C₄×#2339 #513506

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

6782 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:

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

maximal subgroup of	D₄×#2339, #72262066, #72262109, …
maximal normal subgroup of	D₄×#2339, #72262066, #72262109, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420702);