C₂²×#1841 #6371067

order	512
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

2142 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 5 generators on 20 points:

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

maximal subgroup of	C₂²×#20788, C₂²×#29387, C₂²×#29384
maximal normal subgroup of	C₂²×#20788, C₂²×#29387, C₂²×#29384

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278263);