C₂²×M₁₆×ΓL(1,𝔽₈) #13060727

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting, Hall	C₂²×C₇×M₁₆ ⋊ C₃
Sylow	C₇ ⋊ C₂²×C₃×M₁₆

596 conjugacy classes of subgroups; only the 387 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 387 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 — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10016);