C₄×#554 #34167

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1258 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27155);