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C3×C53×AGL(1,𝔽11) #31775824

order17490
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productC3×C53×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C53)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C53)
unambiguous semidirect product(C3×D11)⋊(C5×C53)
unambiguous semidirect product(D11×C53)⋊(C3×C5)
unambiguous semidirect product(C3×D11×C53)⋊C5

Splittings

Fitting, socle, HallC3×C11×C53 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C53
HallC3×C53×C11⋊C5 ⋊ C2
HallC3×D11×C53 ⋊ C5
HallC53×C11⋊C5 ⋊ C2×C3
HallD11×C53 ⋊ C3×C5
HallC11×C53 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C53
HallC3×D11 ⋊ C5×C53
HallC11⋊C5 ⋊ C2×C3×C53
HallC3×C11 ⋊ C2×C5×C53
HallD11 ⋊ C3×C5×C53

Subgroups

subgroupG/H
center, hypercenterC3×C53AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C53
FrattiniC1G
Fitting, socleC3×C11×C53C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1749

Conjugacy classes & character table

1749 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D53×AGL(1,𝔽11), D3×C53×AGL(1,𝔽11), AGL(1,𝔽11)×D159, …
maximal normal subgroup ofC3×D53×AGL(1,𝔽11), D3×C53×AGL(1,𝔽11), AGL(1,𝔽11)×D159, …
maximal quotient ofC3×C53×Dic11⋊C5, C2×C3×C53×AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 19);