C₄×#472 #21553

order	256
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

473 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14541);