C₃²×C₇×C₁₆ #11758952

order	1008
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₇×C₁₆

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1008

A minimal faithful permutation representation — 2 generators on 29 points:

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

1008 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 123);