C₂×#7053 #122212

order	512
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂²×C₄

Aliases

234 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 3 generators on 34 points:

(1,2);(3,4,5,9,6,11,13,17,7,10,12,18,14,8,15,16);(4,8,10,11)(5,12)(9,17,18,16)(13,15)(19,20,21,24,22,25,27,30,23,26,28,31,29,32,33,34)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 29408);