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C3⋊(C5⋊(ΓL(1,𝔽8)⋊D47)) #44444101

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

Aliases

unambiguous semidirect productC3⋊(C5⋊(ΓL(1,𝔽8)⋊D47))
unambiguous semidirect productC5⋊(C3⋊(ΓL(1,𝔽8)⋊D47))
unambiguous semidirect productΓL(1,𝔽8)⋊D705
unambiguous semidirect productC47⋊(C3⋊(C5⋊AGL(1,𝔽7)))
unambiguous semidirect productD4935⋊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 ⋊ C3⋊AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ D235
SylowC47 ⋊ C3⋊(C5⋊AGL(1,𝔽7))
HallC5×C7 ⋊ C3×D141
SylowC7 ⋊ C3×D705
SylowC5 ⋊ C3⋊(ΓL(1,𝔽8)⋊D47)

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

Polycyclic presentation:

2,3^2,5,7,47|c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^46,e^b=e^2

Conjugacy classes & character table

1767 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 38);