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C5×ΓL(1,𝔽8)×C79⋊C3 #38733484

order24885
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×ΓL(1,𝔽8)×C79⋊C3
unambiguous semidirect product(ΓL(1,𝔽8)×C79)⋊(C3×C5)
unambiguous semidirect product(C7×C79⋊C3)⋊(C3×C5)
unambiguous semidirect product#13110305⋊(C3×C5)
unambiguous semidirect product#13110306⋊(C3×C5)
unambiguous semidirect product(C5×C7×C79⋊C3)⋊C3
unambiguous semidirect product(C5×ΓL(1,𝔽8)×C79)⋊C3
unambiguous semidirect product(C5×#13110305)⋊C3
unambiguous semidirect product(C5×#13110306)⋊C3

Splittings

Fitting, socle, HallC5×C7×C79 ⋊ C32
derived, HallC7×C79 ⋊ C32×C5
HallC5×C79 ⋊ C3×ΓL(1,𝔽8)
SylowC79 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C79⋊C3
SylowC7 ⋊ C3×C5×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×C79⋊C3
commutator, cosocle, hypocenterC7×C79C32×C5
FrattiniC1G
Fitting, socleC5×C7×C79C32
LCSG ▷ C7×C79
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2765

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24885, 7);