C₂³×H(3,ℤ/4) #6369738

order	512
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹⁰×C₄

Aliases

8522 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276934);