order	240
isoclinism	isoclinic class of #677
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)×AGL(1,ℤ/8) (order 1280) · Inn(G) = D₂₀ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₂₀

Splittings

Hall	C₃×C₅ ⋊ Q₁₆
Sylow	C₅ ⋊ C₃×Q₁₆

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 37);