C₄×#1819 #354843

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

3326 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

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

maximal subgroup of	#72264285, C₄×#10337, #72264521
maximal normal subgroup of	#72264285, C₄×#10337, #72264521

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 262039);