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D5×ΓL(1,𝔽8)×D59 #37613374

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

Aliases

direct productD5×ΓL(1,𝔽8)×D59
unambiguous semidirect product(D5×C59)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C5×D59)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect productD295⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D5×D59)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C59 ⋊ C22×C3
HallC7×D5×D59 ⋊ C3
HallC5×ΓL(1,𝔽8)×C59 ⋊ C22
HallΓL(1,𝔽8)×C59 ⋊ C2×D5
HallC7×C59 ⋊ C2×C3×D5
HallC5×C59 ⋊ C22×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×D59
SylowC59 ⋊ C2×D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D59
SylowC7 ⋊ C3×D5×D59
SylowC5 ⋊ C2×ΓL(1,𝔽8)×D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C59C22×C3
LCSG ▷ C5×C7×C59
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2065

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 36);