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C11×D9×ΓL(1,𝔽32) #44501681

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D9×ΓL(1,𝔽32)
unambiguous semidirect productC9⋊(C2×C11×ΓL(1,𝔽32))
unambiguous semidirect product(D9×C31)⋊(C5×C11)

Splittings

Fitting, HallC9×C11×C31 ⋊ C2×C5
derived, HallC9×C31 ⋊ C2×C5×C11
HallC9×C11×ΓL(1,𝔽32) ⋊ C2
HallC11×D9×C31 ⋊ C5
HallC9×ΓL(1,𝔽32) ⋊ C2×C11
HallD9×C31 ⋊ C5×C11
HallC11×C31 ⋊ C5×D9
HallC9×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C11×D9
SylowC9 ⋊ C2×C11×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC11D9×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC9×C31C2×C5×C11
FrattiniC3D3×C11×ΓL(1,𝔽32)
FittingC9×C11×C31C2×C5
socleC3×C11×C31C5×D3
LCSG ▷ C9×C31
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 48);