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D7×C9⋊AGL(1,𝔽11) #28357378

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

Aliases

direct productD7×C9⋊AGL(1,𝔽11)
unambiguous semidirect product(C9×D7)⋊AGL(1,𝔽11)
unambiguous semidirect product(D7×C11⋊C5)⋊D9
unambiguous semidirect product(D7×D99)⋊C5

Splittings

Fitting, derived, HallC7×C9×C11 ⋊ C22×C5
HallC7×C9×C11⋊C5 ⋊ C22
HallD7×D99 ⋊ C5
HallC9×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C2×D9
HallC9×C11 ⋊ C2×C5×D7
HallC7×C11 ⋊ C2×C5×D9
HallC7×C9 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D7×D9
SylowC11 ⋊ C5×D7×D9
SylowC9 ⋊ D7×AGL(1,𝔽11)
SylowC7 ⋊ C2×C9⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C9×C11C22×C5
FrattiniC3D7×C3⋊AGL(1,𝔽11)
socleC3×C7×C11C2×C5×D3
LCSG ▷ C7×C9×C11
UCSC1

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 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

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 45);