ΓL(1,𝔽₈)×#459 #13054990

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	ΓL(1,𝔽₈)×#459
unambiguous semidirect product	(C₇×#459)⋊C₃

Fitting, Hall	C₇×#459 ⋊ C₃
Sylow	C₇ ⋊ C₃×#459

280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4279);