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C5×ΓL(1,𝔽8)⋊D79 #30658747

order16590
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊D79
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D79)

Splittings

Fitting, socle, HallC5×C7×C79 ⋊ C2×C3
derived, HallC7×C79 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C79 ⋊ C2
HallC5×D553 ⋊ C3
HallΓL(1,𝔽8)×C79 ⋊ C2×C5
HallD553 ⋊ C3×C5
HallC5×C79 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D79
SylowC79 ⋊ C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×D79
HallΓL(1,𝔽8) ⋊ C5×D79
SylowC7 ⋊ C3×C5×D79

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D79
commutator, cosocle, hypocenterC7×C79C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C79C2×C3
LCSG ▷ C7×C79
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2765

Conjugacy classes & character table

1010 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D79, D5×ΓL(1,𝔽8)⋊D79, (C5⋊AGL(1,𝔽7))⋊D79, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D79, D5×ΓL(1,𝔽8)⋊D79, (C5⋊AGL(1,𝔽7))⋊D79, …
maximal quotient ofC5×ΓL(1,𝔽8)⋊Dic79, C2×C5×ΓL(1,𝔽8)⋊D79

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16590, 30);