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C2×C49⋊AGL(1,𝔽11) #24924704

order10780
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C49⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C49)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊C5)⋊D49
unambiguous semidirect product(C2×D539)⋊C5

Splittings

FittingC2×C11×C49 ⋊ C2×C5
derived, HallC11×C49 ⋊ C22×C5
HallC49×C11⋊C5 ⋊ C22
HallC2×D539 ⋊ C5
HallC11⋊C5 ⋊ C2×D49
SylowC49 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D49

Subgroups

subgroupG/H
center, hypercenterC2C49⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C49C22×C5
FrattiniC7C2×C7⋊AGL(1,𝔽11)
FittingC2×C11×C49C2×C5
socleC2×C7×C11C5×D7
LCSG ▷ C11×C49
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

358 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C11⋊C5)⋊(D49⋊C3), D3×C49⋊AGL(1,𝔽11), C2×C3×C49⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×(C11⋊C5)⋊(D49⋊C3), C2×C3×C49⋊AGL(1,𝔽11)
maximal quotient ofD3×C49⋊AGL(1,𝔽11), C2×C3×C49⋊AGL(1,𝔽11), C2×C3⋊(C49⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 17);