C₂×#2349 #34111

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

2099 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27099);