C₂³×#341 #6369753

order	512
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹¹

Aliases

8546 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 26 points:

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

maximal subgroup of	C₂³×#1810, C₂³×#1765, C₂³×#1938
maximal normal subgroup of	C₂³×#1810, C₂³×#1765, C₂³×#1938

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276949);