C₄×#3169 #6373918

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

2662 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)(7,10)(8,9)(11,12)(14,17)(15,18)(19,20);(6,9)(10,12);(13,14,18,20,16,19,15,17);(5,7,8,11)(6,10,9,12)

maximal subgroup of	#72340738, #72340743
maximal normal subgroup of	#72340738, #72340743

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281114);