C₃×#6382 #10620565

order	672
isoclinism	isoclinic class of #1141
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #106
Sylow	C₇ ⋊ C₃×#106

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 672

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 147);