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ΓL(1,𝔽8)×D615 #38788967

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

Aliases

direct productΓL(1,𝔽8)×D615
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)×D205)
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D123)
unambiguous semidirect productC41⋊(ΓL(1,𝔽8)×D15)
unambiguous semidirect product(C7×D615)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C7×C41 ⋊ C2×C3
HallC3×C5×ΓL(1,𝔽8)×C41 ⋊ C2
HallC3×ΓL(1,𝔽8)×C41 ⋊ D5
HallC5×C7×C41 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ D41
HallC7×C41 ⋊ C3×D15
HallC5×C41 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D205
SylowC41 ⋊ ΓL(1,𝔽8)×D15
HallC5×C7 ⋊ C3×D123
SylowC7 ⋊ C3×D615
SylowC5 ⋊ ΓL(1,𝔽8)×D123

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4305

Conjugacy classes & character table

1545 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 71);