C₇×#4463 #13051243

order	1344
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ #364
Sylow	C₃ ⋊ C₇×#364

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 532);