C₂×C₄×D₉ #3695

order	144
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = #120×AGL(1,ℤ/9) (order 1728) · Inn(G) = D₉ · Out(G) = C₃×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₄×D₉

Fitting	C₂×C₄×C₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂²×C₄

81 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 38);