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C3×D3×C11×ΓL(1,𝔽32) #44501798

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3×C11×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C2×C3×C11×ΓL(1,𝔽32))
unambiguous semidirect product(C3×D3×C31)⋊(C5×C11)

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derivedC3×C31 ⋊ C2×C3×C5×C11
HallC32×C11×ΓL(1,𝔽32) ⋊ C2
HallC3×D3×C11×C31 ⋊ C5
HallC32×ΓL(1,𝔽32) ⋊ C2×C11
HallC3×D3×C31 ⋊ C5×C11
HallC11×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ C2×C5×C11
HallC32×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3×C5×D3×C11
SylowC32 ⋊ C2×C11×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3×C11D3×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2046

Conjugacy classes & character table

1089 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 165);