C₂²×#381 #34005

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 100663296
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹¹

Aliases

4031 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26993);