C₇×#4512 #13051294

order	1344
isoclinism	isoclinic class of #4466
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ #347
Sylow	C₃ ⋊ C₇×#347

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 583);