C₈×Q₈ #445

order	64
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂³×#1020 (order 768) · Inn(G) = C₂² · Out(G) = C₂³×S₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈

51 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(64, 126);