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ΓL(1,𝔽8)×D705 #44444103

order29610
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D705
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)×D235)
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D141)
unambiguous semidirect productC47⋊(ΓL(1,𝔽8)×D15)
unambiguous semidirect product(C7×D705)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C7×C47 ⋊ C2×C3
HallC3×C5×ΓL(1,𝔽8)×C47 ⋊ C2
HallC3×ΓL(1,𝔽8)×C47 ⋊ D5
HallC5×C7×C47 ⋊ C3×D3
HallC7×C47 ⋊ C3×D15
HallC3×C5×ΓL(1,𝔽8) ⋊ D47
HallC5×C47 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ D235
SylowC47 ⋊ ΓL(1,𝔽8)×D15
HallC5×C7 ⋊ C3×D141
SylowC7 ⋊ C3×D705
SylowC5 ⋊ ΓL(1,𝔽8)×D141

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C47C2×C3
LCSG ▷ C3×C5×C7×C47
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4935

Conjugacy classes & character table

1770 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 40);