C₂×#14189 #514674

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰×C₄

Aliases

10310 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)(8,9)(12,13);(7,8,10,9)(11,12,14,13)(16,18);(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, 421870);