C₂²×#1994 #6372215

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4682 conjugacy classes of subgroups.

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

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

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

maximal subgroup of	C₂²×#21415, #72235047, C₂×#186595, …
maximal normal subgroup of	C₂²×#21415, #72235047, C₂×#186595, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279411);