C₈×D₁₆ #12040

order	256
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) = C₂³×#495725 (order 4096) · Inn(G) = D₈ · Out(G) = C₂³×C₄×D₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₁₆

129 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 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);(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 5028);