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C2×C49×C3⋊AGL(1,𝔽11) #44568364

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

Aliases

direct productC2×C49×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C49×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(D3×C49)
unambiguous semidirect product(C2×D33)⋊(C5×C49)
unambiguous semidirect product(C2×C49×D33)⋊C5

Splittings

FittingC2×C3×C11×C49 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C5×C49
HallC3×C49×C11⋊C5 ⋊ C22
HallC2×C49×D33 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×D3
HallC3×C11×C49 ⋊ C22×C5
HallC11×C49 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C49
HallC3×C49 ⋊ C2×AGL(1,𝔽11)
HallC2×D33 ⋊ C5×C49
HallC11⋊C5 ⋊ C2×D3×C49
SylowC11 ⋊ C2×C5×D3×C49
SylowC3 ⋊ C2×C49×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C49C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C5×C49
FrattiniC7C2×C7×C3⋊AGL(1,𝔽11)
FittingC2×C3×C11×C49C2×C5
socleC2×C3×C7×C11C2×C5×C7
prime radicalC2×C7×C3⋊AGL(1,𝔽11)C7
cosocleC3×C7×C11C22×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C49

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 66);