C₂²×C₃³×C₁₃ #13064095

order	1404
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 808704
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂²×C₃³×C₁₃

280 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1404

A minimal faithful permutation representation — 3 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 227);