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C9×C7⋊AGL(1,𝔽11) #20294135

order6930
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C9×D7)
unambiguous semidirect product(C9×D77)⋊C5

Splittings

Fitting, HallC7×C9×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C9
HallC7×C9×C11⋊C5 ⋊ C2
HallC9×D77 ⋊ C5
HallC9×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ C2×C9
HallD77 ⋊ C5×C9
HallC9×C11 ⋊ C5×D7
HallC7×C9 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C9×D7
SylowC11 ⋊ C5×C9×D7
SylowC7 ⋊ C9×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC9C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C5×C9
FrattiniC3C3×C7⋊AGL(1,𝔽11)
FittingC7×C9×C11C2×C5
socleC3×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 22);