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C3×C5×C29×C22⋊ΓL(1,𝔽8) #49141671

order36540
automorphism?
homologyAbelianization (H1) = C32×C5×C29 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×C29×C22⋊ΓL(1,𝔽8)
unambiguous semidirect product(C22×C3)⋊(C5×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C3×C7)⋊(C5×A4×C29)
unambiguous semidirect product(C22×C3×C5)⋊(ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C3×C5×C7)⋊(A4×C29)
unambiguous semidirect product(C22×C3×C29)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7×C29)⋊(C5×A4)
unambiguous semidirect product(C22×C3×C5×C29)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C3×C5×C7×C29)⋊A4

Splittings

Fitting, socleC22×C3×C5×C7×C29 ⋊ C3
derived, HallC22×C7 ⋊ C32×C5×C29
HallC22×C5×C7×C29 ⋊ C32
HallC5×C7×C29 ⋊ C3×A4
HallC22×C7×C29 ⋊ C32×C5
HallC22×C5×C29 ⋊ C3×ΓL(1,𝔽8)
HallC7×C29 ⋊ C3×C5×A4
HallC22×C5×C7 ⋊ C32×C29
HallC22×C29 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×A4×C29
HallC22×C5 ⋊ C3×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C3×C5×A4×C29
SylowC22 ⋊ C3×C5×ΓL(1,𝔽8)×C29

Subgroups

subgroupG/H
center, hypercenterC3×C5×C29C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C5×C29
FrattiniC1G
Fitting, socleC22×C3×C5×C7×C29C3
LCSG ▷ C22×C7
UCSC1 ◁ C3×C5×C29

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12180

Conjugacy classes & character table

5220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 513);