C₂²×#1311 #479894

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

882 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387090);