C₃×#6407 #10620590

order	672
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #100
Sylow	C₇ ⋊ C₃×#100

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 172);