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C3×C49⋊AGL(1,𝔽11) #30633477

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C3×D49)
unambiguous semidirect product(C3×D539)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C2×C5
derived, HallC11×C49 ⋊ C2×C3×C5
HallC3×C49×C11⋊C5 ⋊ C2
HallC3×D539 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×C3
HallD539 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ D49
HallC3×C49 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D49
SylowC49 ⋊ C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D49
SylowC11 ⋊ C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC3C49⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7C3×C7⋊AGL(1,𝔽11)
FittingC3×C11×C49C2×C5
socleC3×C7×C11C5×D7
LCSG ▷ C11×C49
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D49×AGL(1,𝔽11), D3×C49⋊AGL(1,𝔽11), D147⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D49×AGL(1,𝔽11), D3×C49⋊AGL(1,𝔽11), D147⋊AGL(1,𝔽11), …
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, 22);