C₂×#101 #412

order	64
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = #72216366 (order 1024) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

73 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);(3,4,6,10,7,9,15,17)(5,11,12,18,13,8,14,16);(3,5,7,13)(4,8,9,11)(6,14,15,12)(10,18,17,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(64, 93);