C₄×#2417 #514877

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

4250 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)(13,14,17,20)(15,19,16,18);(9,10)(11,12)(13,15,17,16)(14,18,20,19);(6,8)(10,12);(13,16,17,15)(14,19,20,18)

maximal subgroup of	#72305789, #72305802, #72305811, …
maximal normal subgroup of	#72305789, #72305802, #72305811, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422073);