C₇×#634 #92717

order	504
isoclinism	isoclinic class of #634
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₃

Aliases

Hall	C₃²×C₇ ⋊ Q₈
Sylow	C₃² ⋊ C₇×Q₈

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 504

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 143);