C₃×#948 #64071

order	288
automorphism	Aut(G) = C₂³×D₃×S₄ (order 1152) · Inn(G) = C₂²×D₃ · Out(G) = C₂³×D₃
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₃² ⋊ #131

144 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 719);