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Cayley diagram

C2×AGL(1,𝔽16) #92114

order480
isoclinismisoclinic class of AGL(1,𝔽16)
automorphismAut(G) = AΓL(1,𝔽16) (order 960) · Inn(G) = AGL(1,𝔽16) · Out(G) = C4
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×AGL(1,𝔽16)
unambiguous semidirect product(C2×C22⋊A4)⋊C5
unambiguous semidirect product(C2×C24⋊C5)⋊C3

Splittings

Fitting, socle, SylowC25 ⋊ C3×C5
derivedC24 ⋊ C2×C3×C5
HallC2×C24⋊C5 ⋊ C3
HallC2×C22⋊A4 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽16)
commutator, cosocle, hypocenterC24C2×C3×C5
FrattiniC1G
Fitting, socleC25C3×C5
LCSG ▷ C24
UCSC1 ◁ C2

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 30

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2)(4,18,13,7,17,15,9,6,14,11,8,5,10,16,12);(3,18)(4,17)(5,9)(6,12)(7,11)(8,14)(10,16)(13,15)

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#66245⋊C3, C4×AGL(1,𝔽16), C2×((C24⋊C5)⋊C2)⋊C3, …
maximal normal subgroup of#66245⋊C3, C4×AGL(1,𝔽16), C2×((C24⋊C5)⋊C2)⋊C3, …
maximal quotient ofC4×AGL(1,𝔽16), C22×AGL(1,𝔽16), C2×(C24⋊C5)⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1190);