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C3×ΓL(1,𝔽8)×AGL(1,𝔽11) #20294153

order6930
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×ΓL(1,𝔽8))
unambiguous semidirect product(C3×D11)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D11)⋊(C3×C5)
unambiguous semidirect product(C7×AGL(1,𝔽11))⋊C32
unambiguous semidirect product(C3×ΓL(1,𝔽8)×D11)⋊C5
unambiguous semidirect product(C3×C7×AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC3×C7×C11 ⋊ C2×C3×C5
derived, HallC7×C11 ⋊ C2×C32×C5
HallC3×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC3×ΓL(1,𝔽8)×D11 ⋊ C5
HallC7×AGL(1,𝔽11) ⋊ C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C11⋊C5 ⋊ C2×C32
HallC7×D11 ⋊ C32×C5
HallC11⋊C5 ⋊ C2×C3×ΓL(1,𝔽8)
HallD11 ⋊ C3×C5×ΓL(1,𝔽8)
SylowC11 ⋊ C2×C3×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C32×C5
FrattiniC1G
Fitting, socleC3×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×AGL(1,𝔽11), AGL(1,𝔽11)×C3⋊AGL(1,𝔽7), D3×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofC3×AGL(1,𝔽7)×AGL(1,𝔽11), AGL(1,𝔽11)×C3⋊AGL(1,𝔽7), D3×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic11⋊C5, C2×C3×ΓL(1,𝔽8)×AGL(1,𝔽11), C3×ΓL(1,𝔽8)×D11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 40);