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C3×D35×ΓL(1,𝔽32) #45654476

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×D35×ΓL(1,𝔽32)
unambiguous semidirect productC5⋊(C3×D7×ΓL(1,𝔽32))
unambiguous semidirect product(C3×C31×D35)⋊C5

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C5
derivedC5×C7×C31 ⋊ C2×C3×C5
HallC3×C5×C7×ΓL(1,𝔽32) ⋊ C2
HallC5×C7×ΓL(1,𝔽32) ⋊ C2×C3
HallC3×C5×ΓL(1,𝔽32) ⋊ D7
HallC5×ΓL(1,𝔽32) ⋊ C3×D7
HallC3×C7×C31 ⋊ C5×D5
HallC7×C31 ⋊ C3×C5×D5
HallC3×C31 ⋊ C5×D35
SylowC31 ⋊ C3×C5×D35
HallC3×C7 ⋊ D5×ΓL(1,𝔽32)
SylowC7 ⋊ C3×D5×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3D35×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC5×C7×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C5
LCSG ▷ C5×C7×C31
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 112);