C₃×#674 #6644

order	240
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₅) (order 160) · Inn(G) = AGL(1,𝔽₅) · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₃×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅ ⋊ C₃×C₁₆
Hall	C₃×C₅ ⋊ C₁₆

20 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 5);