C₄×#2676 #521172

order	512
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4094 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)(13,14,16,17)(15,19,20,18);(9,10)(11,12)(14,17)(15,20);(6,8)(10,12);(6,8)(13,15,16,20)(14,18,17,19)

maximal subgroup of	#72304051, #72304076, #72304094, …
maximal normal subgroup of	#72304051, #72304076, #72304094, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 428368);