C₃×#89276 #13051145

order	1344
isoclinism	isoclinic class of #89246
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #333
Sylow	C₇ ⋊ C₃×#333

128 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 1344

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 434);