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D5×ΓL(1,𝔽8)⋊D89 #49153147

order37380
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×ΓL(1,𝔽8)⋊D89
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊D89
unambiguous semidirect product(D5×C89)⋊AGL(1,𝔽7)
unambiguous semidirect product(D5×D623)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C89 ⋊ C22×C3
HallD5×D623 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C22
HallΓL(1,𝔽8)×C89 ⋊ C2×D5
HallC7×C89 ⋊ C2×C3×D5
HallC5×C89 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D89
SylowC89 ⋊ D5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D89
HallΓL(1,𝔽8) ⋊ D5×D89
SylowC7 ⋊ C3×D5×D89
SylowC5 ⋊ C2×ΓL(1,𝔽8)⋊D89

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C89C22×C3
LCSG ▷ C5×C7×C89
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3115

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 41);