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C3×AGL(1,𝔽16) #10624317

order720
isoclinismisoclinic class of AGL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,𝔽16)
unambiguous semidirect product(C24⋊C5)⋊C32
unambiguous semidirect product(C3×C22⋊A4)⋊C5
unambiguous semidirect product(C3×C24⋊C5)⋊C3

Splittings

Fitting, socleC24×C3 ⋊ C3×C5
derived, SylowC24 ⋊ C32×C5
HallC3×C22⋊A4 ⋊ C5
HallC24⋊C5 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽16)
commutator, cosocle, hypocenterC24C32×C5
FrattiniC1G
Fitting, socleC24×C3C3×C5
LCSG ▷ C24
UCSC1 ◁ C3

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

derived subgroup of#72241555, D3×AΓL(1,𝔽16)
maximal subgroup ofC3×((C24⋊C5)⋊C2)⋊C3, C3⋊(((C24⋊C5)⋊C2)⋊C3), D3×AGL(1,𝔽16), …
maximal normal subgroup ofC3×((C24⋊C5)⋊C2)⋊C3, C3⋊(((C24⋊C5)⋊C2)⋊C3), D3×AGL(1,𝔽16), …
maximal quotient ofC2×C3×AGL(1,𝔽16), C3×C5×AGL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 786);