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C4×C3⋊AGL(1,𝔽11) #13050330

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

Aliases

direct productC4×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C4×D33)⋊C5

Splittings

FittingC3×C4×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C4×C5
HallC4×D33 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C4
HallC11⋊C5 ⋊ C4×D3
SylowC11 ⋊ C4×C5×D3
SylowC3 ⋊ C4×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC4C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C2×C4×C5
FrattiniC2C2×C3⋊AGL(1,𝔽11)
FittingC3×C4×C11C2×C5
socle, cosocleC2×C3×C11C22×C5
prime radicalC2×C3⋊AGL(1,𝔽11)C2
LCSG ▷ C3×C11
UCSC1 ◁ C4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D3×AGL(1,𝔽11), C2×C4×C3⋊AGL(1,𝔽11), D4×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC4×D3×AGL(1,𝔽11), C2×C4×C3⋊AGL(1,𝔽11), D4×C3⋊AGL(1,𝔽11), …
maximal quotient ofC2×C4×C3⋊AGL(1,𝔽11), C8×C3⋊AGL(1,𝔽11), #72216768, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 34);