C₃×#3776 #88931

order	432
isoclinism	isoclinic class of #3774
automorphism	Aut(G) = C₂×#10596417 (order 1152) · Inn(G) = GO⁺(4,𝔽₂) · Out(G) = C₂×D₄
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃³ ⋊ Q₁₆

72 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)(4,6)(5,8,9)(10,20,14,12)(11,24,17,15)(13,19,23,22)(16,18,21,25);(4,5)(6,9)(7,8)(10,17,14,11)(12,25,20,18)(13,16,23,21)(15,19,24,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 578);