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D5×ΓL(1,𝔽8)×C71 #28415879

order14910
automorphism?
homologyAbelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C71
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C71)
unambiguous semidirect product(C7×D5)⋊(C3×C71)
unambiguous semidirect product(C7×D5×C71)⋊C3

Splittings

Fitting, socle, HallC5×C7×C71 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C71
HallC5×ΓL(1,𝔽8)×C71 ⋊ C2
HallC7×D5×C71 ⋊ C3
HallC7×C71 ⋊ C3×D5
HallC5×C71 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C71
HallC7×D5 ⋊ C3×C71
SylowC7 ⋊ C3×D5×C71
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C71

Subgroups

subgroupG/H
center, hypercenterC71D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C71
FrattiniC1G
Fitting, socleC5×C7×C71C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2485

Conjugacy classes & character table

1420 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC71×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)⋊(C71⋊AGL(1,𝔽5)), AGL(1,𝔽5)×ΓL(1,𝔽8)×C71, …
maximal normal subgroup ofC71×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)⋊(C71⋊AGL(1,𝔽5)), AGL(1,𝔽5)×ΓL(1,𝔽8)×C71, …
maximal quotient ofDic5×ΓL(1,𝔽8)×C71, C2×D5×ΓL(1,𝔽8)×C71

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 42);