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C5×ΓL(1,𝔽8)×Dic59 #37613356

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

Aliases

direct productC5×ΓL(1,𝔽8)×Dic59
unambiguous semidirect productC59⋊(C4×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×Dic59)⋊(C3×C5)
unambiguous semidirect product(C5×C7×Dic59)⋊C3

Splittings

derived, HallC7×C59 ⋊ C3×C4×C5
HallC5×C7×Dic59 ⋊ C3
HallC5×ΓL(1,𝔽8)×C59 ⋊ C4
HallC5×C7×C59 ⋊ C3×C4
HallC7×Dic59 ⋊ C3×C5
HallΓL(1,𝔽8)×C59 ⋊ C4×C5
HallC5×C59 ⋊ C4×ΓL(1,𝔽8)
SylowC59 ⋊ C4×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic59
SylowC7 ⋊ C3×C5×Dic59

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×D59
commutator, hypocenterC7×C59C3×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)×D59
Fitting, socleC2×C5×C7×C59C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C59C2
cosocleC2×C7×C59C2×C3×C5
LCSG ▷ C7×C59
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8260

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 18);