C₃×#89473 #13055135

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #446
Sylow	C₇ ⋊ C₃×#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)(4,5,7,9,10,8,6)(19,20,21,24,22,23,25,26);(11,13,14,18)(12,15,16,17)(20,23)(24,26);(5,6)(7,8)(9,10)(11,12,14,16)(13,17,18,15)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4424);