C₂×#7110 #124064

order	512
nilpotency class	4
isoclinism	isoclinic class of #1339
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³×C₄

Aliases

676 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2);(3,4)(5,7)(6,9)(8,10)(11,12,14,20,17,22,25,26,15,23,24,18,16,21,13,19);(4,7)(5,10)(8,9)(12,18)(13,24)(14,25)(16,17)(19,21)(20,23)(22,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 31260);