C₃×#3990 #91194

order	480
isoclinism	isoclinic class of #700
automorphism	Aut(G) = C₂×#41×AGL(1,𝔽₅) (order 640) · Inn(G) = C₂×AGL(1,𝔽₅) · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₅ ⋊ M₃₂
Sylow	C₅ ⋊ C₃×M₃₂

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 270);