C₂²×#2974 #10574274

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹³

Aliases

10130 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481470);