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C7⋊C9×AGL(1,𝔽11) #20294147

order6930
automorphism?
homologyAbelianization (H1) = C2×C5×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(C7×AGL(1,𝔽11))⋊C9
unambiguous semidirect product(D11×C7⋊C9)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, Frattini, hypercenterC3ΓL(1,𝔽8)×AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C5×C9
Fitting, socleC3×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D7⋊C9, C2×C7⋊C9×AGL(1,𝔽11), C5×C7⋊C9×AGL(1,𝔽11), …
maximal normal subgroup ofAGL(1,𝔽11)×D7⋊C9, C2×C7⋊C9×AGL(1,𝔽11), C5×C7⋊C9×AGL(1,𝔽11)
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, 34);