C₃×#3712 #88770

order	432
isoclinism	isoclinic class of #625
automorphism	Aut(G) = C₂²×#64241 (order 1152) · Inn(G) = D₃² · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃³ ⋊ M₁₆

118 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 17 points:

(1,2,8,3,5,7,4,6)(9,10,11)(13,14)(15,16,17);(1,6,8,2,5,3,4,7)(12,13,14)(16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 417);