C₇×#4978 #13056007

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₇ ⋊ #387
Sylow	C₃ ⋊ C₇×#387

308 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)(11,12,13,14)(21,25)(23,26);(16,18)(19,21,22,25)(20,23,24,26);(9,10)(15,16)(17,18)(19,20,22,24)(21,23,25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5296);