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C4×C5×ΓL(1,𝔽8)×C59 #37613340

order24780
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×ΓL(1,𝔽8)×C59
unambiguous semidirect product(C4×C7)⋊(C3×C5×C59)
unambiguous semidirect product(C4×C5×C7)⋊(C3×C59)
unambiguous semidirect product(C4×C7×C59)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C7×C59)⋊C3

Splittings

Fitting, HallC4×C5×C7×C59 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C5×C59
HallC5×C7×C59 ⋊ C3×C4
HallC4×C7×C59 ⋊ C3×C5
HallC7×C59 ⋊ C3×C4×C5
HallC4×C5×C7 ⋊ C3×C59
HallC5×C7 ⋊ C3×C4×C59
HallC4×C7 ⋊ C3×C5×C59

Subgroups

subgroupG/H
center, hypercenterC4×C5×C59ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C5×C59
FrattiniC2C2×C5×ΓL(1,𝔽8)×C59
FittingC4×C5×C7×C59C3
socleC2×C5×C7×C59C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C59C2
cosocleC2×C7C2×C3×C5×C59
LCSG ▷ C7
UCSC1 ◁ C4×C5×C59

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8260

Conjugacy classes & character table

5900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 2);