C₇³ #66805

order	343
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇³

Aliases

C₇³

116 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 343

A minimal faithful permutation representation — 3 generators on 21 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(343, 5);