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AGL(1,𝔽11)×D49⋊C3 #44568336

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

Aliases

direct productAGL(1,𝔽11)×D49⋊C3
unambiguous semidirect productD11⋊(C5×D49⋊C3)
unambiguous semidirect productD49⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(D11×D49⋊C3)⋊C5
unambiguous semidirect product(D49×AGL(1,𝔽11))⋊C3
unambiguous semidirect product(AGL(1,𝔽11)×C49⋊C3)⋊C2
unambiguous semidirect product(C11⋊C5×D49⋊C3)⋊C2
unambiguous semidirect product((C11⋊C5)⋊(D49⋊C3))⋊C2

Splittings

Fitting, derived, HallC11×C49 ⋊ C22×C3×C5
HallD49×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×C49⋊C3 ⋊ C22
HallD11×D49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C22×C3
HallD11×D49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC49⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D49⋊C3
SylowC49 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7AGL(1,𝔽7)×AGL(1,𝔽11)
socleC7×C11C2×C5×AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 539

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 38);