C₂²×#382 #34007

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 100663296
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

2143 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26995);