C₂×C₁₆×#41 #7622649

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₆ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₁₆×#41

1702 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18);(19,20)(21,24)(22,23)(25,26);(20,23)(24,26);(19,21,22,25)(20,24,23,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529845);