C₃×#8202 #10626809

order	768
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

570 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 384

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1190);