order	240
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₄×D₃×AGL(1,ℤ/8) (order 768) · Inn(G) = D₁₂ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×Dic₁₂

Splittings

Hall	C₃×C₅ ⋊ Q₁₆
Sylow	C₃ ⋊ C₅×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)(6,7,8,9,10,11,12,13)(14,21,20,19,18,17,16,15)(22,23,24);(6,14,10,18)(7,15,11,19)(8,16,12,20)(9,17,13,21)(23,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 53);