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ΓL(1,𝔽8)×D71⋊C5 #28415883

order14910
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D71⋊C5
unambiguous semidirect productD71⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C71⋊C5)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D71)⋊C5
unambiguous semidirect product(C7×D71⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC7×C71 ⋊ C2×C3×C5
HallΓL(1,𝔽8)×C71⋊C5 ⋊ C2
HallC7×D71⋊C5 ⋊ C3
HallΓL(1,𝔽8)×D71 ⋊ C5
HallC7×C71⋊C5 ⋊ C2×C3
HallΓL(1,𝔽8)×C71 ⋊ C2×C5
HallC7×D71 ⋊ C3×C5
HallC71⋊C5 ⋊ C2×ΓL(1,𝔽8)
HallD71 ⋊ C5×ΓL(1,𝔽8)
SylowC71 ⋊ C2×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D71⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C71C2×C3×C5
LCSG ▷ C7×C71
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 497

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D71⋊C5, C2×ΓL(1,𝔽8)×D71⋊C5
maximal normal subgroup ofAGL(1,𝔽7)×D71⋊C5, C2×ΓL(1,𝔽8)×D71⋊C5
maximal quotient ofΓL(1,𝔽8)×Dic71⋊C5, C2×ΓL(1,𝔽8)×D71⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 46);