C₂×#7331 #149497

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₂ · Schur multiplier (H₂) = C₂²×C₄

Aliases

226 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 3 generators on 42 points:

(1,2);(3,4,5,8,6,7,9,10);(4,7)(8,10)(11,12,13,17,14,18,21,27,15,19,22,28,24,30,33,37,16,20,23,29,25,31,34,38,26,32,35,39,36,40,41,42)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 56693);