C₉³×C₁₇ #27136706

order	12393
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3537271296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉³

Aliases

C₉³×C₁₇

890 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 12393

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5,6,7,8,9)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(10,11,12,13,14,15,16,17,18);(19,20,21,22,23,24,25,26,27)

12393 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12393, 102);