C₂×ΓL(1,𝔽₈)×#102 #13054945

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₂×ΓL(1,𝔽₈)×#102
unambiguous semidirect product	(C₂×C₇×#102)⋊C₃

Fitting, Hall	C₂×C₇×#102 ⋊ C₃
Sylow	C₇ ⋊ C₂×C₃×#102

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

normal subgroups only

This group has 404 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) = 224

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4234);