C₃×#830 #63616

order	288
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂²

Aliases

C₃² ⋊ C₂²⋊C₈

127 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 264);