C₃×#89318 #13051183

order	1344
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #339
Sylow	C₇ ⋊ C₃×#339

220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

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

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 22 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 472);