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C49×AGL(1,𝔽11) #19129115

order5390
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C49)
unambiguous semidirect product(C11⋊C5)⋊(C2×C49)
unambiguous semidirect product(D11×C49)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC49AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C49
FrattiniC7C7×AGL(1,𝔽11)
FittingC11×C49C2×C5
socleC7×C11C2×C5×C7
LCSG ▷ C11
UCSC1 ◁ C49

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

539 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C49×AGL(1,𝔽11), C49×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×C49⋊C3, …
maximal normal subgroup ofC3×C49×AGL(1,𝔽11), AGL(1,𝔽11)×C49⋊C3, C5×C49×AGL(1,𝔽11)
maximal quotient ofC3×C49×AGL(1,𝔽11), C49×C3⋊AGL(1,𝔽11), C49×D11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5390, 2);