C₇×#4701 #13055737

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

Aliases

Hall	C₃×C₇ ⋊ #446
Sylow	C₃ ⋊ C₇×#446

188 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)(19,20,21,24,22,23,25,26);(11,13,14,18)(12,15,16,17)(20,23)(24,26);(9,10)(11,12,14,16)(13,17,18,15)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5026);