C₅×#926 #91729

order	480
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₅ ⋊ #117
Sylow	C₃ ⋊ C₅×#117

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 805);