C₃×#89273 #13051138

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #356
Sylow	C₇ ⋊ C₃×#356

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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)(11,13,14,20,16,22,12,17)(15,21,18,19,24,25,23,26);(5,6)(7,8)(9,10)(11,12,16,14)(13,19,22,26)(15,23,24,18)(17,25,20,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 427);