C₃×#89306 #13051171

order	1344
isoclinism	isoclinic class of #1141
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ #364
Sylow	C₇ ⋊ C₃×#364

92 conjugacy classes of subgroups.

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 460);