D₆₀ #1218

order	120
isoclinism	isoclinic class of Dic₃₀
automorphism	Aut(G) = D₃×D₄×AGL(1,𝔽₅) (order 960) · Inn(G) = C₂×D₁₅ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₆₀
unambiguous semidirect product	C₄⋊D₁₅

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 12 points:

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

Polycyclic presentation:

2^3,3,5|b^2=c,b^a=bc,d^a=d^2,e^a=e^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(120, 28);