C₂×#13824 #513538

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄²

Aliases

8234 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420734);