C₄×#421 #20404

order	256
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

809 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);(5,6,9,12,10,13,8,17)(7,14,16,11,15,20,18,19);(5,7)(6,11)(8,18)(9,16)(10,15)(12,20)(13,19)(14,17);(7,15)(11,19)(14,20)(16,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13392);