C₉×#226 #88593

order	432
isoclinism	isoclinic class of #226
automorphism	Aut(G) = C₂²×C₃×S₄ (order 288) · Inn(G) = S₄ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

45 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 240);