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C3×C11×C3⋊AGL(1,𝔽11) #24926151

order10890
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC32×C112 ⋊ C2×C5
derivedC3×C11 ⋊ C2×C3×C5×C11
HallC32×C11×C11⋊C5 ⋊ C2
HallC3×C11×D33 ⋊ C5
HallC11×C11⋊C5 ⋊ C3×D3
SylowC112 ⋊ C3×C5×D3
SylowC32 ⋊ C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3×C11C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C3×C11

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

594 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×C11×AGL(1,𝔽11), C3×D11×C3⋊AGL(1,𝔽11), C3×(C3⋊AGL(1,𝔽11))⋊D11, …
maximal normal subgroup ofC3×D3×C11×AGL(1,𝔽11), C3×D11×C3⋊AGL(1,𝔽11), C3×(C3⋊AGL(1,𝔽11))⋊D11, …
maximal quotient ofC3×C11×C3⋊(Dic11⋊C5), C2×C3×C11×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 100);