ΣL(2,𝔽₁₆) #72224462

order	16320
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

projective general semilinear	PΓL(2,𝔽₁₆)
special semilinear	ΣL(2,𝔽₁₆)
projective special semilinear	PΣL(2,𝔽₁₆)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	SL(2,𝔽₁₆)	C₄
prime radical, cosocle	GO⁻(4,𝔽₄)	C₂
LCS	G ▷ SL(2,𝔽₁₆)
UCS	C₁

69 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 17

A minimal faithful permutation representation — 2 generators on 17 points:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,16,5,15,10,3,9,17)(2,13,8,14,12,6,4,7), (2,6)(3,12)(4,14)(5,8)(7,11)(9,16)(10,15)(13,17));