C₂×#108 #429

order	64
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×#23882 (order 512) · Inn(G) = D₄ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

53 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2);(3,4,7,10,8,11,6,16)(5,12,14,17,15,18,13,9);(3,5,6,13,8,15,7,14)(4,9,10,12,11,17,16,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(64, 110);