C₄×#542 #34094

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1147 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);(6,9)(7,11)(13,14)(15,17)(16,18)(19,20);(5,6,8,9)(7,10,11,12)(13,15,16,19)(14,17,18,20);(6,9)(10,12)(14,18)(17,20);(5,7,8,11)(6,10,9,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27082);