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C7×C9×AGL(1,𝔽11) #20294133

order6930
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC7×C9×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C7×C9
HallC7×C9×C11⋊C5 ⋊ C2
HallC7×C9×D11 ⋊ C5
HallC9×C11⋊C5 ⋊ C2×C7
HallC7×C11⋊C5 ⋊ C2×C9
HallC9×D11 ⋊ C5×C7
HallC7×D11 ⋊ C5×C9
HallC9×C11 ⋊ C2×C5×C7
HallC7×C11 ⋊ C2×C5×C9
HallC11⋊C5 ⋊ C2×C7×C9
HallD11 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C7×C9
FrattiniC3C3×C7×AGL(1,𝔽11)
FittingC7×C9×C11C2×C5
socleC3×C7×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

693 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×D7×AGL(1,𝔽11), C7×D9×AGL(1,𝔽11), AGL(1,𝔽11)×D63, …
maximal normal subgroup ofC9×D7×AGL(1,𝔽11), C7×D9×AGL(1,𝔽11), AGL(1,𝔽11)×D63, …
maximal quotient ofC7×C9×Dic11⋊C5, C2×C7×C9×AGL(1,𝔽11), C7×C9×D11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 20);