C₂²×#1380 #492854

order	512
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁸

Aliases

2066 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2);(3,4);(5,6)(7,8)(9,10,11,12)(14,19)(15,23)(16,25)(17,24)(20,21)(22,28)(26,27);(6,8)(13,14,16,20,17,21,15,19,18,22,23,27,24,26,25,28)

maximal subgroup of	C₂²×#12637, C₂²×#12937, C₂²×#13012, …
maximal normal subgroup of	C₂²×#12637, C₂²×#12937, C₂²×#13012, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400050);