C₃²×#672 #10623620

order	720
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₆ · Schur multiplier (H₂) = C₃

Aliases

derived, Sylow	C₅ ⋊ C₃²×C₁₆
Hall	C₃²×C₅ ⋊ C₁₆

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 89);