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C9×D11×ΓL(1,𝔽32) #44501669

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D11×ΓL(1,𝔽32)

Splittings

Fitting, HallC9×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C5×C9
HallC9×C11×ΓL(1,𝔽32) ⋊ C2
HallC9×D11×C31 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C9
HallD11×C31 ⋊ C5×C9
HallC9×C31 ⋊ C5×D11
HallC9×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C9×D11
SylowC11 ⋊ C2×C9×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC9D11×ΓL(1,𝔽32)
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C3×D11×ΓL(1,𝔽32)
FittingC9×C11×C31C2×C5
socle, cosocleC3×C11×C31C2×C3×C5
prime radicalC3×D11×ΓL(1,𝔽32)C3
LCSG ▷ C11×C31
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 36);