C₂²×SD₁₆⋊C₈ #6344509

order	512
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂²×SD₁₆⋊C₈

2402 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251705);