C₅×D₃×Q₈ #6810

order	240
automorphism	Aut(G) = C₂×C₄×D₃×S₄ (order 1152) · Inn(G) = C₂²×D₃ · Out(G) = C₂×C₄×D₃
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

C₅×D₃×Q₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 171);