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AΓL(1,𝔽16) #11757164

order960
isoclinismisoclinic class of AΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

affine general semilinearAΓL(1,𝔽16)

Splittings

Fitting, socleC24 ⋊ ΓL(1,𝔽16)
derivedAGL(1,𝔽16) ⋊ C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterAGL(1,𝔽16)C4
Fitting, socleC24ΓL(1,𝔽16)
prime radical, cosocle((C24⋊C5)⋊C2)⋊C3C2
LCSG ▷ AGL(1,𝔽16)
UCSC1

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 16

Polycyclic presentation:

2^2,3,5,2^4|a^2=b,c^a=c^2,d^a=d^2,e^a=eg,f^a=egh,g^a=fg,h^a=e,d^b=d^4,e^b=ef,g^b=efh,h^b=eg,e^c=efh,f^c=efgh,g^c=efg,h^c=fgh,e^d=efgh,f^d=efg,g^d=fgh,h^d=eg

Conjugacy classes & character table

13 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AΓL(1,𝔽16), AΓL(2,𝔽4), ΣL(2,𝔽16), …
maximal normal subgroup ofC2×AΓL(1,𝔽16), C3×AΓL(1,𝔽16)
maximal quotient of#14514269, C2×AΓL(1,𝔽16), #72219852, …
automorphism group ofC24⋊C5, (C24⋊C5)⋊C2, C2×C24⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11359);