C₂×#7145 #126602

order	512
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂³×C₄

Aliases

506 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 256

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 33798);