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C3×C49×AGL(1,𝔽11) #30633475

order16170
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C49)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C49)
unambiguous semidirect product(C3×D11)⋊(C5×C49)
unambiguous semidirect product(C3×D11×C49)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C49
HallC3×C49×C11⋊C5 ⋊ C2
HallC3×D11×C49 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×C3
HallD11×C49 ⋊ C3×C5
HallC11×C49 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C49
HallC3×D11 ⋊ C5×C49
HallC11⋊C5 ⋊ C2×C3×C49
HallC3×C11 ⋊ C2×C5×C49
HallD11 ⋊ C3×C5×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49AGL(1,𝔽11)
commutator, hypocenterC11C2×C3×C5×C49
FrattiniC7C3×C7×AGL(1,𝔽11)
FittingC3×C11×C49C2×C5
socleC3×C7×C11C2×C5×C7
prime radicalC3×C7×AGL(1,𝔽11)C7
cosocleC7×C11C2×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C3×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D49×AGL(1,𝔽11), D3×C49×AGL(1,𝔽11), AGL(1,𝔽11)×D147, …
maximal normal subgroup ofC3×D49×AGL(1,𝔽11), D3×C49×AGL(1,𝔽11), AGL(1,𝔽11)×D147, …
maximal quotient ofC3×C49×Dic11⋊C5, C2×C3×C49×AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 20);