C₂×#1764 #20418

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

779 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4)(5,6)(7,8,11,15,12,16,10,13)(9,14,18,21,19,22,17,20);(4,6)(8,13,16,15)(14,20,22,21);(7,9,11,18,12,19,10,17)(8,14,15,21,16,22,13,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13406);