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C3×D39×ΓL(1,𝔽32) #49136603

order36270
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×D39×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C3×D13×ΓL(1,𝔽32))
unambiguous semidirect product(C3×C31×D39)⋊C5

Splittings

Fitting, socle, HallC32×C13×C31 ⋊ C2×C5
derivedC3×C13×C31 ⋊ C2×C3×C5
HallC32×C13×ΓL(1,𝔽32) ⋊ C2
HallC3×C31×D39 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3×D3
HallC32×ΓL(1,𝔽32) ⋊ D13
HallC13×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ C5×D13
HallC32×C13 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3×C5×D39
SylowC13 ⋊ C3×D3×ΓL(1,𝔽32)
SylowC32 ⋊ D13×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3D39×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC3×C13×C31C2×C3×C5
FrattiniC1G
Fitting, socleC32×C13×C31C2×C5
LCSG ▷ C3×C13×C31
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2418

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(36270, 123);