C₂×#2365 #34138

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 2097152
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

1579 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27126);