C₃×AΓL(1,𝔽₁₆) #72241551

order	2880
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle	C₂⁴×C₃ ⋊ ΓL(1,𝔽₁₆)
derived	AGL(1,𝔽₁₆) ⋊ C₃×C₄

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 19 points:

(1,9)(2,13,5,6)(3,12,4,7)(8,14,11,15)(17,18,19);(2,4,13,16,8,7,5,11,10,15,3,12,14,9,6)

maximal subgroup of	C₃×AΓL(2,𝔽₄), D₃×AΓL(1,𝔽₁₆)
maximal normal subgroup of	D₃×AΓL(1,𝔽₁₆)

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

gap> G := Group((1,9)(2,13,5,6)(3,12,4,7)(8,14,11,15)(17,18,19), (2,4,13,16,8,7,5,11,10,15,3,12,14,9,6));