C₃×#3708 #88765

order	432
isoclinism	isoclinic class of #157
automorphism	Aut(G) = C₂×C₄×AΓL(1,𝔽₉) (order 1152) · Inn(G) = #157 · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₃×C₁₆ · Schur multiplier (H₂) = C₃

Aliases

derived	C₃² ⋊ C₃×C₁₆
Sylow	C₃³ ⋊ C₁₆

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 412);