C₂²×C₁₃×C₂₇ #13063886

order	1404
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₃×C₂₇

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1404

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2)(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);(3,4)

1404 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 18);