C₃×C₁₆² #10625658

order	768
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 49152
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

C₃×C₁₆²

166 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 768

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(33,34,35);(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)

768 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 39);