C₃×#8276 #10626883

order	768
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂³

Aliases

414 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 768

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1264);