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C7×D9×AGL(1,𝔽11) #28357376

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D9×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C7×D9)
unambiguous semidirect product(D9×D11)⋊(C5×C7)
unambiguous semidirect product(C9×AGL(1,𝔽11))⋊(C2×C7)
unambiguous semidirect product(D9×C11⋊C5)⋊(C2×C7)
unambiguous semidirect product(C9⋊AGL(1,𝔽11))⋊(C2×C7)
unambiguous semidirect product(C7×D9×D11)⋊C5

Splittings

Fitting, HallC7×C9×C11 ⋊ C22×C5
derived, HallC9×C11 ⋊ C22×C5×C7
HallC7×C9×C11⋊C5 ⋊ C22
HallC7×D9×D11 ⋊ C5
HallC9×C11⋊C5 ⋊ C22×C7
HallD9×D11 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C2×D9
HallC7×C11 ⋊ C2×C5×D9
HallC7×C9 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C7×D9
SylowC11 ⋊ C2×C5×C7×D9
SylowC9 ⋊ C2×C7×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC7D9×AGL(1,𝔽11)
commutator, cosocle, hypocenterC9×C11C22×C5×C7
FrattiniC3D3×C7×AGL(1,𝔽11)
FittingC7×C9×C11C22×C5
socleC3×C7×C11C2×C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C7

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 693

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 43);