C₂×#12905 #494154

order	512
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

914 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401350);