C₄×#2081 #359279

order	512
nilpotency class	3
isoclinism	isoclinic class of #2081
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

1085 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 20 points:

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

maximal subgroup of	#72224744, #72224755, #72224756
maximal normal subgroup of	#72224744, #72224755, #72224756

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 266475);