C₂×#1937 #21096

order	256
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

557 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)(9,17,19,14,20,21,18,22);(8,13,16,15)(14,17,22,21);(4,6)(7,9,10,18,12,20,11,19)(8,14,15,21,16,22,13,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14084);