order	216
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₃×D₃×D₄ (order 288) · Inn(G) = C₂×D₃ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₉×D₁₂
unambiguous semidirect product	C₄⋊(D₃×C₉)

Splittings

Fitting	C₃×C₄×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 48);