C₃×#817 #63603

order	288
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₃² ⋊ #106

83 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 251);