C₄×#346 #12538

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₂×C₄²

Aliases

255 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4);(9,10,11,15,12,16,17,22,13,14,18,20,19,21,23,24);(5,6,7,8)(10,14)(15,20)(16,21)(22,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 5526);