SD₁₆×C₉⋊C₉ #13046896

order	1296
nilpotency class	3
isoclinism	isoclinic class of D₈×H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	SD₁₆×C₉⋊C₉
unambiguous semidirect product	(C₉×SD₁₆)⋊C₉

170 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 648

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 614);