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ΓL(1,𝔽8)⋊(D151⋊C5) #44540301

order31710
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productΓL(1,𝔽8)⋊(D151⋊C5)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D151)⋊C5

Splittings

Fitting, socle, derived, HallC7×C151 ⋊ C2×C3×C5
HallΓL(1,𝔽8)×C151⋊C5 ⋊ C2
HallC7⋊(D151⋊C5) ⋊ C3
HallΓL(1,𝔽8)⋊D151 ⋊ C5
HallC7×C151⋊C5 ⋊ C2×C3
HallΓL(1,𝔽8)×C151 ⋊ C2×C5
HallD1057 ⋊ C3×C5
HallC151⋊C5 ⋊ AGL(1,𝔽7)
SylowC151 ⋊ C5×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D151⋊C5
SylowC7 ⋊ C3×D151⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C151C2×C3×C5
LCSG ▷ C7×C151
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1057

Polycyclic presentation:

2,3,5,7,151|d^a=d^6,e^a=e^150,d^b=d^2,e^c=e^59

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 70);