C₂×#2933 #60137

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

1463 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53125);