C₄×#489 #21649

order	256
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³×C₄

Aliases

443 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14637);