Finite Group Databasebeta

← Prev (#26040488) Next (#26040490) →

C5×C7×C3⋊AGL(1,𝔽11) #26040489

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

Aliases

direct productC5×C7×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C5×C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C5×D3×C7)
unambiguous semidirect productD33⋊(C52×C7)
unambiguous semidirect product(C5×D33)⋊(C5×C7)
unambiguous semidirect product(C7×D33)⋊C52
unambiguous semidirect product(C5×C7×D33)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C52×C7
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ C2×C7
HallC7×D33 ⋊ C52
HallC5×C11⋊C5 ⋊ D3×C7
HallC3×C7×C11 ⋊ C2×C52
HallC7×C11 ⋊ C52×D3
HallD33 ⋊ C52×C7
HallC3×C7 ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×D3×C7
SylowC3 ⋊ C5×C7×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C52×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C5×C7

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

630 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×C7×AGL(1,𝔽11), C5×D7×C3⋊AGL(1,𝔽11), C5×D21⋊AGL(1,𝔽11), …
maximal normal subgroup ofC5×D3×C7×AGL(1,𝔽11), C5×D7×C3⋊AGL(1,𝔽11), C5×D21⋊AGL(1,𝔽11), …
maximal quotient ofC5×C7×C3⋊(Dic11⋊C5), C2×C5×C7×C3⋊AGL(1,𝔽11), C5×C7×C9⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 53);