Finite Group Databasebeta

← Prev (#49151201) Next (#49151203) →

C3×C5×ΓL(1,𝔽8)⋊D59 #49151202

order37170
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)⋊D59
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C5×D59)
unambiguous semidirect productC59⋊(C3×C5×AGL(1,𝔽7))
unambiguous semidirect productD413⋊(C32×C5)
unambiguous semidirect product(C3×D413)⋊(C3×C5)
unambiguous semidirect product(C5×D413)⋊C32
unambiguous semidirect product(C3×C5×D413)⋊C3

Splittings

Fitting, socleC3×C5×C7×C59 ⋊ C2×C3
derived, HallC7×C59 ⋊ C2×C32×C5
HallC3×C5×ΓL(1,𝔽8)×C59 ⋊ C2
HallC5×D413 ⋊ C32
HallC3×ΓL(1,𝔽8)×C59 ⋊ C2×C5
HallC5×C7×C59 ⋊ C2×C32
HallD413 ⋊ C32×C5
HallC3×C5×ΓL(1,𝔽8) ⋊ D59
HallC5×C59 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C5×D59
SylowC59 ⋊ C3×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C32×D59
SylowC7 ⋊ C32×C5×D59

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D59
commutator, cosocle, hypocenterC7×C59C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C59C2×C3
LCSG ▷ C7×C59
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6195

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37170, 27);