C₅×#216 #6702

order	240
isoclinism	isoclinic class of #213
automorphism	Aut(G) = C₂×C₄×D₃×D₄ (order 384) · Inn(G) = #67 · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 63);