C₂×ΓL(1,𝔽₈)×#106 #13054956

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

Aliases

direct product	C₂×ΓL(1,𝔽₈)×#106
unambiguous semidirect product	(C₂×C₇×#106)⋊C₃

Fitting, Hall	C₂×C₇×#106 ⋊ C₃
Sylow	C₇ ⋊ C₂×C₃×#106

260 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(16,17,18)(19,21,20);(3,4,5,6)(8,11)(9,13)(12,14)(15,16,17,19,18,20,21);(7,8,9,11,10,12,13,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4245);