C₂²×#2274 #7625207

order	512
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄² · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

16098 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 6 generators on 20 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532403);