C₈×D₈ #1575

order	128
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂³×#3003 (order 1024) · Inn(G) = D₄ · Out(G) = C₂⁴×D₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₈

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 307);