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AGL(1,𝔽7)×D445 #49153146

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

Aliases

direct productAGL(1,𝔽7)×D445
unambiguous semidirect productD7⋊(C3×D445)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊D89
unambiguous semidirect product(AGL(1,𝔽7)×C89)⋊D5
unambiguous semidirect product(D7×D445)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C89 ⋊ C22×C3
HallD7×D445 ⋊ 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) ⋊ C2×D445
SylowC7 ⋊ C2×C3×D445
SylowC5 ⋊ AGL(1,𝔽7)×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

1568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 40);