C₄×#2406 #514818

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

5954 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)(7,8)(13,14)(15,20)(16,18)(17,19);(9,10)(11,12)(13,15,17,16)(14,18,19,20);(6,8)(10,12)(13,16,17,15)(14,18,19,20);(14,19)(18,20)

maximal subgroup of	#72264102, D₄×#2406, #72264109, …
maximal normal subgroup of	#72264102, D₄×#2406, #72264109, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422014);