C₂×#17647 #6343752

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4568 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 18 points:

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

maximal subgroup of	#72306438, C₂×#6343804
maximal normal subgroup of	#72306438, C₂×#6343804

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250948);