Finite Group Databasebeta

← Prev (#49088985) Next (#49088987) →

C11×ΓL(1,𝔽8)×ΓL(1,𝔽32) #49088986

order35805
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×ΓL(1,𝔽32)
unambiguous semidirect productC7⋊(C3×C11×ΓL(1,𝔽32))
unambiguous semidirect product(ΓL(1,𝔽8)×C31)⋊(C5×C11)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C3×C5
derived, HallC7×C31 ⋊ C3×C5×C11
HallC7×C11×ΓL(1,𝔽32) ⋊ C3
HallC11×ΓL(1,𝔽8)×C31 ⋊ C5
HallC7×ΓL(1,𝔽32) ⋊ C3×C11
HallΓL(1,𝔽8)×C31 ⋊ C5×C11
HallC11×C31 ⋊ C5×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC7×C31C3×C5×C11
FrattiniC1G
Fitting, socleC7×C11×C31C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

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(35805, 18);