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C49×C3⋊AGL(1,𝔽11) #30633479

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

Aliases

direct productC49×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C49×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D3×C49)
unambiguous semidirect productD33⋊(C5×C49)
unambiguous semidirect product(C49×D33)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C49
HallC3×C49×C11⋊C5 ⋊ C2
HallC49×D33 ⋊ C5
HallC49×C11⋊C5 ⋊ D3
HallC11×C49 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C49
HallC3×C49 ⋊ AGL(1,𝔽11)
HallD33 ⋊ C5×C49
HallC11⋊C5 ⋊ D3×C49
SylowC11 ⋊ C5×D3×C49
SylowC3 ⋊ C49×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC49C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C2×C5×C49
FrattiniC7C7×C3⋊AGL(1,𝔽11)
FittingC3×C11×C49C2×C5
socle, cosocleC3×C7×C11C2×C5×C7
prime radicalC7×C3⋊AGL(1,𝔽11)C7
LCSG ▷ C3×C11
UCSC1 ◁ C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C49×AGL(1,𝔽11), D49×C3⋊AGL(1,𝔽11), D147⋊AGL(1,𝔽11), …
maximal normal subgroup ofD3×C49×AGL(1,𝔽11), D49×C3⋊AGL(1,𝔽11), D147⋊AGL(1,𝔽11), …
maximal quotient ofC49×C3⋊(Dic11⋊C5), C2×C49×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 24);