C₅×#798 #91041

order	480
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂²×C₄²×D₃ (order 384) · Inn(G) = C₂×D₃ · Out(G) = C₂×C₄²
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

52 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)(4,11,13,19,7,9,18,10,8,16,6,17,14,5,12,15)(20,21,22,23,24);(2,3)(5,9)(10,15)(11,16)(17,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 117);