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C2×C11×C3⋊AGL(1,𝔽11) #20300059

order7260
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C11×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(D3×C11)
unambiguous semidirect product(C2×D33)⋊(C5×C11)

Splittings

Fitting, socleC2×C3×C112 ⋊ C2×C5
derivedC3×C11 ⋊ C22×C5×C11
HallC3×C11×C11⋊C5 ⋊ C22
HallC2×C11×D33 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D3
HallC3×C112 ⋊ C22×C5
SylowC112 ⋊ C2×C5×D3
SylowC3 ⋊ C2×C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C11

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11×C9⋊AGL(1,𝔽11), D3×C11×C3⋊AGL(1,𝔽11), C2×C3×C11×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×C3×C11×C3⋊AGL(1,𝔽11), C2×C11⋊C5×C3⋊AGL(1,𝔽11), C2×C5×C11×C3⋊AGL(1,𝔽11)
maximal quotient ofC2×C11×C9⋊AGL(1,𝔽11), D3×C11×C3⋊AGL(1,𝔽11), C2×C3×C11×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 159);