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C13×C3⋊D3×ΓL(1,𝔽32) #49136605

order36270
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×C3⋊D3×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(D3×C13×ΓL(1,𝔽32))
unambiguous semidirect product(C3⋊D3×C31)⋊(C5×C13)
unambiguous semidirect product(C13×C3⋊D3×C31)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC13C3⋊D3×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC32×C31C2×C5×C13
FrattiniC1G
Fitting, socleC32×C13×C31C2×C5
LCSG ▷ C32×C31
UCSC1 ◁ C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3627

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 125);