C₂×#102 #414

order	64
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = #72214271 (order 1024) · Inn(G) = D₄ · Out(G) = #2403
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

101 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(64, 95);