C₂×#1918 #21028

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14016);