C₄×#471 #21552

order	256
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	Aut(G) order 4096
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

457 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)(7,13)(8,16)(12,18)(14,15)(17,19);(5,6,8,10,9,12,16,18)(7,11,14,17,15,20,13,19);(5,7)(6,11)(8,14)(9,15)(10,17)(12,20)(13,16)(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14540);