C₂×#1921 #21031

order	256
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

543 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14019);