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C5×ΓL(1,𝔽8)×D71 #28415876

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

Aliases

direct productC5×ΓL(1,𝔽8)×D71
unambiguous semidirect product(C5×C7×D71)⋊C3

Splittings

Fitting, socle, HallC5×C7×C71 ⋊ C2×C3
derived, HallC7×C71 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C71 ⋊ C2
HallC5×C7×D71 ⋊ C3
HallΓL(1,𝔽8)×C71 ⋊ C2×C5
HallC7×D71 ⋊ C3×C5
HallC5×C71 ⋊ C2×ΓL(1,𝔽8)
SylowC71 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D71
SylowC7 ⋊ C3×C5×D71

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D71
commutator, cosocle, hypocenterC7×C71C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C71C2×C3
LCSG ▷ C7×C71
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2485

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D71, D71×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)×D71, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D71, D71×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)×D71, …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic71, C2×C5×ΓL(1,𝔽8)×D71

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 39);