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C5×ΓL(1,𝔽8)⋊D151 #44540273

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

Aliases

direct productC5×ΓL(1,𝔽8)⋊D151
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D151)

Splittings

Fitting, socle, HallC5×C7×C151 ⋊ C2×C3
derived, HallC7×C151 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C151 ⋊ C2
HallC5×D1057 ⋊ C3
HallΓL(1,𝔽8)×C151 ⋊ C2×C5
HallD1057 ⋊ C3×C5
HallC5×C151 ⋊ AGL(1,𝔽7)
SylowC151 ⋊ C5×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D151
HallC5×C7 ⋊ C3×D151
HallΓL(1,𝔽8) ⋊ C5×D151
SylowC7 ⋊ C3×C5×D151

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D151
commutator, cosocle, hypocenterC7×C151C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C151C2×C3
LCSG ▷ C7×C151
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5285

Conjugacy classes & character table

1910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 42);