C₂²×#1547 #6343969

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

4706 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);(6,10)(7,8)(11,12)(13,14,16,18,17,20,15,19);(5,6)(7,10)(8,12)(9,11)(14,18)(15,16)(19,20);(5,7,9,8)(6,10,11,12)

maximal subgroup of	C₂×#197777, C₂²×#18786, C₂×#233080, …
maximal normal subgroup of	C₂×#197777, C₂²×#18786, C₂×#233080, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251165);