C₂²×C₈×#41 #10574226

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂²×C₈×#41

9618 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 6 generators on 20 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481422);