C₇×#4682 #13055717

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #500
Sylow	C₃ ⋊ C₇×#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:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5006);