C₂²×#1970 #6371985

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰×C₄

Aliases

7218 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);(6,8)(9,10,11,12)(14,15)(16,17)(19,20);(5,6,7,8)(10,12)(13,14,17,19,18,20,16,15);(13,15,16,20,18,19,17,14)

maximal subgroup of	C₂²×#22870, C₂²×#25779, C₂²×#23193, …
maximal normal subgroup of	C₂²×#22870, C₂²×#25779, C₂²×#23193, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279181);