C₉×#672 #10623533

order	720
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅ ⋊ C₉×C₁₆
Hall	C₅×C₉ ⋊ C₁₆

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9)(11,12)(13,14)(15,16,17,20,18,21,23,26,19,22,24,27,25,28,29,30);(10,11,13,14,12)

288 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 2);