C₄×#2430 #514829

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

6180 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)(13,14)(15,19)(16,18)(17,20);(9,10)(11,12)(13,15,16,20)(14,17,18,19);(5,6,7,8)(10,12);(14,18)(17,19)

maximal subgroup of	#72261970, #72262079, #72262102, …
maximal normal subgroup of	#72261970, #72262079, #72262102, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422025);