C₄×#2352 #513502

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

4706 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);(6,8)(9,10,11,12)(13,14)(15,18)(16,20)(17,19);(5,6)(7,8)(13,15,17,16)(14,18,19,20);(13,16,17,15)(14,18,19,20);(6,8)

maximal subgroup of	#72305508, #72305520, #72305560, …
maximal normal subgroup of	#72305508, #72305520, #72305560, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420698);