C₂×#1772 #20442

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

551 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);(8,12,14,17)(13,19,20,21);(3,4,5,6)(7,8)(9,13)(10,17)(11,14)(12,18)(15,21)(16,20)(19,22);(7,9,10,15,11,16,18,22)(8,13,17,21,14,20,12,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13430);