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C5×C11×C3⋊AGL(1,𝔽11) #31827647

order18150
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C5

Aliases

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

Splittings

Fitting, socleC3×C5×C112 ⋊ C2×C5
derivedC3×C11 ⋊ C2×C52×C11
HallC3×C5×C11×C11⋊C5 ⋊ C2
HallC5×C11×C11⋊C5 ⋊ D3
HallC11×D33 ⋊ C52
HallC3×C112 ⋊ C2×C52
SylowC112 ⋊ C52×D3
SylowC3 ⋊ C5×C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C52×C11
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C5×C11

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D3×C11×AGL(1,𝔽11), C5×D11×C3⋊AGL(1,𝔽11), C5×(C3⋊AGL(1,𝔽11))⋊D11, …
maximal normal subgroup ofC5×D3×C11×AGL(1,𝔽11), C5×D11×C3⋊AGL(1,𝔽11), C5×(C3⋊AGL(1,𝔽11))⋊D11, …
maximal quotient ofC5×C11×C3⋊(Dic11⋊C5), C2×C5×C11×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 131);