Finite Group Databasebeta

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C3×D11×AGL(1,𝔽11) #20299999

order7260
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socle, HallC3×C112 ⋊ C22×C5
derived, SylowC112 ⋊ C22×C3×C5
HallC3×C11×C11⋊C5 ⋊ C22
HallC3×D112 ⋊ C5
HallC11×C11⋊C5 ⋊ C22×C3
HallD112 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC3D11×AGL(1,𝔽11)
commutator, hypocenterC112C22×C3×C5
FrattiniC1G
Fitting, socleC3×C112C22×C5
LCSG ▷ C112
UCSC1 ◁ C3

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×D11×AGL(1,𝔽11), C32×D11×AGL(1,𝔽11), C3×D11×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC9×D11×AGL(1,𝔽11), C32×D11×AGL(1,𝔽11), C3×AGL(1,𝔽11)2, …
maximal quotient ofC9×D11×AGL(1,𝔽11), C32×D11×AGL(1,𝔽11), C3×D11×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 99);