Finite Group Databasebeta

← Prev (#44501692) Next (#44501694) →

ΓL(1,𝔽32)×D99 #44501693

order30690
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽32)×D99
unambiguous semidirect productC9⋊(D11×ΓL(1,𝔽32))

Splittings

Fitting, derived, HallC9×C11×C31 ⋊ C2×C5
HallC9×C11×ΓL(1,𝔽32) ⋊ C2
HallC31×D99 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ D9
HallC9×ΓL(1,𝔽32) ⋊ D11
HallC11×C31 ⋊ C5×D9
HallC9×C31 ⋊ C5×D11
HallC9×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D99
SylowC11 ⋊ D9×ΓL(1,𝔽32)
SylowC9 ⋊ D11×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C11×C31C2×C5
FrattiniC3D33×ΓL(1,𝔽32)
socleC3×C11×C31C5×D3
LCSG ▷ C9×C11×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 60);