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C2×AGL(1,𝔽11)×C49⋊C3 #44568339

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽11)×C49⋊C3
unambiguous semidirect productD11⋊(C2×C5×C49⋊C3)
unambiguous semidirect product(C2×D11)⋊(C5×C49⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C22×C49⋊C3)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C49⋊C3)
unambiguous semidirect product(C2×D11×C49⋊C3)⋊C5
unambiguous semidirect product(C2×C49×AGL(1,𝔽11))⋊C3

Splittings

FittingC2×C11×C49 ⋊ C2×C3×C5
derived, HallC11×C49 ⋊ C22×C3×C5
HallC2×C49×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×C49⋊C3 ⋊ C22
HallC2×D11×C49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C22×C3
HallC2×D11×C49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C49⋊C3
SylowC49 ⋊ C2×C3×AGL(1,𝔽11)
HallC2×D11 ⋊ C5×C49⋊C3
SylowC11 ⋊ C22×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽11)×C49⋊C3
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C2×ΓL(1,𝔽8)×AGL(1,𝔽11)
FittingC2×C11×C49C2×C3×C5
socleC2×C7×C11C2×C5×ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1078

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 41);