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C3×C5×C7×AGL(1,𝔽11) #26040482

order11550
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C7×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C52×C7)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C5×C7)
unambiguous semidirect product(C3×D11)⋊(C52×C7)
unambiguous semidirect product(C5×D11)⋊(C3×C5×C7)
unambiguous semidirect product(C3×C5×D11)⋊(C5×C7)
unambiguous semidirect product(C3×C7×D11)⋊C52
unambiguous semidirect product(C3×C5×C7×D11)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C52×C7
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ C2×C7
HallC3×C7×D11 ⋊ C52
HallC5×C11⋊C5 ⋊ C2×C3×C7
HallC3×C7×C11 ⋊ C2×C52
HallC7×D11 ⋊ C3×C52
HallC7×C11 ⋊ C2×C3×C52
HallC3×D11 ⋊ C52×C7
HallC3×C11 ⋊ C2×C52×C7
HallD11 ⋊ C3×C52×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C52×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C5×C7

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D7×AGL(1,𝔽11), C3×C7×D5×AGL(1,𝔽11), C3×D35×AGL(1,𝔽11), …
maximal normal subgroup ofC3×C5×D7×AGL(1,𝔽11), C3×C7×D5×AGL(1,𝔽11), C3×D35×AGL(1,𝔽11), …
maximal quotient ofC3×C5×C7×Dic11⋊C5, C2×C3×C5×C7×AGL(1,𝔽11), C5×C7×C9×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 46);