order	144
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄ (order 48) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄
holomorph	G ⋊ Aut(G) = AGL(1,ℤ/9)×AGL(1,ℤ/16)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₄
abelian	C₉×C₁₆

Subgroups

15 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 1 generator on 25 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 2);