C₄×C₉×C₁₉² #27188709

order	12996
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₉

Aliases

C₄×C₉×C₁₉²

198 conjugacy classes of subgroups.

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 12996

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51)

12996 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12996, 52);