C₃×#6507 #10621255

order	672
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ C₄⋊Q₈
Sylow	C₇ ⋊ C₃×C₄⋊Q₈

136 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 837);