ΓL(1,𝔽₈)×#1792 #72277138

order	2688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting, Hall	C₇×#1792 ⋊ C₃
Sylow	C₇ ⋊ C₃×#1792

1240 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 19 points:

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

maximal subgroup of	#72277222, AGL(1,𝔽₇)×#1792, ΓL(1,𝔽₈)×#13343
maximal normal subgroup of	#72277222, AGL(1,𝔽₇)×#1792, ΓL(1,𝔽₈)×#13343

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

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