C₇×#4982 #13056011

order	1344
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #398
Sylow	C₃ ⋊ C₇×#398

300 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)(12,14)(15,17,18,16);(16,17)(19,21,22,26)(20,23,24,25);(9,10)(11,12)(13,14)(15,16,18,17)(19,20,22,24)(21,25,26,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5300);