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C5×C11×A4×ΓL(1,𝔽8) #28357632

order13860
automorphism?
homologyAbelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C11×A4×ΓL(1,𝔽8)
unambiguous semidirect product(C22×ΓL(1,𝔽8))⋊(C3×C5×C11)
unambiguous semidirect product(C7×A4)⋊(C3×C5×C11)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8))⋊(C3×C5×C11)
unambiguous semidirect product(C22×C5×ΓL(1,𝔽8))⋊(C3×C11)
unambiguous semidirect product(C5×C7×A4)⋊(C3×C11)
unambiguous semidirect product(C5×C22⋊ΓL(1,𝔽8))⋊(C3×C11)
unambiguous semidirect product(C22×C5×C11×ΓL(1,𝔽8))⋊C3
unambiguous semidirect product(C5×C7×C11×A4)⋊C3
unambiguous semidirect product(C5×C11×C22⋊ΓL(1,𝔽8))⋊C3

Splittings

Fitting, socle, HallC22×C5×C7×C11 ⋊ C32
derived, HallC22×C7 ⋊ C32×C5×C11
HallC5×C7×C11 ⋊ C3×A4
HallC22×C7×C11 ⋊ C32×C5
HallC22×C5×C11 ⋊ C3×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C32×C11
HallC7×C11 ⋊ C3×C5×A4
HallC22×C11 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C11×A4
HallC22×C5 ⋊ C3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×C11×A4
SylowC22 ⋊ C3×C5×C11×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5×C11A4×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C7×C11C32
LCSG ▷ C22×C7
UCSC1 ◁ C5×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 299);