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C2×C3×C49×AGL(1,𝔽11) #44568361

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C49 · Schur multiplier (H2) = C2

Aliases

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

Splittings

FittingC2×C3×C11×C49 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C5×C49
HallC3×C49×C11⋊C5 ⋊ C22
HallC2×C3×D11×C49 ⋊ C5
HallC49×C11⋊C5 ⋊ C22×C3
HallC2×D11×C49 ⋊ C3×C5
HallC3×C11×C49 ⋊ C22×C5
HallC11×C49 ⋊ C22×C3×C5
HallC3×C11⋊C5 ⋊ C22×C49
HallC2×C3×D11 ⋊ C5×C49
HallC11⋊C5 ⋊ C22×C3×C49
HallC2×D11 ⋊ C3×C5×C49
HallC3×C11 ⋊ C22×C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C49AGL(1,𝔽11)
commutator, hypocenterC11C22×C3×C5×C49
FrattiniC7C2×C3×C7×AGL(1,𝔽11)
FittingC2×C3×C11×C49C2×C5
socleC2×C3×C7×C11C2×C5×C7
prime radicalC2×C3×C7×AGL(1,𝔽11)C7
cosocleC7×C11C22×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C2×C3×C49

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

3234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 63);