C₁₆×Q₁₆ #12052

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂²×C₄×#3003 (order 2048) · Inn(G) = D₄ · Out(G) = C₂³×C₄×D₄
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

C₁₆×Q₁₆

109 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);(17,18,19,20,21,22,23,24)(25,32,31,30,29,28,27,26);(17,25,21,29)(18,26,22,30)(19,27,23,31)(20,28,24,32)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 5040);