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C2×D57×ΓL(1,𝔽32) #47977684

order35340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D57×ΓL(1,𝔽32)
unambiguous semidirect product(C2×C3)⋊(D19×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C19)⋊(D3×ΓL(1,𝔽32))
unambiguous semidirect product(C2×C31×D57)⋊C5

Splittings

Fitting, socleC2×C3×C19×C31 ⋊ C2×C5
derived, HallC3×C19×C31 ⋊ C22×C5
HallC3×C19×ΓL(1,𝔽32) ⋊ C22
HallC2×C31×D57 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×D3
HallC19×C31 ⋊ C2×C5×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×D19
HallC3×C31 ⋊ C2×C5×D19
HallC3×C19 ⋊ C22×ΓL(1,𝔽32)
SylowC31 ⋊ C2×C5×D57
SylowC19 ⋊ C2×D3×ΓL(1,𝔽32)
SylowC3 ⋊ C2×D19×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2D57×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC3×C19×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C19×C31C2×C5
LCSG ▷ C3×C19×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3534

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 156);