C₄×#338 #10698

order	256
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	Aut(G) order 196608
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

429 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 3686);