C₂²×#387 #34015

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 12582912
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×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);(6,8)(9,10,12,11)(14,17)(15,19);(9,11,12,10)(13,14)(15,18)(16,17)(19,20);(5,6)(7,8)(13,15,16,19)(14,18,17,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27003);