order	288
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂²×D₃×C₈ (order 192) · Inn(G) = D₃ · Out(G) = C₂²×C₈
homology	Abelianization (H₁) = C₃×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₃⋊C₃₂
unambiguous semidirect product	C₃⋊(C₃×C₃₂)

Splittings

derived	C₃ ⋊ C₃×C₃₂
Sylow	C₃² ⋊ C₃₂

29 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3)(5,6)(7,13,17,15,20,33,19,27,22,35,37,8,10,23,18,26,12,25,30,28,32,38,9,14,11,24,29,16,21,34,31,36);(4,5,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 64);