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C32×C7×AGL(1,𝔽11) #20294159

order6930
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C32×C5×C7)
unambiguous semidirect product(C11⋊C5)⋊(C2×C32×C7)
unambiguous semidirect product(C3×D11)⋊(C3×C5×C7)
unambiguous semidirect product(C32×D11)⋊(C5×C7)
unambiguous semidirect product(C32×C7×D11)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C32×C5×C7
HallC32×C7×C11⋊C5 ⋊ C2
HallC32×C7×D11 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C7
HallC7×C11⋊C5 ⋊ C2×C32
HallC32×D11 ⋊ C5×C7
HallC7×D11 ⋊ C32×C5
HallC32×C11 ⋊ C2×C5×C7
HallC7×C11 ⋊ C2×C32×C5
HallC11⋊C5 ⋊ C2×C32×C7
HallD11 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC32×C7AGL(1,𝔽11)
commutator, hypocenterC11C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

693 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×D7×AGL(1,𝔽11), C3×D3×C7×AGL(1,𝔽11), C3×D21×AGL(1,𝔽11), …
maximal normal subgroup ofC32×D7×AGL(1,𝔽11), C3×D3×C7×AGL(1,𝔽11), C3×D21×AGL(1,𝔽11), …
maximal quotient ofC32×C7×Dic11⋊C5, C2×C32×C7×AGL(1,𝔽11), C32×C7×D11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 46);