C₅×#217 #6703

order	240
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₄×D₃×#120 (order 768) · Inn(G) = C₂×D₃ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ C₂²⋊C₄
Sylow	C₃ ⋊ C₅×C₂²⋊C₄

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,3)(9,11)(12,13,14,15,16);(2,3)(4,5,6,7)(8,9)(10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 64);