C₄×#397 #13861

order	256
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

895 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);(5,6,7,8)(13,14)(15,18)(16,17)(19,20);(9,10)(11,12)(14,17)(18,20);(6,8)(10,12)(13,15,16,19)(14,18,17,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6849);