C₄×#551 #34162

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1366 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27150);