3
HallC7×C41 ⋊ C3×C5×D3
HallC41⋊C5 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D41⋊C5
SylowC41 ⋊ C5×D3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C3⋊(D41⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C41C2×C3×C5
LCSG ▷ C3×C7×C41
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 861

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 43);