C₇×#4559 #13051341

order	1344
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #344
Sylow	C₃ ⋊ C₇×#344

180 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

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

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7)(8,9,10)(11,13,15,22,16,23,14,21)(12,17,18,25,19,20,24,26);(9,10)(11,12,14,18,16,19,15,24)(13,20,21,26,23,17,22,25)

294 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 630);