C₂²×#2988 #10574342

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

Aliases

9162 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

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

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

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

maximal subgroup of	C₂²×#61947, C₂²×#62096, C₂²×#60283
maximal normal subgroup of	C₂²×#61947, C₂²×#62096, C₂²×#60283

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481538);