ΓL(1,𝔽₈)×#442 #13054973

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product	ΓL(1,𝔽₈)×#442
unambiguous semidirect product	(C₇×#442)⋊C₃

Fitting, Hall	C₇×#442 ⋊ C₃
Sylow	C₇ ⋊ C₃×#442

264 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 105 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)(8,9,11,10)(12,13,15,17)(14,16,19,18);(1,2,3,5,4,6,7)(13,16)(14,19)(17,18);(8,10,11,9)(13,17)(16,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4262);