C₇×#818 #10620616

order	672
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #107
Sylow	C₃ ⋊ C₇×#107

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 198);