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ΓL(1,𝔽16)⋊AGL(1,𝔽5) #11925744

order1200
isoclinismisoclinic class of ΓL(1,𝔽16)⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

unambiguous semidirect productΓL(1,𝔽16)⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC3×C52 ⋊ C42
SylowC52 ⋊ C4×Dic3
SylowC3 ⋊ AGL(1,𝔽5)2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52C42
prime radical, cosocleC3×D52C22
LCSG ▷ C3×C52
UCSC1

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 60

Polycyclic presentation:

2^4,3,5^2|a^2=c,b^2=cd,e^a=e^2,g^a=g^2,f^b=f^2,g^b=g^2,g^c=g^4,f^d=f^4

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)2, C3×ΓL(1,𝔽16)⋊AGL(1,𝔽5), C2×ΓL(1,𝔽16)⋊AGL(1,𝔽5), …
maximal normal subgroup ofD3×AGL(1,𝔽5)2, C3×ΓL(1,𝔽16)⋊AGL(1,𝔽5), C2×ΓL(1,𝔽16)⋊AGL(1,𝔽5)
maximal quotient ofC3×ΓL(1,𝔽16)⋊AGL(1,𝔽5), #72229763, #72229772, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 954);