Finite Group Databasebeta

← Prev (#37613367) Next (#37613369) →

ΓL(1,𝔽8)×C59⋊AGL(1,𝔽5) #37613368

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

Aliases

direct productΓL(1,𝔽8)×C59⋊AGL(1,𝔽5)
unambiguous semidirect productC59⋊(AGL(1,𝔽5)×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C59⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C59 ⋊ C3×C4
HallC7×C59⋊AGL(1,𝔽5) ⋊ C3
HallC5×ΓL(1,𝔽8)×C59 ⋊ C4
HallΓL(1,𝔽8)×C59 ⋊ AGL(1,𝔽5)
HallC7×C59 ⋊ C3×AGL(1,𝔽5)
HallC5×C59 ⋊ C4×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ Dic59
SylowC59 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic59
SylowC7 ⋊ C3×C59⋊AGL(1,𝔽5)
SylowC5 ⋊ ΓL(1,𝔽8)×Dic59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C59C3×C4
prime radicalD5×ΓL(1,𝔽8)×C59C2
cosocleC7×D5×C59C2×C3
LCSG ▷ C5×C7×C59
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2065

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 30);