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D3×C11×AGL(1,𝔽11) #20300003

order7260
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D3×C11)
unambiguous semidirect product(D3×D11)⋊(C5×C11)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C2×C11)
unambiguous semidirect product(D3×C11⋊C5)⋊(C2×C11)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C2×C11)

Splittings

Fitting, socle, HallC3×C112 ⋊ C22×C5
derivedC3×C11 ⋊ C22×C5×C11
HallC3×C11×C11⋊C5 ⋊ C22
HallD3×C11×D11 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D3
SylowC112 ⋊ C2×C5×D3
SylowC3 ⋊ C2×C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC11D3×AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C5×C11
FrattiniC1G
Fitting, socleC3×C112C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C11

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

363 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D9×AGL(1,𝔽11), C3×D3×C11×AGL(1,𝔽11), D3×C11×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D3×C11×AGL(1,𝔽11), D3×C11⋊C5×AGL(1,𝔽11), C5×D3×C11×AGL(1,𝔽11)
maximal quotient ofC11×D9×AGL(1,𝔽11), C3×D3×C11×AGL(1,𝔽11), D3×C11×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 103);