C₄×#462 #21500

order	256
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

492 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14488);