C₄²×#97 #353105

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄⁴ · Schur multiplier (H₂) = C₂×C₄⁵

Aliases

C₄²×#97

2850 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 20 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260301);