C₃×#89454 #13055115

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #500
Sylow	C₇ ⋊ C₃×#500

196 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1344

A minimal faithful permutation representation — 3 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4404);