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D3×C49×AGL(1,𝔽11) #44568341

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

Aliases

direct productD3×C49×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D3×C49)
unambiguous semidirect product(D3×D11)⋊(C5×C49)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C2×C49)
unambiguous semidirect product(D3×C11⋊C5)⋊(C2×C49)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C2×C49)
unambiguous semidirect product(D3×D11×C49)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C22×C5
derived, HallC3×C11 ⋊ C22×C5×C49
HallC3×C49×C11⋊C5 ⋊ C22
HallD3×D11×C49 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×D3
HallC11×C49 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C49
HallC3×C49 ⋊ C2×AGL(1,𝔽11)
HallD3×D11 ⋊ C5×C49
HallC11⋊C5 ⋊ C2×D3×C49
SylowC11 ⋊ C2×C5×D3×C49
SylowC3 ⋊ C2×C49×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC49D3×AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C5×C49
FrattiniC7D3×C7×AGL(1,𝔽11)
FittingC3×C11×C49C22×C5
socle, cosocleC3×C7×C11C22×C5×C7
prime radicalD3×C7×AGL(1,𝔽11)C7
LCSG ▷ C3×C11
UCSC1 ◁ C49

120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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) = 1617

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 43);