C₃×C₇⋊#338 #13051219

order	1344
isoclinism	isoclinic class of #89261
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #338
Sylow	C₇ ⋊ C₃×#338

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

normal subgroups only

This group has 172 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)(4,5,7,9,10,8,6)(11,13,14,23,16,24,15,22)(12,17,19,21,20,25,18,26);(5,6)(7,8)(9,10)(11,12,14,18,16,20,15,19)(13,21,22,25,24,26,23,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 508);