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C9×ΓL(1,𝔽32)⋊D11 #44501675

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

Aliases

direct productC9×ΓL(1,𝔽32)⋊D11

Splittings

Fitting, HallC9×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C5×C9
HallC9×C11×ΓL(1,𝔽32) ⋊ C2
HallC9×D341 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C9
HallC9×ΓL(1,𝔽32) ⋊ D11
HallD341 ⋊ C5×C9
HallC9×C31 ⋊ C5×D11
HallΓL(1,𝔽32) ⋊ C9×D11
HallC9×C11 ⋊ D31⋊C5
SylowC31 ⋊ C5×C9×D11
SylowC11 ⋊ C9×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC9ΓL(1,𝔽32)⋊D11
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C3×ΓL(1,𝔽32)⋊D11
FittingC9×C11×C31C2×C5
socle, cosocleC3×C11×C31C2×C3×C5
prime radicalC3×ΓL(1,𝔽32)⋊D11C3
LCSG ▷ C11×C31
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 42);