C₃×#819 #63605

order	288
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃² ⋊ #108

71 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 253);