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D5×ΓL(1,𝔽8)×C151 #44540277

order31710
automorphism?
homologyAbelianization (H1) = C2×C3×C151 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C151
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C151)
unambiguous semidirect product(C7×D5)⋊(C3×C151)

Splittings

Fitting, socle, HallC5×C7×C151 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C151
HallC5×ΓL(1,𝔽8)×C151 ⋊ C2
HallC7×D5×C151 ⋊ C3
HallC7×C151 ⋊ C3×D5
HallC5×C151 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C151
HallC7×D5 ⋊ C3×C151
SylowC7 ⋊ C3×D5×C151
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C151

Subgroups

subgroupG/H
center, hypercenterC151D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C151
FrattiniC1G
Fitting, socleC5×C7×C151C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C151

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5285

Conjugacy classes & character table

3020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 46);