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C2×C5×ΓL(1,𝔽8)⋊D59 #37613376

order24780
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×ΓL(1,𝔽8)⋊D59
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C5×D59)
unambiguous semidirect product(C2×C59)⋊(C5×AGL(1,𝔽7))
unambiguous semidirect product(C2×D413)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D413)⋊C3

Splittings

Fitting, socleC2×C5×C7×C59 ⋊ C2×C3
derived, HallC7×C59 ⋊ C22×C3×C5
HallC2×C5×D413 ⋊ C3
HallC5×ΓL(1,𝔽8)×C59 ⋊ C22
HallC5×C7×C59 ⋊ C22×C3
HallC2×D413 ⋊ C3×C5
HallΓL(1,𝔽8)×C59 ⋊ C22×C5
HallC5×C59 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D59
SylowC59 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D59
HallΓL(1,𝔽8) ⋊ C2×C5×D59
SylowC7 ⋊ C2×C3×C5×D59

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D59
commutator, cosocle, hypocenterC7×C59C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C59C2×C3
LCSG ▷ C7×C59
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4130

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 38);