C₂²×#1549 #6343972

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4338 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)(7,9)(8,10)(11,12)(13,14,17,20,18,15,16,19);(6,9)(7,12)(10,11)(13,15,18,14)(16,19,17,20);(6,10)(9,11)

maximal subgroup of	C₂²×#18758, C₂×#197726, C₂×#233060, …
maximal normal subgroup of	C₂²×#18758, C₂×#197726, C₂×#233060, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251168);