C₃×#888 #64011

order	288
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

C₃² ⋊ C₄⋊Q₈

149 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 659);