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C3×C4×AGL(1,𝔽11) #13050320

order1320
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C4×C5)
unambiguous semidirect product(C4×D11)⋊(C3×C5)
unambiguous semidirect product(C3×C4×D11)⋊C5

Splittings

FittingC3×C4×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C4×C5
HallC3×C4×D11 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C4
HallC4×D11 ⋊ C3×C5
HallC11⋊C5 ⋊ C2×C3×C4
HallC3×C11 ⋊ C2×C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4AGL(1,𝔽11)
commutator, hypocenterC11C2×C3×C4×C5
FrattiniC2C2×C3×AGL(1,𝔽11)
FittingC3×C4×C11C2×C5
socleC2×C3×C11C22×C5
prime radicalC2×C3×AGL(1,𝔽11)C2
cosocleC2×C11C22×C3×C5
LCSG ▷ C11
UCSC1 ◁ C3×C4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D3×AGL(1,𝔽11), C2×C3×C4×AGL(1,𝔽11), C3×D4×AGL(1,𝔽11), …
maximal normal subgroup ofC4×D3×AGL(1,𝔽11), C2×C3×C4×AGL(1,𝔽11), C3×D4×AGL(1,𝔽11), …
maximal quotient ofC2×C3×C4×AGL(1,𝔽11), C3×C8×AGL(1,𝔽11), C3×#4313⋊C5, …
automorphism group ofC13×D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 24);