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AGL(1,𝔽11)×D7⋊C9 #28357371

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽11)×D7⋊C9
unambiguous semidirect productD7⋊(C9×AGL(1,𝔽11))
unambiguous semidirect productD11⋊(C5×D7⋊C9)
unambiguous semidirect product(D7×AGL(1,𝔽11))⋊C9
unambiguous semidirect product(D11×D7⋊C9)⋊C5
unambiguous semidirect product(C7⋊C9×AGL(1,𝔽11))⋊C2
unambiguous semidirect product(C11⋊C5×D7⋊C9)⋊C2
unambiguous semidirect product((C11⋊C5)⋊(D7⋊C9))⋊C2

Splittings

derived, HallC7×C11 ⋊ C22×C5×C9
HallC11⋊C5×C7⋊C9 ⋊ C22
HallD11×D7⋊C9 ⋊ C5
HallD7×AGL(1,𝔽11) ⋊ C9
HallC11×C7⋊C9 ⋊ C22×C5
HallC7×C11⋊C5 ⋊ C22×C9
HallD7×D11 ⋊ C5×C9
HallC7⋊C9 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D7⋊C9
SylowC11 ⋊ C2×C5×D7⋊C9
SylowC7 ⋊ C2×C9×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC3AGL(1,𝔽7)×AGL(1,𝔽11)
commutator, hypocenterC7×C11C22×C5×C9
Fitting, socle, cosocleC3×C7×C11C22×C3×C5
prime radicalC3×D7×AGL(1,𝔽11)C3
LCSG ▷ C7×C11
UCSC1 ◁ C3

120 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 46 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

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 38);