C₂²×#2972 #10574272

order	512
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈ · Schur multiplier (H₂) = C₂¹⁴

Aliases

11138 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 6 generators on 20 points:

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

272 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481468);