C₃×#3928 #90929

order	480
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	Aut(G) = C₂×C₈×AGL(1,𝔽₅) (order 320) · Inn(G) = AGL(1,𝔽₅) · Out(G) = C₂×C₈
homology	Abelianization (H₁) = C₃×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅ ⋊ C₃×C₃₂
Hall	C₃×C₅ ⋊ C₃₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(2,5,4,3)(6,12,16,14,19,32,18,26,21,34,36,7,9,22,17,25,11,24,29,27,31,37,8,13,10,23,28,15,20,33,30,35)(38,39,40);(1,2,3,5,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 5);