C₂²×#1788 #6370709

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹²

Aliases

18906 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)(9,10,11,12)(14,18)(15,16)(19,20);(13,14)(15,18)(16,20)(17,19);(6,8)(13,15,17,16)(14,18,19,20)

maximal subgroup of	C₂²×#22419, C₂²×#21456, C₂²×#22442, …
maximal normal subgroup of	C₂²×#22419, C₂²×#21456, C₂²×#22442, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277905);