C₂×#2344 #34105

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 2097152
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

1763 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);(3,4,6,5)(7,8,9,10)(13,17)(15,18);(4,5)(11,12,14,16)(13,15,17,18);(11,13)(12,15)(14,17)(16,18);(3,5,6,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27093);